Dissertations / Theses: 'Structural dynamics – Mathematical models'

1

鄭定陽 and Dingyang Zheng. "Vibration and stability analysis of plate-type structures under movingloads by analytical and numercial methods." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 1999. http://hub.hku.hk/bib/B31239791.

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2

Hang, Huajiang Engineering &amp Information Technology Australian Defence Force Academy UNSW. "Prediction of the effects of distributed structural modification on the dynamic response of structures." Awarded by:University of New South Wales - Australian Defence Force Academy. Engineering & Information Technology, 2009. http://handle.unsw.edu.au/1959.4/44275.

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The aim of this study is to investigate means of efficiently assessing the effects of distributed structural modification on the dynamic properties of a complex structure. The helicopter structure is normally designed to avoid resonance at the main rotor rotational frequency. However, very often military helicopters have to be modified (such as to carry a different weapon system or an additional fuel tank) to fulfill operational requirements. Any modification to a helicopter structure has the potential of changing its resonance frequencies and mode shapes. The dynamic properties of the modified structure can be determined by experimental testing or numerical simulation, both of which are complex, expensive and time-consuming. Assuming that the original dynamic characteristics are already established and that the modification is a relatively simple attachment such as beam or plate modification, the modified dynamic properties may be determined numerically without solving the equations of motion of the full-modified structure. The frequency response functions (FRFs) of the modified structure can be computed by coupling the original FRFs and a delta dynamic stiffness matrix for the modification introduced. The validity of this approach is investigated by applying it to several cases, 1) 1D structure with structural modification but no change in the number of degree of freedom (DOFs). A simply supported beam with double thickness in the middle section is treated as an example for this case; 2) 1D structure with additional DOFs. A cantilever beam to which a smaller beam is attached is treated as an example for this case, 3) 2D structure with a reduction in DOFs. A four-edge-clamped plate with a cut-out in the centre is treated as an example for this case; and 4) 3D structure with additional DOFs. A box frame with a plate attached to it as structural modification with additional DOFs and combination of different structures. The original FRFs were obtained numerically and experimentally except for the first case. The delta dynamic stiffness matrix was determined numerically by modelling the part of the modified structure including the modifying structure and part of the original structure at the same location. The FRFs of the modified structure were then computed. Good agreement is obtained by comparing the results to the FRFs of the modified structure determined experimentally as well as by numerical modelling of the complete modified structure.

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3

DITOLLA, ROBERT JOHN. "RANDOM VIBRATION ANALYSIS BY THE POWER SPECTRUM AND RESPONSE SPECTRUM METHODS (WHITE NOISE, FINITE-ELEMENT, VANMARCKE, DENSITY, NASTRAN)." Diss., The University of Arizona, 1986. http://hdl.handle.net/10150/183836.

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Determination of the stresses and displacements which occur in response to random excitations cannot be accomplished by traditional deterministic analysis methods. As the specification of the excitation and the response of the structure become more complex, solutions by direct, closed-form methods require extensive computations. Two methods are presented which can be used in the analysis of structures which are subjected to random excitations. The Power Spectrum Method is a procedure which determines the random vibration response of the structure based upon a frequency response analysis of a structural model. The Response Spectrum Method is a method which is based upon specified forces or displacements as a function of time. A derivation of each of the methods is presented and followed by comparisons of the results which were obtained for single and multiple-degree-of-freedom systems. Assumptions and limitations of the methods are discussed as well as their accuracy over ranges of frequency, damping and loading specification. As a direct application and comparison of the two methods, an analysis of the support system for the primary mirror of the Space Infrared Telescope Facility (SIRTF) has been performed. In addition, a method for the evaluation of the critical damping in a single-degree-of-freedom structure is demonstrated.

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4

Burnham, Christian James. "Structural and dynamical properties of mathematical water models." Thesis, University of Salford, 1998. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.299208.

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5

Lindholm, Brian Eric. "Reconciliation of a Rayleigh-Ritz beam model with experimental data." Thesis, This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-06102009-063201/.

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6

Stiles, Peter A. "Improvement of structural dynamic models via system identification." Thesis, Virginia Tech, 1988. http://hdl.handle.net/10919/44086.

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Proper mathematical models of structures are beneficial for designers and analysts. The accuracy of the results is essential. Therefore, verification and/or correction of the models is vital. This can be done by utilizing experimental results or other analytical solutions. There are different methods of generating the accurate mathematical models. These methods range from completely analytically derived models, completely experimentally derived models, to a combination of the two. These model generation procedures are called System Identification. Today a popular method is to create an analytical model as accurately as possible and then improve this model using experimental results. This thesis provides a review of System Identification methods as applied to vibrating structures. One simple method and three more complex methods, chosen from current engineering literature, are implemented on the computer. These methods offer the capability to correct a discrete (for example, finite element based) model through the use of experimental measurements. The validity of the methods is checked on a two degree of freedom problem, an eight degree of freedom example frequently used in the literature, and with experimentally derived vibration results of a free-free beam.
Master of Science

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7

Montgomery, David Eric. "Modeling and visualization of laser-based three-dimensional experimental spatial dynamic response." Diss., This resource online, 1994. http://scholar.lib.vt.edu/theses/available/etd-10052007-143439/.

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8

Borges, Rutz Ricardo. "Mathematical models of physiologically structured cell populations." Doctoral thesis, Universitat Autònoma de Barcelona, 2012. http://hdl.handle.net/10803/96187.

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En aquesta tesi es té en compte un model no lineal de creixement de població de cèl·lules que s'estructuren pel seu contingut de ciclina i cinases depenents de ciclina (CDK). Aquest model condueix a un sistema no lineal d'equacions en derivades parcials de primer ordre amb termes no locals. Per estudiar aquest sistema utilitzem la teoria de semigrups lineals positius i la formulació semilineal, que són eines molt poderoses per fer front a l'anàlisi d'aquest tipus de models, tant des del punt de vista del problema de valor inicial, com de l'existència i l'estabilitat d'estats estacionaris. El model que es considera a la tesi descriu la següent situació biològica: les cèl·lules s'estructuren en relació amb el contingut d'un determinat grup de proteïnes anomenades ciclines i CDK i es divideixen en dos tipus: proliferants i quiescents. Les cèl·lules proliferants creixen i es divideixen, donant a lloc al final del cicle cel·lular a noves cèl·lules, o bé van cap al compartiment de les quiescents, mentre que les cèl·lules quiescents no envelleixen ni es divideixen, ni canvien el seu contingut de ciclina, però o tornen cap al compartiment de proliferació o bé romanen en l’estat de repòs. D'altra banda, tant les cèl·lules proliferants com les quiescents poden experimentar l'apoptosi, la mort cel·lular programada. L'únic terme no lineal en el model és un terme de reclutament de cèl·lules quiescents cap a la fase de proliferació. En aquest treball demostrem l'existència global, unicitat i positivitat de les solucions del problema de valor inicial. Reescrivint el nostre sistema en una forma abstracta podem demostrar que un cert operador lineal és el generador infinitesimal d'un semigrup positiu fortament continu. D'altra banda s'utilitza la formulació semilineal estàndard per a l’equació no lineal abstracta i obtenim una única solució global positiva per a qualsevol condició inicial positiva a L1. També es prova l'existència i unicitat d'un estat estacionari no trivial del nostre sistema sota hipòtesis adequades. Com es fa sovint en situacions similars, el problema és relacionat amb provar l'existència (i unicitat) d'un vector propi positiu normalitzat. Això correspon als vectors propis del valor propi dominant d'un determinat operador lineal positiu parametritzat pel valor de la variable de feedback. L'existència tant del valor propi dominant i de (l’únic) vector propi positiu està donat per una versió del teorema de Perron- Frobenius en dimensió infinita. També s’inclouen simulacions numèriques basades en la integració al llarg de les línies característiques. Amb l'ajuda d'aquestes simulacions numèriques trobem inestabilitat de l'estat estacionari per a valors de paràmetres compatibles amb els que donen inestabilitat en el model de dimensió finita. També s'inclou la demostració de l'existència de solucions independents del contingut de ciclina per a una elecció molt particular dels valors dels paràmetres i funcions que defineixen el model. Finalment s'utilitza la formulació anomenada cumulativa (o en retard) de la dinàmica de poblacións estructurades. En particular s'ha considerat una versió diferent del model estudiat abans, on es suposa que el pas de proliferants a quiescents només pot ocórrer una sola vegada, enfocament oposat al primer model on aquestes transicions poden ocórrer infinites vegades. A més a més, també suposem que hi ha un valor particular x del contingut de ciclina que separa les cèl·lules que encara no es poden dividir de les altres que sí que poden dividir-se. L'equació del model resulta ser una equació amb retard que relaciona els valors actuals d'aquestes variables amb la seva història (el seu valor en el passat). Fent servir aquest enfocament, es pot provar l'existència i unicitat de solucions del problema de valor inicial, i el principi d'estabilitat lineal a través d'una formulació semilineal en el marc dels semigrups duals.
In this thesis we consider a nonlinear cell population model where cells are structured with respect to the content of cyclin and cyclin dependent kinases (CDK). This model leads to a first order nonlinear partial differential equations system with non local terms. To study this system we use the theory of positive linear semigroups and the semilinear formulation, which are very powerful tools to deal with the analysis of this kind of models, both from the point of view of the initial value problem as well as the existence and stability of steady states. The model considered in the thesis describes the following biological situation: cells are structured with respect to the content of a certain group of proteins called cyclin and CDK and are distributed into two types: proliferating and quiescent cells. The proliferating cells grow and divide, giving birth at the end of the cell cycle to new cells, or else transit to the quiescent compartment, whereas quiescent cells do not age nor divide nor change their cyclin content but either transit back to the proliferating compartment or else stay in the quiescent compartment. Moreover, both proliferating and quiescent cells may experiment apoptosis, i.e. programmed cell death. The only nonlinear term is a recruitment term of quiescent cells going back to the proliferating phase. In this work we start proving global existence, uniqueness and positiveness of the solutions of the initial value problem. We rewrite our system in an abstract form and show that some linear operator is the infinitesimal generator of a positive strongly continuous semigroup. On the other hand we use the standard semilinear formulation for the nonlinear (abstract) equation and obtain a unique global positive solution for any positive initial condition in L1. We also prove the existence and uniqueness of a nontrivial steady state of our system under suitable hypotheses. As it is often done in similar situations, the problem is related to proving the existence (and uniqueness) of a positive normalized eigenvector. This eigenvector corresponds to the dominant eigenvalue of a certain positive linear operator parameterized by the value of the (one dimensional) feedback variable G. The existence of both dominant eigenvalue and (unique) positive eigenvector is given by a version of the infinite dimensional Perron-Frobenius theorem. We include numerical simulations based on the integration along characteristic lines. With the help of these numerical simulations we find instability of the steady state for parameter values compatible with the ones which give instability in the finite dimensional model. We also include a computation showing the existence of cyclin-independent solutions for a very particular choice of the parameter values and functions defining the model. Finally we use the so-called cumulative or delayed formulation of the structured population dynamics. In particular we have considered a different version of the model studied before, where one assumes that proliferating cells can become quiescent only once opposed to the other approach where these transitions can occur infinitely many times and moreover, we also assume that there is a particular value x of the cyclin content that separates cells which still cannot divide from the others which are able to divide. The model equation turns out to be a delay equation relating the current values of these variables with their history (their value in the past). Using this approach, one can prove existence and uniqueness of solutions of the initial value problem, and the linear stability principle by means of a semi-linear formulation in the framework of dual semigroups.

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9

Yu, Albert Chun-ming. "The dynamics of capital structure choice." Thesis, University of British Columbia, 1985. http://hdl.handle.net/2429/24408.

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This thesis employs two-period state-contingent model based upon the "tax shield plus bankruptcy costs" approach to examine the dynamic capital structure decision. By allowing recapitalization at the end of period one, we can analyse the dynamics of the firm's capital structure choice. Also, the effect of a call provision on bonds can be examined. Simulated results show that the firm will recapitalize at the end of period one only if the gain in firm value, with- or ex-dividend, resulting from recapitalization exceeds the after-tax flotation costs. There exists a tolerable recapitalization boundary within which the firm will not recapitalize. This implies that the empirically observed capital structure is not necessarily at the acme of the firm value function, as most empirical studies assume. Another important result is that a call provision on bonds may be wealth reducing; the call provision may reduce the wealth of shareholders by inducing recapitalization in states which is suboptimal if there is no call provision, and incurs flotation costs which could have been avoided. The gain in firm value resulting from recapitalization may be too small to justify the extra flotation costs and thus reduces the overall firm value.
Business, Sauder School of
Graduate

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10

Chang, Min-Yung. "Active vibration control of composite structures." Diss., This resource online, 1990. http://scholar.lib.vt.edu/theses/available/etd-09162005-115021/.

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11

Ziaei, Rad Saeed. "Methods of updating numerical models in structural dynamics." Thesis, Imperial College London, 1997. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.286263.

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12

HaQuang, Ninh. "The response of multidegree-of-freedom systems with quadratic and cubic nonlinearities subjected to parametric and external excitations." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/49787.

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13

Geyer, Traver Adelina. "Dynamics and structural evolution of collapse calderas: A comparison between field evidence, analogue and mathematical models." Doctoral thesis, Universitat de Barcelona, 2007. http://hdl.handle.net/10803/1921.

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Collapse calderas are defined as the volcanic depression that result from the disruption of the geometry of the magma chamber roof due to down faulting during the course of an eruption. These structures have received considerable attention due to their link to Earth's ore deposits and geothermal energy resources, but also because large pyroclastic eruptions and associated caldera collapse structures represent one of the most catastrophic geologic events that have occurred on the Earth's surface in the Phanerozoic time and in the historical time.
After several pioneering works, collapse calderas have been the subject of studies of diverse disciplines. However, some important aspects on caldera dynamics and structure remain poorly understood yet.

First, we have revised important works concerning field data about collapse calderas and summarized the most relevant aspects and results. We have created a database to record existing information about collapse calderas: Collapse Caldera DataBase (CCDB). After an exhaustive analysis of the included information we have observed two types of collapse caldera: type-A and type-B.

Experiments on caldera collapse modelling allow a qualitative study of the structural evolution of a caldera collapse process and suggest which of factors play a more relevant role. Analogue models have verified that caldera collapse formation is influenced by multiple aspects (e.g. regional tectonics). We have performed three types of semi-quantitative analyses of particular interest for volcanic hazard: the measurement of the erupted magma chamber volume fraction required to achieve each step of the collapse process, the estimation of the subsidence pattern and the study of the influence of the roof aspect ratio in the dimensions of the collapse parts at surface.

This work includes also a summary of the most important aspects concerning mathematical models of collapse calderas. In base of a mathematical analysis of the pressure evolution inside the chamber during volcanic cycles, we have defined two collapse caldera end-members: under- and overpressure calderas. We have (1) reproduced numerically some of the analogue experiments set out in this work; (2) studied the influence of the selected geometrical setting (e.g. axial symmetric or three-dimensional) in the obtained results and subsequent interpretations and (3) demonstrated that results obtained with mathematical models not strictly related to collapse caldera processes are also applicable to the study of collapse mechanisms and controlling factors.

Finally, we compare the different results obtained by the three distinct disciplines, in order to propose a genetic classification for collapse calderas and to describe the dynamic and structural evolution of the defined end-members. We distinguish between "Cordilleran type" and "Composite volcano type" calderas. Calderas related to the first group correspond to commonly rhyolitic or dacitic, large plate/piston or trap-door calderas formed from a sill-like overpressurized magma chamber in the presence of a regional extensive stress field and a large scale doming or underplating. These calderas tend to occur in areas of thick or thin continental crust and in evolved transitional thick crust. They are associated with C-type subduction zones and areas of continental rifting. "Composite volcano type" calderas occur at the culmination of a long eruptive cycle in composite volcanoes. They take place at the summit of a long-lived volcanic edifice, which has undergone various periods of magma chamber inflation and deflation and different eruptions. The caldera-forming eruption begins with overpressure inside the chamber that triggers, once overcome the tensile strength of the host rock, magma injection into the host rock and finally, an eruption. Calderas included in this group tend to be smaller and not too voluminous.

Concluding, the combination of field studies with experimental and theoretical/mathematical and modelling allows us to identify and quantify the main factors controlling collapse calderas.

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14

Uribe, Guillermo. "On the relationship between continuous and discrete models for size-structured population dynamics." Diss., The University of Arizona, 1993. http://hdl.handle.net/10150/186197.

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We address the problem of the consistency between discrete and continuous models for density-dependent size-structured populations. Some earlier works have discussed the consistency of density independent age and size-structured models. Although the issue of consistency between these models has raised interest in recent years, it has not been discussed in depth, perhaps because of the non-linear nature of the equations involved. We construct a numerical scheme of the continuous model and show that the transition matrix of this scheme has the form of the standard discrete model. The construction is based on the theory of Upwind Numerical Schemes for non-Linear Hyperbolic Conservation Laws with one important difference, that we do have a non-linear source at the boundary; interestingly, this case has not been explored in depth from the purely mathematical point of view. We prove the consistency, non-linear stability and hence convergence of the numerical scheme which guarantee that both models yield results that are completely consistent with each other. Several examples are worked out: a simple linear age-structured problem, a density-independent size-structured problem and a non-linear size-structured problem. These examples confirm the convergence just proven theoretically. An ample revision of relevant biological and computational literature is also presented and used to establish realistic restrictions on the objects under consideration and to prepare significant examples to illustrate our points.

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15

Uliana, David A. "The effects of earthquake excitations on reticulated domes." Thesis, Virginia Tech, 1985. http://hdl.handle.net/10919/45667.

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Comparisons were made on the behavior of two full-sized reticulated domes subjected to uniform static loads only and uniform static loads with earthquake excitations. Space truss elements were used in the dome models. The stiffness matrix of the space truss element allows for the nonlinear strain-displacement behavior and the stress-strain behavior of the material is modeled with a bilinear approximation. The nonlinear solution technique is the Newton-Raphson method while the direct integration technique is the Newmark- Beta method.

The joint displacements for the static and the dynamic analyses were compared for both domes along with the axial stresses in all members. The percentage increases in the axial stresses of the dynamic analyses as compared to those of the static analyses were determined.

The reticulated domes used in the study were found to bet capable of withstanding the earthquake excitations when subjected to various uniform loads without failure.

Master of Science

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16

Lupi, Victor D. (Victor Dominick). "The use of mathematically exact solutions of structural dynamics models for structural control design." Thesis, Massachusetts Institute of Technology, 1992. http://hdl.handle.net/1721.1/43252.

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17

Juston, John M. "Theoretical and experimental study into the dynamics and control of a flexible beam with a DC-servo motor actuator." Thesis, Virginia Polytechnic Institute and State University, 1985. http://hdl.handle.net/10919/50029.

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Position and vibration control of a flexible beam is studied analytically and in the laboratory. Two different motor types are compared as actuators throughout the thesis: a standard voltage controlled motor and a torque controlled motor. The experimental beam is controlled with a dc-servo motor at its base and is instrumented with strain gages and a potentiometer. The control law is a form of linear, direct-output feedback. State estimators augment the control law to provide rate information that is not available from the instrumentation. Accurate modeling of the system’s inherent damping characteristics is achieved by analyzing experimental data. Gains were iterated yielding minimum-gain norm and minimum-sensitivity norm solutions to meet imposed eigenvalue placement constraints. Results for the two solutions and the two systems are compared and contrasted. Experimental verification of analytical results is hampered by unmodeled system non-linearities. Several attempts at bypassing these obstacles are shown. Finally, conclusions and recommendations are made.
Master of Science
incomplete_metadata

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18

Romanel, Celso. "A global-local approach for dynamic soil-structure interaction analysis of deeply embedded structures in a layered medium." Diss., The University of Arizona, 1989. http://hdl.handle.net/10150/184762.

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The most popular method for dynamic soil-structure interaction analysis is the finite element method. The versatility in problems involving different materials and complex geometries is its main advantage, yet the FEM can not simulate unbounded domains completely. Several schemes have been proposed to overcome this shortcoming, such as the use of either imperfect or perfect transmitting boundaries, infinite elements and hybrid techniques. However, most of them were derived on the assumption that the soil mass can be represented as a homogeneous material despite the fact that stratified soil deposits are a common occurrence in nature. A hybrid method is proposed in this research for soil-structure interaction analysis in the frequency domain involving a multilayered linear elastic half-space. The near field region (structure and a portion of soil surrounding it) is modeled by finite elements while the far field formulation is obtained through the classical wave propagation theory based on the assumption that the actual scattered wave fields can be represented by a set of line sources. Traction reciprocity between the two regions is satisfied exactly, while the displacement continuity across the common interface is enforced in a least-squares sense. The two-dimensional system is excited by harmonic body waves (P and SV) propagating with oblique incidence. The structure can be considered either on the surface or deeply embedded in the multilayered half-space. Analytic solutions for the far field domain is obtained through the combined response of four simple problems that take into account the overall effects of the incident, reflected and scattered wave fields. The delta matrix technique is employed in order to eliminate the loss of precision problem associated with the Thomson-Haskell matrix method in its original form. Special numerical schemes are used to transform the solution from the κ- into the ω-plane due to the presence of poles on the path of integration. The few numerical examples studied in this research validate the proposed hybrid technique, but the relatively high computational cost required for evaluation of the Green's functions is still a serious drawback. Some suggestions are made to minimize the problem as well as to extend this technique to cases involving material attenuation and forced vibrations.

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19

O???Brien, Peter Banking &amp Finance Australian School of Business UNSW. "Term structure modelling and the dynamics of Australian interest rates." Awarded by:University of New South Wales. School of Banking and Finance, 2006. http://handle.unsw.edu.au/1959.4/28283.

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This thesis consists of two related parts. In the first part we conduct an empirical examination of the dynamics of Australian interest rates of six different maturities, covering the whole yield curve. This direct study of the long rates is quite novel. We use maximum likelihood estimation on a variety of models and find some results that are in stark contrast to previous studies. We estimate Poisson-jump diffusion (PJD) models and find very strong evidence for the existence of jumps in all daily interest rate series. We find that the PJD model fits short-rate data significantly better than a Bernoulli-jump diffusion model. We also estimate the CKLS model for our data and find that the only model not rejected for all six maturities is the CEV model in stark contrast to previous findings. Also, we find that the elasticity of variance estimate in the CKLS model is much higher for the short-rates than for the longer rates where the estimate is only about 0.25, indicating that different dynamics seem to be at work for different maturities. We also found that adding jumps to the simple diffusion model gives a larger improvement than comes from going from the simple diffusion to the CKLS model. In the second part of the thesis we examine the Flesaker and Hughston (FH) term structure model. We derive the dynamics of the short rate under both the original measure and the risk-neutral measure, and show that some criticisms of the bounds for the short rate may not be significant in actual applications. We also derive the dynamics of bond prices in the FH model and compare them to the HJM model. We also extend the FH model by allowing the martingale to follow a jump-diffusion process, rather than just a diffusion process. We derive the unique change of measure that guarantees the family of bond prices is arbitrage-free. We derive prices for caps and swaptions, and extend the results to include Bermudan swaptions and show how to price options with the jump-diffusion version of the FH model.

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20

Brown, Andrew Michael. "Development of a probabilistic dynamic synthesis method for the analysis of non-deterministic structures." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/19065.

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21

Lopez, Dominguez Jose Carlos. "Reconstruction of 3-D structural dynamic response fields: an experimental, laser-based approach with statistical emphasis." Diss., Virginia Tech, 1994. http://hdl.handle.net/10919/38274.

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This dissertation is concerned with the evaluation of a new statistically sound reconstruction methodology for continuous 3-D dynamic response fields of harmonically excited structures in steady-state vibration. This results in an experimental process which reconstructs the response field from a set of 3-D projections based on Laser-Doppler-Vibrometer (LDV) localized instantaneous velocity measurements. Included along with an estimate of the 3-D velocity field, are its statistical characteristics and the inferential tools required to test the quality of the estimation. This dissertation documents in detail the development and evaluation of the proposed reconstruction methodology and its relevant subprocesses which inc1ude the formulation of a deterministic laser-structure kinematic model, and regression models that afford statistical inference for the time-domain and spatial-domain structural dynamics, as well as for the projection recombination process.
Ph. D.

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22

Alawneh, Zakaria Mohammad. "A numerical method for solving certain nonlinear integral equations arising in age-structured populations dynamics." Diss., The University of Arizona, 1990. http://hdl.handle.net/10150/184984.

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In this thesis we study the existence and stability of positive equilibrium of a general model for the dynamics of several interacting, age-structured population. We begin with the formulation and proof of a global existence theorem for the initial value problem. The proof of this theorem is used to develop an algorithm and a FORTRAN code for the numerical solution of initial value problems for the single species case. This computer program is used to study prototype models for the dynamics of a population whose fertility and mortality rates exhibit an "Allee effect". This is done from a bifurcation theoretic point of view, using the inherent net reproductive rate as a bifurcating parameter. An unstable "left" bifurcation is found. Multi-equilibria and various kinds of oscillations are studied as a function of r, the fertility window, and the nature of the density dependence.

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23

Gentry, Jeanette J. "Nonlinear oscillations under multifrequency parametric excitation." Thesis, Virginia Tech, 1988. http://hdl.handle.net/10919/43402.

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A second-order system of differential equations containing a multifrequency parametric excitation and weak quadratic and cubic nonlinearities is investigated. The method of multiple scales is used to carry out a general analysis, and three resonance conditions are considered in detail. First, the case in which the sum of two excitation frequencies is near two times a natural frequency, Î»_s + Î»_t ~2Ï _q, is examined. Second, the influence of an internal resonance, Ï _q~3Ï r, on the previous case is studied. Finally, the effect of the internal resonance w_r~3w_q on the resonance Î»_s + Î»_t ~2Ï _q is investigated. Results are presented as plots of response amplitudes as functions of a detuning parameter, excitation amplitude, and, for the first case, a measure of the relative values of Î»_s + Î»_t.

Master of Science

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24

Foliente, Greg C. "Stochastic dynamic response of wood structural systems." Diss., This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-05042006-164535/.

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25

Lucas, Geoffrey Iain Mechanical &amp Manufacturing Engineering Faculty of Engineering UNSW. "Vibrational characteristics of structures with uncertainty." Publisher:University of New South Wales. Mechanical & Manufacturing Engineering, 2008. http://handle.unsw.edu.au/1959.4/41274.

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This thesis is concerned with the prediction of the vibro-acoustic response of structures with uncertain properties in the mid frequency region. The motivation for this research is the growing need of engineers to understand the responses of a group of similar structures ranging from vehicles, aircraft and aerospace structures, to household whitegood appliances. These structures are complex in geometry and may possess variability in their material or geometric properties, as well as variation arising from the assembly and manufacturing processes. Small variations can have a significant effect on a dynamic response of a structure, and the effect of structural uncertainties increases as the frequency increases. Deterministic modelling techniques such as finite element analysis are only suitable to model complex structures at low frequencies. Furthermore, FEA cannot easily account for uncertainty or randomness in structural parameters. High frequency dynamic predictive techniques such as Statistical Energy Analysis can account for structural uncertainty but is limited to structures with high modal density. There exists a frequency range between the two methods in which neither technique can be applied with great confidence. The objective of this thesis is to investigate predictive techniques for mid frequency vibration analysis of dynamic systems with structural uncertainties. The first part of this work is to numerically characterise the effect of a range of uncertainties on the modal statistics of structures. The degree of uncertainty required to achieve universality of the statistical properties is investigated. This is achieved by examining the modal statistics of dynamic systems with a range of uncertainty, corresponding to uncertainty due to mass and stiffness perturbations, uncertainty at the boundaries of a structure, uncertainty in the coupling between structures, uncertainty in the material properties of a structure and uncertainty in the geometry of a structure. Several structures are examined corresponding to a plate with masses and/or linear springs added at random locations, a plate with torsional springs attached at random locations along its boundary edges, two plates coupled by linear springs at random locations, a mass-loaded coupled L-shaped plate, a mass-loaded frame-plate structure, and a plate with varying Young's modulus, density and thickness. The natural frequencies of the aforementioned structures have been derived using either the Lagrange-Rayleigh-Ritz technique, finite element analysis, or the use of interval analysis in conjunction with FEA. The natural frequency statistics of structures with uncertain properties are observed using two statistical measures; the statistical overlap factor and the probability density function of the spacing between successive natural frequencies. The statistical overlap factor is defined by the variation in a natural frequency from its mean value measured across an ensemble of nominally identical structures with uncertainty. For a single ensemble member, the probability density function of the spacing between successive natural frequencies is compared to a Rayleigh distribution of the mean frequency spacing. A Rayleigh distribution of modal spacings is a feature of the universality exhibited by structures with uncertainty. To further investigate the effect of structural uncertainty on the vibrational characteristics of structures, the interval analysis is applied to finite element models of a plate with uncertainty in its material properties and dimensions. Using this method, the Young's modulus, density and thickness of a rectangular plate were set to vary by a small amount within predefined bounds. Using finite element equations, the natural frequencies and modeshapes of the structure were then determined in terms of the Young's modulus, density and plate thickness. For the mass and spring loaded plates, the springs were shown to affect the lower order modes while the masses had a significant effect on the higher order modes. As the frequency increased, only a small amount of perturbation was sufficient to affect the natural frequencies of a structure. Using the interval analysis method, the variation of the natural frequencies from their deterministic value increased as the frequency increased. An ergodic hypothesis was used to examine the responses statistics of structures with uncertainty. Three structures have been computationally studied corresponding to two plates coupled by springs, an L-shaped plate and a frame plate structure. Uncertainty has been generated for the two coupled plates by locating the springs randomly across the surface of the two plates. For the L-shaped plate and a frame plate structure, uncertainty was generated by randomly positioning small masses across the plates. Using the ergodic hypothesis, the frequency averaged response on one member of an ensemble is compare with the ensemble averaged response. It was found that the ensemble averaged response was well predicted by a frequency averaged response of a single ensemble member. The width of the frequency averaging band was shown to have a large influence on the quality of the match between the frequency and ensemble averaged responses. Results were significantly improved using a frequency averaging bandwidth which varies proportionally to frequency. Finally, experiments have been conducted on an L-shaped plate, a frame plate structure and a vehicle to validate the computational results for the natural frequency and response statistics.

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Rodriguez, Jesus. "Modeling of complex systems using nonlinear, flexible multibody dynamics." Diss., Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/12344.

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De, Antonio Liedo David. "Structural models for macroeconomics and forecasting." Doctoral thesis, Universite Libre de Bruxelles, 2010. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210142.

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This Thesis is composed by three independent papers that investigate

central debates in empirical macroeconomic modeling.

Chapter 1, entitled “A Model for Real-Time Data Assessment with an Application to GDP Growth Rates”, provides a model for the data

revisions of macroeconomic variables that distinguishes between rational expectation updates and noise corrections. Thus, the model encompasses the two polar views regarding the publication process of statistical agencies: noise versus news. Most of the studies previous studies that analyze data revisions are based

on the classical noise and news regression approach introduced by Mankiew, Runkle and Shapiro (1984). The problem is that the statistical tests available do not formulate both extreme hypotheses as collectively exhaustive, as recognized by Aruoba (2008). That is, it would be possible to reject or accept both of them simultaneously. In turn, the model for the

DPP presented here allows for the simultaneous presence of both noise and news. While the “regression approach” followed by Faust et al. (2005), along the lines of Mankiew et al. (1984), identifies noise in the preliminary

figures, it is not possible for them to quantify it, as done by our model.

The second and third chapters acknowledge the possibility that macroeconomic data is measured with errors, but the approach followed to model the missmeasurement is extremely stylized and does not capture the complexity of the revision process that we describe in the first chapter.

Chapter 2, entitled “Revisiting the Success of the RBC model”, proposes the use of dynamic factor models as an alternative to the VAR based tools for the empirical validation of dynamic stochastic general equilibrium (DSGE) theories. Along the lines of Giannone et al. (2006), we use the state-space parameterisation of the factor models proposed by Forni et al. (2007) as a competitive benchmark that is able to capture weak statistical restrictions that DSGE models impose on the data. Our empirical illustration compares the out-of-sample forecasting performance of a simple RBC model augmented with a serially correlated noise component against several specifications belonging to classes of dynamic factor and VAR models. Although the performance of the RBC model is comparable

to that of the reduced form models, a formal test of predictive accuracy reveals that the weak restrictions are more useful at forecasting than the strong behavioral assumptions imposed by the microfoundations in the model economy.

The last chapter, “What are Shocks Capturing in DSGE modeling”, contributes to current debates on the use and interpretation of larger DSGE

models. Recent tendency in academic work and at central banks is to develop and estimate large DSGE models for policy analysis and forecasting. These models typically have many shocks (e.g. Smets and Wouters, 2003 and Adolfson, Laseen, Linde and Villani, 2005). On the other hand, empirical studies point out that few large shocks are sufficient to capture the covariance structure of macro data (Giannone, Reichlin and

Sala, 2005, Uhlig, 2004). In this Chapter, we propose to reconcile both views by considering an alternative DSGE estimation approach which

models explicitly the statistical agency along the lines of Sargent (1989). This enables us to distinguish whether the exogenous shocks in DSGE

modeling are structural or instead serve the purpose of fitting the data in presence of misspecification and measurement problems. When applied to the original Smets and Wouters (2007) model, we find that the explanatory power of the structural shocks decreases at high frequencies. This allows us to back out a smoother measure of the natural output gap than that

resulting from the original specification.
Doctorat en Sciences économiques et de gestion
info:eu-repo/semantics/nonPublished

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Lemmon, Jack David Jr. "Three-dimensional computational modeling of fluid-structure interaction : study of diastolic function in a thin-walled left heart model." Diss., Georgia Institute of Technology, 1998. http://hdl.handle.net/1853/15912.

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Abou-Rayan, Ashraf M. "A study of full displacement design of frame structures using displacement sensitivity analysis." Thesis, Virginia Tech, 1985. http://hdl.handle.net/10919/45557.

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The intent of this study is to develop an algorithm for structural design based on allowable displacements for structural members, independent of stresses caused by the configurations imposed. Structural design can be based on displacement constraints applied in the same basic format as stress constraints so that convergence is based on allowable displacements rather than on stresses.

Master of Science

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Bennighof, Jeffrey Kent. "Modeling and control of flexible structures." Diss., Virginia Polytechnic Institute and State University, 1986. http://hdl.handle.net/10919/49982.

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This dissertation is concerned with some topics in the modeling and control of large flexible structures. In the finite element convergence toward the natural modes and frequencies of a structure, it is found that two mechanisms limiting the accuracy of higher modes are, first, a decrease in the number of active degrees of freedom for higher mode approximations due to orthogonality constraints, and, second, the fact that lower computed, rather than actual, eigenfunctions appear in the orthogonality constraints, so that inaccuracy in lower modes inhibits convergence to higher modes. Refining the elements using the hierarchical p-version proves to be far superior to refining the mesh, as demonstrated by numerical examples. In the third chapter, a method is presented for solving the algebraic eigenvalue problem for a structure, which combines attractive features of the subspace iteration method and the component-mode synthesis methods. Reduced substructure models are generated automatically and coupled exactly to form a reduced structure model, whose eigensolution is used to refine the substructure models. Convergence is much faster than in the subspace iteration method, as demonstrated by numerical examples. In the fourth chapter, the effectiveness of modal control (IMSC) and direct feedback control, in which the actuator force depends only on the local velocity and displacement, are investigated for suppressing traveling waves on a string and on a beam, both with slight material damping. Direct feedback proves superior for the string, as more modes must be controlled than can be handled by modal control with a limited number of actuators, but inferior for the beam, as effort is wasted suppressing motion in higher modes where damping is pervasive, while modal control focuses effort on those lower modes which need to be controlled. The optimal vibration control for a distributed system subjected to persistent excitation is not available, so a two-part control is proposed in chapter five for suppressing the motion of a distributed system with a moving support. The first part cancels the moving support's excitation to an optimal extent, and the second is a direct velocity feedback control. A numerical example demonstrates the effectiveness of this control method.
Ph. D.
incomplete_metadata

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Chu, Juhui, and 储聚慧. "Dynamic analysis of coupled structure foundation system by the finite element method." Thesis, The University of Hong Kong (Pokfulam, Hong Kong), 2010. http://hub.hku.hk/bib/B46599150.

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Errigo, Michael. "Structured Errors in Modeling Fishery Population Dynamics and in Stock Assessment." Fogler Library, University of Maine, 2008. http://www.library.umaine.edu/theses/pdf/ErrigoM2008.pdf.

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Farhoomand, Ali F. "A dynamic hierarchical structural model of information systems success : the case of electronic data interchange." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=39305.

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The purpose of this dissertation is to explicate the meaning of information systems (IS) success in the realm of a dynamic hierarchical structure model of IS success. Through an empirical study of 382 firms using internal and Electronic Data Interchange (EDI) systems, different characteristics of this model are examined via four hypotheses.
First, using linear structural modelling techniques, it is shown that successful information systems share certain properties common to all systems, in addition to certain properties specific to each class of systems. Four generic factors influencing IS success are identified as (i) output reliability, (ii) system's characteristics, (iii) efficiency outcomes, and (iv) users' requirements. Second, the role of time in the IS adoption and assessment process is explored. By comparing firms that have adopted EDI with those that have not adopted EDI, it is shown that the decision maker's perception of IS success changes during different stages of the adoption and assessment process. Third, the role of stakeholders in the assessment process is examined by comparing perceptions of different managerial groups based on their educational background, management echelon, and functional area. It is shown that different stakeholders evaluate the success of IS differently. Finally, through an examination of various types of evaluation functions, it is shown that IS success is a multi-dimensional construct.
Overall, cross-group comparisons of the dynamic hierarchical structural model of IS success provide sufficient evidence regarding the instability of IS success across time, type of system, and stakeholders involved in the evaluation process.
In addition to the major hypotheses, two corollaries have also been examined. It is shown that user involvement in an IS project has a positive effect on the system's success. Further, the results of the study indicate that respondents in smaller companies are more satisfied with the support and services of the MIS department than their counterparts in larger companies.
Finally, by comparing three versions of the questionnaire used in the study, it is shown that question order has a significant effect on responses. The implications of this finding for survey studies are discussed.

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Choi, Joonho. "Concurrent fire dynamic models and thermomechanical analysis of steel and concrete structures." Diss., Atlanta, Ga. : Georgia Institute of Technology, 2008. http://hdl.handle.net/1853/26679.

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Roithmayr, Carlos. "Relating constrained motion to force through Newton's second law." Diss., Available online, Georgia Institute of Technology, 2007, 2007. http://etd.gatech.edu/theses/available/etd-03302007-125659/.

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Thesis (Ph. D.)--Aerospace Engineering, Georgia Institute of Technology, 2007.
Bauchau, Olivier, Committee Member ; Hodges, Dewey, Committee Chair ; Singhose, William, Committee Member ; Costello, Mark, Committee Member ; Flannery, Raymond, Committee Member.

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Taylor, Richard. "Finite element modelling of three dimensional fluid-structure interaction." Thesis, Swansea University, 2013. https://cronfa.swan.ac.uk/Record/cronfa42308.

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This work is focused on the numerical modelling of fluid-structure interaction in three dimensions. Both internal and external laminar flow around flexible bodies are considered. The fluid flow simulated is based on the incompressible Navier-Stokes equations and the general focus is on laminar Newtonian flow. The streamline upwind/ pressure stabilising Petrov-Galerkin (SUPG/PSPG) method is employed to achieve a stable low order finite element discretisation of the fluid, while the solid is discretised spatially by a standard Galerkin finite element approach. The behavior of the solid is governed by Neo-Hooke elasticity. For temporal discretisation the discrete implicit generalised-alpha method is employed for both the fluid and the solid domains. The motion of the fluid mesh is solved using an arbitrary Lagrangian-Eulerian (ALE) scheme employing a nonlinear pseudo-elastic mesh update method. The fluid-solid interface is modelled using a finite element interpolation method that allows for non-matching meshes and satisfies the required conservation laws. The resulting sets of fully implicit strongly coupled nonlinear equations are then decomposed into a general framework consisting of fluid, interface and solid domains. These equations are then solved using different solution techniques consisting of strongly coupled monolithic Newton and block Gauss-Seidel methods as well as a weakly coupled novel staggered scheme. These solvers are employed to solve a number of three dimensional numerical examples consisting of: External flow: o a soft elastic beam fixed at both ends o a thin cantilever plate.

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Patel, Nayan V. "Simulation of Hydrodynamic Fragmentation from a Fundamental and an Engineering Perspective." Diss., Georgia Institute of Technology, 2007. http://hdl.handle.net/1853/16225.

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Liquid fragmentation phenomenon is explored from both a fundamental (fully resolved) and an engineering (modeled) perspective. The dual objectives compliment each other by providing an avenue to gain further understanding into fundamental processes of atomization as well as to use the newly acquired knowledge to address practical concerns. A compressible five-equation interface model based on a Roe-type scheme for the simulation of material boundaries between immiscible fluids with arbitrary equation of state is developed and validated. The detailed simulation model accounts for surface-tension, viscous, and body-force effects, in addition to acoustic and convective transport. The material interfaces are considered as diffused zones and a mixture model is given for this transition region. The simulation methodology combines a high-resolution discontinuity capturing method with a low-dissipation central scheme resulting in a hybrid approach for the solution of time- and space-accurate interface problems. Several multi-dimensional test cases are considered over a wide range of physical situations involving capillary, viscosity, and gravity effects with simultaneous presence of large viscosity and density ratios. The model is shown to accurately capture interface dynamics as well as to deal with dynamic appearance and disappearance of material boundaries. Simulation of atomization processes and its interaction with the flow field in practical devices is the secondary objective of this study. Three modeling requirements are identified to perform Large-Eddy Simulation (LES) of spray combustion in engineering devices. In concurrence with these requirements, LES of an experimental liquid-fueled Lean Direct Injection (LDI) combustor is performed using a subgrid mixing and combustion model. This approach has no adjustable parameters and the entire flow-path through the inlet swirl vanes is resolved. The inclusion of the atomization aspects within LES eliminates the need to specify dispersed-phase size-velocity correlations at the inflow boundary. Kelvin-Helmholtz (or aerodynamic) breakup model by Reitz is adopted for the combustor simulation. Two simulations (with and without breakup) are performed and compared with measurements of Cai et al. Time-averaged velocity prediction comparison for both gas- and liquid-phase with available data show reasonable agreement. The major impact of breakup is on the fuel evaporation in the vicinity of the injector. Further downstream, a wide range of drop sizes are recovered by the breakup simulation and produces similar spray quality as in the no-breakup case.

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Decouvreur, Vincent. "Updating acoustic models: a constitutive relation error approach." Doctoral thesis, Universite Libre de Bruxelles, 2008. http://hdl.handle.net/2013/ULB-DIPOT:oai:dipot.ulb.ac.be:2013/210572.

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In the global framework of improving vibro-acoustic numerical prediction quality together with the need to decrease the number of prototyping stages, this manuscript focuses on achieving greater accuracy for acoustic numerical simulations by making use of a parametric updating technique, which enables tuning the model parameters inside physically meaningful boundaries. The improved model is used for the next prototyping stages, allowing more accurate results within reduced simulation times. The updating technique is based on recent works dealing with the constitutive relation error method (CRE) applied to acoustics. The updating process focuses on improving the acoustic damping matrix related to the absorbing properties of the materials covering the borders of the acoustic domain.
Doctorat en sciences appliquées
info:eu-repo/semantics/nonPublished

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Sternchüss, Arnaud. "Multi-level parametric reduced models of rotating bladed disk assemblies." Phd thesis, Ecole Centrale Paris, 2009. http://tel.archives-ouvertes.fr/tel-00366252.

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Les disques aubagés, que l'on trouve dans les turbomachines, sont des structures complexes dont le comportement vibratoire est généralement déterminé par l'exploitation de conditions de symétrie dans leur configuration nominale. Cette symétrie disparaît lorsque l'on assemble plusieurs de ces disques pour former un rotor ou que l'on introduit une variabilité spatiale des paramètres mécaniques (on parle de désaccordage intentionnel ou non). Le raffinement des maillages, nécessaire à une évaluation correcte de la répartition des contraintes, conduirait à des modèles de rotor complet de taille prohibitive (plusieurs dizaines de millions de degrés de liberté). L'objectif de cette thèse est donc l'introduction de méthodologies de réduction qui par combinaison de calculs acceptables permettent d'étudier de façon fine la dynamique d'ensemble sur des modèles 3D fins multi-étages et potentiellement désaccordés. L'étude des transformations de Fourier séparées des réponses de chaque étage permet, dans un premier temps, de bien comprendre les effets de couplage inter-harmonique liés au couplage inter-disque et au désaccordage. A partir de ce constat, une première méthode utilise les résultats de calculs en symétrie cyclique et à secteur encastré pour construire un modèle de secteur exact pour certains modes dits cibles et de très bonne qualité pour les autres modes. Cette méthode est ensuite étendue au cas multi-étage en construisant des bases de réduction de secteur par combinaison de solutions mono-harmoniques. Les illustrations montrent que la méthodologie proposée permet le traitement de modèles de très grande taille, tout en restant compatible avec une grande richesse de post-traitements (calculs de modes, calculs de réponses forcées, analyses de leur contenu harmonique spatial, répartition d'énergie et effets de localisation...). La méthodologie est enfin étendue à la gestion de modèles paramétrés en vitesse de rotation. L'enrichissement des ensembles de modes cibles par des calculs à trois vitesses permet ainsi une reconstruction rapide de l'évolution des fréquences pour l'ensemble d'un intervalle.

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Kahle, Matthew Gilbert. "Partially restrained composite connections : design and analysis of a prototype structure." Thesis, Georgia Institute of Technology, 2002. http://hdl.handle.net/1853/20830.

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Widjaja, Budi R. "Analytical investigation of composite diaphragms strength and behavior." Thesis, This resource online, 1993. http://scholar.lib.vt.edu/theses/available/etd-07112009-040307/.

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Pitsillis, Zachry Steven. "Estimating dynamic affine term structure models." Master's thesis, University of Cape Town, 2015. http://hdl.handle.net/11427/15731.

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Duffee and Stanton (2012) demonstrated some pointed problems in estimating affine term structure models when the price of risk is dynamic, that is, risk factor dependent. The risk neutral parameters are estimated with precision, while the price of risk parameters are not. For the Gaussian models they investigated, these problems are replicated and are shown to stem from a lack of curvature in the log-likelihood function. This geometric issue for identifying the maximum of an essentially horizontal log-likelihood has statistical meaning. The Fisher information for the price of risk parameters is multiple orders of magnitude smaller than that of the risk neutral parameters. Prompted by the recent results of Christoffersen et al. (2014) a remedy to the lack of curvature is attempted. An unscented Kalman filter is used to estimate models where the observations are portfolios of FRAs, Swaps and Zero Coupon Bond Options. While the unscented Kalman filter performs admirably in identifying the unobserved risk factor processes, there is little improvement in the Fisher information.

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Morris-Thomas, Michael. "An investigation into wave run-up on vertical surface piercing cylinders in monochromatic waves." University of Western Australia. School of Oil and Gas Engineering, 2003. http://theses.library.uwa.edu.au/adt-WU2004.0010.

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[Formulae and special characters can only be approximated here. Please see the pdf version of the abstract for an accurate reproduction.] Wave run-up is the vertical uprush of water when an incident wave impinges on a free- surface penetrating body. For large volume offshore structures the wave run-up on the weather side of the supporting columns is particularly important for air-gap design and ultimately the avoidance of pressure impulse loads on the underside of the deck structure. This investigation focuses on the limitations of conventional wave diffraction theory, where the free-surface boundary condition is treated by a Stokes expansion, in predicting the harmonic components of the wave run-up, and the presentation of a simplified procedure for the prediction of wave run-up. The wave run-up is studied on fixed vertical cylinders in plane progressive waves. These progressive waves are of a form suitable for description by Stokes' wave theory whereby the typical energy content of a wave train consists of one fundamental harmonic and corresponding phase locked Fourier components. The choice of monochromatic waves is indicative of ocean environments for large volume structures in the diffraction regime where the assumption of potential flow theory is applicable, or more formally A/a < Ο(1) (A and a being the wave amplitude and cylinder radius respectively). One of the unique aspects of this work is the investigation of column geometry effects - in terms of square cylinders with rounded edges - on the wave run-up. The rounded edges of each cylinder are described by the dimensionless parameter rc/a which denotes the ratio of edge corner radius to half-width of a typical column with longitudinal axis perpendicular to the quiescent free-surface. An experimental campaign was undertaken where the wave run-up on a fixed column in plane progressive waves was measured with wire probes located close to the cylinder. Based on an appropriate dimensional analysis, the wave environment was represented by a parametric variation of the scattering parameter ka and wave steepness kA (where k denotes the wave number). The effect of column geometry was investigated by varying the edge corner radius ratio within the domain 0 <=rc/a <= 1, where the upper and lower bounds correspond to a circular and square shaped cylinder respectively. The water depth is assumed infinite so that the wave run-up caused purely by wave-structure interaction is examined without the additional influence of a non-decaying horizontal fluid velocity and finite depth effects on wave dispersion. The zero-, first-, second- and third-harmonics of the wave run-up are examined to determine the importance of each with regard to local wave diffraction and incident wave non-linearities. The modulus and phase of these harmonics are compared to corresponding theoretical predictions from conventional diffraction theory to second-order in wave steepness. As a result, a basis is formed for the applicability of a Stokes expansion to the free-surface boundary condition of the diffraction problem, and its limitations in terms of local wave scattering and incident wave non-linearities. An analytical approach is pursued and solved in the long wavelength regime for the interaction of a plane progressive wave with a circular cylinder in an ideal fluid. The classical Stokesian assumption of infinitesimal wave amplitude is invoked to treat the free-surface boundary condition along with an unconventional requirement that the cylinder width is assumed much smaller than the incident wavelength. This additional assumption is justified because critical wavelengths for wave run-up on a fixed cylinder are typically much larger in magnitude than the cylinder's width. In the solution, two coupled perturbation schemes, incorporating a classical Stokes expansion and cylinder slenderness expansion, are invoked and the boundary value problem solved to third-order. The formulation of the diffraction problem in this manner allows for third-harmonic diffraction effects and higher-order effects operating at the first-harmonic to be found. In general, the complete wave run-up is not well accounted for by a second-order Stokes expansion of the free-surface boundary condition and wave elevation. This is however, dependent upon the coupling of ka and kA. In particular, whilst the modulus and phase of the second-harmonic are moderately predicted, the mean set-up is not well predicted by a second-order Stokes expansion scheme. This is thought to be caused by higher than second-order non-linear effects since experimental evidence has revealed higher-order diffraction effects operating at the first-harmonic in waves of moderate to large steepness when k < < 1. These higher-order effects, operating at the first-harmonic, can be partially accounted for by the proposed long wavelength formulation. For small ka and large kA, subsequent comparisons with measured results do indeed provide a better agreement than the classical linear diffraction solution of Havelock (1940). To account for the complete wave run-up, a unique approach has been adopted where a correction is applied to a first-harmonic analytical solution. The remaining non-linear portion is accounted for by two methods. The first method is based on regression analysis in terms of ka and kA and provides an additive correction to the first-harmonic solution. The second method involves an amplification correction of the first-harmonic. This utilises Bernoulli's equation applied at the mean free-surface position where the constant of proportionality is empirically determined and is inversely proportional to ka. The experimental and numerical results suggest that the wave run-up increases as rc/a--› 0, however this is most significant for short waves and long waves of large steepness. Of the harmonic components, experimental evidence suggests that the effect of a variation in rc/a on the wave run-up is particularly significant for the first-harmonic only. Furthermore, the corner radius effect on the first-harmonic wave run-up is well predicted by numerical calculations using the boundary element method. Given this, the proposed simplified wave run-up model includes an additional geometry correction which accounts for rc/a to first-order in local wave diffraction. From a practical view point, it is the simplified model that is most useful for platform designers to predict the wave run-up on a surface piercing column. It is computationally inexpensive and the comparison of this model with measured results has proved more promising than previously proposed schemes.

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Karpodinis, George. "The dynamic response of an impacting driven beam : experiments and mathematical model." Thesis, University College London (University of London), 2002. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.268854.

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Moore, Matthew Richard. "New mathematical models for splash dynamics." Thesis, University of Oxford, 2014. http://ora.ox.ac.uk/objects/uuid:c94ff7f2-296a-4f13-b04b-e9696eda9047.

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In this thesis, we derive, extend and generalise various aspects of impact theory and splash dynamics. Our methods throughout will involve isolating small parameters in our models, which we can utilise using the language of matched asymptotics. In Chapter 1 we briefly motivate the field of impact theory and outline the structure of the thesis. In Chapter 2, we give a detailed review of classical small-deadrise water entry, Wagner theory, in both two and three dimensions, highlighting the key results that we will use in our extensions of the theory. We study oblique water entry in Chapter 3, in which we use a novel transformation to relate an oblique impact with its normal-impact counterpart. This allows us to derive a wide range of solutions to both two- and three-dimensional oblique impacts, as well as discuss the limitations and breakdown of Wagner theory. We return to vertical water-entry in Chapter 4, but introduce the air layer trapped between the impacting body and the liquid it is entering. We extend the classical theory to include this air layer and in the limit in which the density ratio between the air and liquid is sufficiently small, we derive the first-order correction to the Wagner solution due to the presence of the surrounding air. The model is presented in both two dimensions and axisymmetric geometries. In Chapter 5 we move away from Wagner theory and systematically derive a series of splash jet models in order to find possible mechanisms for phenomena seen in droplet impact and droplet spreading experiments. Our canonical model is a thin jet of liquid shot over a substrate with a thin air layer trapped between the jet and the substrate. We consider a variety of parameter regimes and investigate the stability of the jet in each regime. We then use this model as part of a growing-jet problem, in which we attempt to include effects due to the jet tip. In the final chapter we summarise the main results of the thesis and outline directions for future work.

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Daukste, Liene. "Mathematical Modelling of Cancer Cell Population Dynamics." Thesis, University of Canterbury. Department of Mathematics and Statistics, 2012. http://hdl.handle.net/10092/10057.

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Mathematical models, that depict the dynamics of a cancer cell population growing out of the human body (in vitro) in unconstrained microenvironment conditions, are considered in this thesis. Cancer cells in vitro grow and divide much faster than cancer cells in the human body, therefore, the effects of various cancer treatments applied to them can be identified much faster. These cell populations, when not exposed to any cancer treatment, exhibit exponential growth that we refer to as the balanced exponential growth (BEG) state. This observation has led to several effective methods of estimating parameters that thereafter are not required to be determined experimentally. We present derivation of the age-structured model and its theoretical analysis of the existence of the solution. Furthermore, we have obtained the condition for BEG existence using the Perron-Frobenius theorem. A mathematical description of the cell-cycle control is shown for one-compartment and two-compartment populations, where a compartment refers to a cell population consisting of cells that exhibit similar kinetic properties. We have incorporated into our mathematical model the required growing/aging times in each phase of the cell cycle for the biological viability. Moreover, we have derived analytical formulae for vital parameters in cancer research, such as population doubling time, the average cell-cycle age, and the average removal age from all phases, which we argue is the average cell-cycle time of the population. An estimate of the average cell-cycle time is of a particular interest for biologists and clinicians, and for patient survival prognoses as it is considered that short cell-cycle times correlate with poor survival prognoses for patients. Applications of our mathematical model to experimental data have been shown. First, we have derived algebraic expressions to determine the population doubling time from single experimental observation as an alternative to empirically constructed growth curve. This result is applicable to various types of cancer cell lines. One option to extend this model would be to derive the cell cycle time from a single experimental measurement. Second, we have applied our mathematical model to interpret and derive dynamic-depicting parameters of five melanoma cell lines exposed to radiotherapy. The mathematical result suggests there are shortcomings in the experimental methods and provides an insight into the cancer cell population dynamics during post radiotherapy. Finally, a mathematical model depicting a theoretical cancer cell population that comprises two sub-populations with different kinetic properties is presented to describe the transition of a primary culture to a cell line cell population.

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47

Romanel, Celso 1952. "DYNAMIC SOIL-STRUCTURE INTERACTION IN A LAYERED MEDIUM." Thesis, The University of Arizona, 1987. http://hdl.handle.net/10150/276511.

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The most popular method in dynamic soil-structure interaction analysis is the finite element method. The versatility in problems involving different materials and complex geometries is its main advantage, yet FEM can not simulate unbounded domains completely. A hybrid method is proposed in this research, which models the near field (structure and surrounding soil) by finite elements and the far field by a continuum approach. The system is excited by monochromatic body waves (P and SV) propagating with oblique incidence and harmonic time dependence. The far field problem is solved using Thomson-Haskell formulation associated with the delta matrix technique. The soil profile does not contain any soft layer and the layers are assumed to be linearly elastic, isotropic, homogeneous and perfectly bonded at the interfaces. Two-dimensional (in-plane) formulation is considered and the analysis is performed on both k- and o-planes through time and spatial Fourier transforms of the field equations and boundary conditions. (Abstract shortened with permission of author.)

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Morin, Benjamin R. "The Effect of Static and Dynamic Spatially Structured Disturbances on a Locally Dispersing Population Model." Fogler Library, University of Maine, 2006. http://www.library.umaine.edu/theses/pdf/MorinBR2006.pdf.

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Mosqueda, Gilberto 1974. "Interactive educational models for structural dynamics." Thesis, Massachusetts Institute of Technology, 1998. http://hdl.handle.net/1721.1/50365.

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Thölken, Denise. "Efeito da rigidez de pilar parede no comportamento sísmico de edifício de concreto armado." Universidade Tecnológica Federal do Paraná, 2013. http://repositorio.utfpr.edu.br/jspui/handle/1/962.

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Este trabalho tem como objeto o estudo do efeito da rigidez de pilar parede no comportamento estrutural de edifícios de concreto armado submetidos a sismos. Foram consideradas as premissas da norma brasileira ABNT NBR15421:2006, que apresenta os critérios para projeto de estruturas resistentes a sismo. A análise linear com emprego dos métodos da norma - método das forças horizontais equivalentes, método espectral e histórico de aceleração no tempo - foi aplicada em edifícios com dois tipos de sistemas estruturais, sendo eles pórtico de concreto e sistema dual pórtico de concreto e pilar parede. Os resultados foram analisados nos pórticos de extremidade das estruturas nos sentidos longitudinal (x) e transversal (y), comparando-se os deslocamentos de cada pavimento e esforços cortantes, momento fletor e normal nas bases dos pilares. A comparação foi realizada entre os três métodos aplicados e os sistemas estruturais analisados.
The aim of this work is to study the stiffness effect of wall columns on structural behavior of reinforced concrete buildings subjected to seismic action. The premises of the Brazilian standard ABNT NBR14521:2006 were considered, which presents criteria for earthquake resistant design of structures. The linear analysis employed the methods of the Brazilian standard - equivalent static load method, response spectrum analysis and time history method - were applied to buildings with two types of structural systems, namely concrete frame and dual system concrete frame and wall columns. The results were analyzed in edge frames structures in the longitudinal and transverse directions, comparing the displacement of each floor and shear, bending moment and axial forces on the bases of the columns. A comparison was made between the three methods applied and the structural systems analyzed.

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Dissertations / Theses on the topic 'Structural dynamics – Mathematical models'

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