Dissertations / Theses on the topic 'Dynamic stiffne'

Il carico di traffico trasferito sulle pavimentazioni stradali include sia sollecitazioni verticali che orizzontali. Queste ultime diventano particolarmente critiche nelle zone soggette a frequenti frenate, in curva o con pendenze elevate. Poiché la pavimentazione stradale è una struttura multistrato, l'esistenza di uno scarso collegamento all’interfaccia tra gli strati bituminosi potrebbe influire negativamente sulle prestazioni e funzionalità della pavimentazione. Pertanto, una corretta valutazione del grado di collegamento tra gli strati è di fondamentale importanza. Finora, tale valutazione viene effettuata misurando la resistenza a taglio dell'interfaccia utilizzando prove di laboratorio statiche. Un miglioramento significativo dell'attuale approccio di prova è lo sviluppo di dispositivi dinamici, che potrebbero simulare in modo più realistico le condizioni in sito. La presente Tesi di dottorato descrive le attività sperimentali svolte presso l'Università Politecnica delle Marche, la North Carolina State University e l'University of Limoges nell'ambito del Task Group 3 "Pavement multilayer system" del RILEM TC 272-PIM. Le attività si sono concentrate sulla progettazione e lo sviluppo di un nuovo dispositivo di prova per l'esecuzione di prove dinamiche all’interfaccia presso l'Università Politecnica delle Marche e sull’esecuzione di prove dinamiche con altri dispositivi esistenti. Il comportamento a taglio delle interfacce è stato studiato sia con prove di taglio diretto che di torsione su campioni carotati da lastre bistrato compattate in laboratorio e preparate con un'unica miscela bituminosa. I risultati presentati in questa tesi, sia in termini di rigidità che di danno cumulativo, hanno dimostrato che le prove di taglio dinamico possono essere utilizzate con successo per valutare le prestazioni delle interfacce bituminose e fornire un notevole aiuto per definire la vita utile delle pavimentazioni in modo più realistico rispetto alle prove di taglio statico.
The traffic loading on pavement structures includes both vertical and horizontal stresses (normal and tangent to the pavement surface). The latter become critical in regions that are prone to frequent braking, cornering or on steep grades. Since bituminous pavement is a multilayer structure, the existence of a poor interlayer bonding between bituminous layers could adversely affect the pavement performance and serviceability. Hence, a proper evaluation of the interlayer bonding has the utmost importance in pavement performance. The evaluation of interlayer bonding in bituminous pavements is typically carried out by measuring the interlayer shear strength (ISS) at failure using static laboratory tests. A significant improvement of the current testing approach is the development of dynamic testing devices, which could simulate the field conditions more realistically since the traffic loads applied to the pavement are dynamic. In this context, this PhD thesis describes the experimental activities carried out at Università Politecnica delle Marche, North Carolina State University and University of Limoges within the Task Group 3 “Pavement multilayer system” of the RILEM TC 272-PIM. The activities focused on the design and development of a new testing device for performing dynamic interlayer bond testing at Università Politecnica delle Marche along with carrying out dynamic bond testing using other existing devices. The interlayer behaviour has been investigated through both direct shear and torque tests on double-layered specimens extracted from laboratory compacted slabs prepared using a single bituminous mixture. The stimulating results presented in this thesis, reported both in terms of stiffness and cumulative damage, showed that dynamic bond testing can successfully be used to evaluate the bituminous interlayer performance and can provide a noticeable help for defining the service life of the pavement sections realistically compared to the static bond tests.

Studies of upright stance commonly model its biomechanics as an inverted pendulum, defining an overall postural stiffness, generated by the ankle joints, needed to overcome gravity's destabilizing effects. This model assumes symmetric left and right ankle stiffness, fixed throughout upright stance. However, the relative contributions of the intrinsic and reflex components of dynamic stiffness and how lower limbs interact during upright standing is not well understood. This thesis estimated the dynamic stiffness in both ankles simultaneously during upright standing and examined coordination between the two limbs. During bilateral perturbation trials, where angular position perturbations were applied to both ankles simultaneously, a strong intrinsic and reflex response was observed. For all subjects, intrinsic stiffness was lower than the required postural stiffness to maintain standing. Dynamic ankle stiffness also changed for different levels of postural sway torque, such that intrinsic and reflex stiffness was higher during forward lean and lower when leaning back. Contralateral responses were observed between input ankle position and the torques generated from the opposite ankle. These findings suggest that the overall postural control is not a simple summation of independent, fixed intrinsic stiffness responses from individual ankles. Intrinsic elastic stiffness is not sufficient for maintaining balance and contributing stiffness pathways are modulated throughout upright standing sway. Upright standing models must incorporate dynamic ankle stiffness measurements, variable stiffness parameters, and interactions between each supporting limbs.
Les études de la posture érigée sont couramment fondées sur le modèle biomécanique du pendule inversé définissant une raideur posturale générale produite par les articulations des chevilles et nécessaire pour compenser les effets déstabilisants de la gravité. Ce modèle est basé sur l'hypothèse d'une raideur symétrique des chevilles gauche et droite qui demeure fixe pendant la tenue de la posture érigée. Toutefois, les contributions relatives des composantes intrinsèques et réflexes de la raideur dynamique ainsi que l'interaction des membres inférieurs pendant la position érigée debout ne sont pas bien comprises. Ce mémoire fait état d'une estimation de la raideur dynamique des deux chevilles simultanément durant la position érigée debout, ainsi que d'une étude de la coordination entre les deux membres. Au cours de tests de perturbation bilatérale, pendant lesquels des perturbations de la position angulaire ont été appliquées aux deux chevilles simultanément, une nette réponse intrinsèque et réflexe a été observée. Chez tous les sujets, la raideur intrinsèque était inférieure à la raideur posturale nécessaire pour maintenir la station debout. La raideur dynamique des chevilles a également évolué en fonction de différents niveaux du couple du balancement postural, de telle sorte que la raideur intrinsèque et réflexe était plus élevée pendant l'inclinaison avant et moins élevée pendant l'inclinaison arrière. Des réponses controlatérales ont été observées entre la position de départ de la cheville et les couples générés depuis la cheville opposée. Ces résultats donnent à penser que le contrôle postural général ne consiste pas en la simple sommation de réponses indépendantes fixes de raideur intrinsèque des chevilles individuelles. La raideur élastique intrinsèque ne suffit pas pour maintenir l'équilibre, et les voies de raideur contributives sont modulées pendant le balancement de la position érigée debout. Les modèles de la position érigée debout doivent intégrer des mesures de la raideur dynamique des chevilles, des paramètres variables de la raideur et des interactions entre les membres d'appui.

Thesis (S.B.)--Massachusetts Institute of Technology, Dept. of Mechanical Engineering, 2005.
Includes bibliographical references (leaf 31).
This study examines the dynamic characteristics of the in-plane tunable stiffness scanning microscope probe for an atomic force microscope (AFM). The analysis was carried out using finite element analysis (FEA) methods for the micro scale device and its macro scale counterpart, which was designed specifically for this study. Experimental system identification testing using sound wave and high-speed camera recordings was clone on the macro scale version to identify trends that were then verified in the micro scale predictions. The results for the micro scale device followed the trends predicted by the macro scale experimental data. The natural frequencies of the device corresponded to the three normal directions of motion, in ascending order from the vertical direction, the out-of- plane direction, and the horizontal direction. The numerical values for these frequencies in the micro scale are 81.314 kHz, 51.438 kHz, and 54.899 kHz for the X, Y, and Z directions of vibration respectively. The error associated with these measurements is 6.6% and is attributed to the high tolerance necessary for measurements in the micro scale, which was not matched by the macro scale data acquisition methods that predict the natural frequency range.
(cont.) The vertical vibrations are therefore the limiting factor in the scanning speed of the probe across a sample surface, thus requiring the AFM to scan at an effective frequency of less than 81.3 kHz to avoid resonance.
by Myraida Angélica Vega González.
S.B.

This thesis is primarily concerned with the development and coding of a Levy-type spectral plate element to analyze the harmonic response of simply supported plates in the mid to high frequency range. The development includes the governing PDE, displacement field, shape function, and dynamic stiffness matrix. A two DOF spectral Love bar element and both a four DOF spectral Euler-Bernoulli and a four DOF spectral Timoshenko beam element are also developed to gain insight into the performance of spectral elements. A cantilever beam example is used to show how incorporating eigenfunctions for the dynamic governing PDE into the displacement field enables spectral beam elements to represent the structural dynamics exactly. A simply supported curved beam example is used to show that spectral beam elements can converge the effects of curved geometry with up to a 50% reduction in the number of elements when compared to conventional FE. The curved beam example is also used to show that the rotatory inertia and shear deformation, from Timoshenkoâ s beam theory, can result in up to a 28% shift in natural frequency over the first three bending modes. Finally, a simply supported Levy-plate model is used to show that the spectral Levy-type plate element converges the dynamic solution with up to three orders of magnitude fewer DOF then the conventional FE plate formulation. A simply-supported plate example problem is used to illustrate how the coefficients of the Fourier series expansion can be used as edge DOF for the spectral Levy-plate element. The Levy-plate element development gives insight to future research developing a general spectral plate element.
Master of Science

This thesis is primarily concerned with the development and coding of a Levy-type spectral plate element to analyze the harmonic response of simply supported plates in the mid to high frequency range. The development includes the governing PDE, displacement field, shape function, and dynamic stiffness matrix. A two DOF spectral Love bar element and both a four DOF spectral Euler-Bernoulli and a four DOF spectral Timoshenko beam element are also developed to gain insight into the performance of spectral elements. A cantilever beam example is used to show how incorporating eigenfunctions for the dynamic governing PDE into the displacement field enables spectral beam elements to represent the structural dynamics exactly. A simply supported curved beam example is used to show that spectral beam elements can converge the effects of curved geometry with up to a 50% reduction in the number of elements when compared to conventional FE. The curved beam example is also used to show that the rotatory inertia and shear deformation, from Timoshenkoâ s beam theory, can result in up to a 28% shift in natural frequency over the first three bending modes. Finally, a simply supported Levy-plate model is used to show that the spectral Levy-type plate element converges the dynamic solution with up to three orders of magnitude fewer DOF then the conventional FE plate formulation. A simply-supported plate example problem is used to illustrate how the coefficients of the Fourier series expansion can be used as edge DOF for the spectral Levy-plate element. The Levy-plate element development gives insight to future research developing a general spectral plate element.
Master of Science

The technological advancements of the last decades are making dynamic monitoring an efficient and widespread resource to investigate the safety and health of engineering structures. In the wake of these developments, the thesis proposes methodological tools supporting the seismic assessment of existing buildings through the use of ambient vibration tests. In this context, the literature highlights considerable room to broaden the ongoing research, especially regarding masonry buildings. The recent earthquakes, once again, highlighted the significant vulnerability of this structural typology as an important part of our built heritage, remarking the importance of risk mitigation strategies for the territorial scale. The thesis builds upon a simplified methodology recently proposed in the literature, conceived to assess the post-seismic serviceability of strategic buildings based on their operational modal parameters. The original contributions of the work pursue the theoretical and numerical validation of its basic simplifying assumptions, in structural modelling – such as the in-plane rigid behaving floor diaphragms – and seismic analysis – related to the nonlinear fundamental frequency variations induced by earthquakes. These strategies are commonly employed in the seismic assessment of existing buildings, but require further developments for masonry buildings. The novel proposal of the thesis takes advantage of ambient vibration data to establish direct and inverse mechanical problems in the frequency domain targeted at, first, qualitatively distinguishing between rigid and nonrigid behaving diaphragms and, second, quantitatively identifying their in-plane shear stiffness, mechanical feature playing a primary role in the seismic behaviour of masonry buildings. The application of these tools to real case studies points out their relevance in the updating and validation of structural models for seismic assessment purposes. In the light of these achievements, a model-based computational framework is proposed to develop frequency decay-damage control charts for masonry buildings, which exploit ambient vibration measurements for quick damage evaluations in post-earthquake scenarios. The results of the simulations, finally, highlight the generally conservative nature of ambient vibration-based simplified methodologies, confirming their suitability for the serviceability assessment of existing masonry buildings.

Uncertainties in load and system properties play a significant role in reliability analysis of vibrating structural systems. The subject of random vibrations has evolved over the last few decades to deal with uncertainties in external loads. A well developed body of literature now exists which documents the status of this subject. Studies on the influ­ence of system property uncertainties on reliability of vibrating structures is, however, of more recent origin. Currently, the problem of dynamic response characterization of sys­tems with parameter uncertainties has emerged as a subject of intensive research. The motivation for this research activity arises from the need for a more accurate assess­ment of the safety of important and high cost structures like nuclear plant installations, satellites and long span bridges. The importance of the problem also lies in understand­ing phenomena like mode localization in nearly periodic structures and deviant system behaviour at high frequencies. It is now well established that these phenomena are strongly influenced by spatial imperfections in the vibrating systems. Design codes, as of now, are unable to systematically address the influence of scatter and uncertainties. Therefore, there is a need to develop robust design algorithms based on the probabilistic description of the uncertainties, leading to safer, better and less over-killed designs. Analysis of structures with parameter uncertainties is wrought with diffi­culties, which primarily arise because the response variables are nonlinearly related to the stochastic system parameters; this being true even when structures are idealized to display linear material and deformation characteristics. The problem is further com­pounded when nonlinear structural behaviour is included in the analysis. The analysis of systems with parameter uncertainties involves modeling of random fields for the system parameters, discretization of these random fields, solutions of stochastic differential and algebraic eigenvalue problems, inversion of random matrices and differential operators, and the characterization of random matrix products. It should be noted that the mathematical nature of many of these problems is substantially different from those which are encountered in the traditional random vibration analysis. The basic problem lies in obtaining the solution of partial differential equations with random coefficients which fluctuate in space. This has necessitated the development of methods and tools to deal with these newer class of problems. An example of this development is the generalization of the finite element methods of structural analysis to encompass problems of stochastic material and geometric characteristics. The present thesis contributes to the development of methods and tools to deal with structural uncertainties in the analysis of vibrating structures. This study is a part of an ongoing research program in the Department, which is aimed at gaining insights into the behaviour of randomly parametered dynamical systems and to evolve computational methods to assess the reliability of large scale engineering structures. Recent studies conducted in the department in this direction, have resulted in the for­mulation of the stochastic dynamic stiffness matrix for straight Euler-Bernoulli beam elements and these results have been used to investigate the transient and the harmonic steady state response of simple built-up structures. In the present study, these earlier formulations are extended to derive the stochastic dynamic stiffness matrix for a more general beam element, namely, the curved Timoshenko beam element. Furthermore, the method has also been extended to study the mean and variance of the stationary response of built-up structures when excited by stationary stochastic forces. This thesis is organized into five chapters and four appendices. The first chapter mainly contains a review of the developments in stochas­tic finite element method (SFEM). Also presented is a brief overview of the dynamics of curved beams and the essence of the dynamic stiffness matrix method. This discussion also covers issues pertaining to modeling rotary inertia and shear deformations in the study of curved beam dynamics. In the context of SFEM, suitability of different methods for modeling system uncertainties, depending on the type of problem, is discussed. The relative merits of several schemes of discretizing random fields, namely, local averaging, series expansions using orthogonal functions, weighted integral approach and the use of system Green functions, are highlighted. Many of the discretization schemes reported in the literature have been developed in the context of static problems. The advantages of using the dynamic stiffness matrix approach in conjunction with discretization schemes based on frequency dependent shape functions, are discussed. The review identifies the dynamic analysis of structures built-up of randomly parametered curved beams, using dynamic stiffness matrix method, as a problem requiring further research. The review also highlights the need for studies on the treatment of non-Gaussian nature of system parameters within the framework of stochastic finite element analysis and simulation methods. The problem of deterministic analysis of curved beam elements is consid­ered first. Chapter 2 reports on the development of the dynamic stiffness matrix for a curved Timoshenko beam element. It is shown that when the beam is uniformly param-etered, the governing field equations can be solved in a closed form. These closed form solutions serve as the basis for the formulation of damping and frequency dependent shape functions which are subsequently employed in the thesis to develop the dynamic stiffness matrix of stochastically inhomogeneous, curved beams. On the other hand, when the beam properties vary spatially, the governing equations have spatially varying coefficients which discount the possibility of closed form solutions. A numerical scheme to deal with this problem is proposed. This consists of converting the governing set of boundary value problems into a larger class of equivalent initial value problems. This set of Initial value problems can be solved using numerical schemes to arrive at the element dynamic stiffness matrix. This algorithm forms the basis for Monte Carlo simulation studies on stochastic beams reported later in this thesis. Numerical results illustrating the formulations developed in this chapter are also presented. A satisfactory agreement of these results has been demonstrated with the corresponding results obtained from independent finite element code using normal mode expansions. The formulation of the dynamic stiffness matrix for a curved, randomly in-homogeneous, Timoshenko beam element is considered in Chapter 3. The displacement fields are discretized using the frequency dependent shape functions derived in the pre­vious chapter. These shape functions are defined with respect to a damped, uniformly parametered beam element and hence are deterministic in nature. Lagrange's equations are used to derive the 6x6 stochastic dynamic stiffness matrix of the beam element. In this formulation, the system property random fields are implicitly discretized as a set of damping and frequency dependent Weighted integrals. The results for a straight Timo- shenko beam are obtained as a special case. Numerical examples on structures made up of single curved/straight beam elements are presented. These examples also illustrate the characterization of the steady state response when excitations are modeled as stationary random processes. Issues related to ton-Gaussian features of the system in-homogeneities are also discussed. The analytical results are shown to agree satisfactorily with corresponding results from Monte Carlo simulations using 500 samples. The dynamics of structures built-up of straight and curved random Tim-oshenko beams is studied in Chapter 4. First, the global stochastic dynamic stiffness matrix is assembled. Subsequently, it is inverted for calculating the mean and variance, of the steady state stochastic response of the structure when subjected to stationary random excitations. Neumann's expansion method is adopted for the inversion of the stochastic dynamic stiffness matrix. Questions on the treatment of the beam characteris­tics as non-Gaussian random fields, are addressed. It is shown that the implementation of Neumann's expansion method and Monte-Carlo simulation method place distinc­tive demands on strategy of modeling system parameters. The Neumann's expansion method, on one hand, requires the knowledge of higher order spectra of beam properties so that the non-Gaussian features of beam parameters are reflected in the analysis. On the other hand, simulation based methods require the knowledge of the range of the stochastic variations and details of the probability density functions. The expediency of implementing Gaussian closure approximation in evaluating contributions from higher order terms in the Neumann expansion is discussed. Illustrative numerical examples comparing analytical and Monte-Carlo simulations are presented and the analytical so­lutions are found to agree favourably with the simulation results. This agreement lends credence to the various approximations involved in discretizing the random fields and inverting the global dynamic stiffness matrix. A few pointers as to how the methods developed in the thesis can be used in assessing the reliability of these structures are also given. A brief summary of contributions made in the thesis together with a few suggestions for further research are presented in Chapter 5. Appendix A describes the models of non-Gaussian random fields employed in the numerical examples considered in this thesis. Detailed expressions for the elements of the covariance matrix of the weighted integrals for the numerical example considered in Chapter 5, are presented in Appendix B; A copy of the paper, which has been ac­cepted for publication in the proceedings of IUTAM symposium on 'Nonlinearity and Stochasticity in Structural Mechanics' has been included as Appendix C.

Engineering design models for the torsion and axial dynamic stiffness of carbon black filled rubber bushings in the frequency domain including amplitude dependence are presented. They are founded on a developed material model which is the result of applying a separable elastic, viscoelastic and friction rubber component model to the material level. Moreover, the rubber model is applied to equivalent strains of the strain states inside the torsion or axial deformed bushing previously obtained by the classical linear theory of elasticity, thus yielding equivalent shear moduli which are inserted into analytical formulas for the stiffness. Therefore, unlike other simplified approaches, this procedure includes the Fletcher-Gent effect inside the bushing due to non-homogeneous strain states. The models are implemented in Matlab®. In addition, an experimental verification is carried out on a commercially available bushing thus confirming the accuracy of these models which become a fast engineering tool to design the most suitable rubber bushing to fulfil user requirements. Finally, they can be easily employed in multi-body and finite element simulations

In many engineering applications there is need to reduce the level of vibrations that are transmitted from a source to a receiver. Amongst several different techniques, the most commonly adopted solution is to interpose an isolation mount between the source and the receiver. Ideally, a vibration isolation mount would have a high static stiff- ness to prevent too large a static displacement to occur, but a low dynamic stiffness which reduces the natural frequency and extends the frequency range of isolation. For linear mounts these two features are mutually exclusive. However, an improved com- promise can be reached by employing nonlinear mounts. In this thesis the advantages and the limitations of nonlinear isolation mechanisms with a high-static-low-dynamic- stiffness(HSLDS) characteristic are investigated. A study of the static characteristics of two mechanisms with HSLDS is presented. This desired property is obtained by connecting in parallel elements with positive and negative stiffness. For both systems the positive stiffness is given by linear springs. In one model the geometry of the system is exploited to achieve the desired negative stiffness. This is obtained by a pair of linear springs placed at a certain angle to the horizontal (oblique springs). In the second model considered the required negative stiffness is provided by a set of magnets in attracting configuration. In both cases the force and stiffness are approximated to a symmetric cubic polynomial and a quadratic function of the displacement respectively. From a dynamical point of view this allows the system to be treated as a Duffing oscillator. It is argued that for small oscillations about the static equilibrium position the mechanism behaves linearly. A lab-scale rig which reproduces the HSLDS system with magnets and springs is designed and built. The excitation level is chosen to comply with the assumption of small displacement so that the experimental results show that the system responds in a rather linear fashion. The natural frequency of the HSLDS is half that of a linear model with the same static displacement and its transmissibility also compares favourably. A nonlinear analysis is also carried out in order to predict the response of the system when the assumption of linearity no longer holds true. Both cases of harmonic excita- tion of the payload and of the base are studied. For the two instances an approximate solution to the nonlinear equation of motion is found by applying the method of Har- monic Balance to a first order expansion. The main feature of the dynamic response of a Duffing oscillator is the jump phenomenon. Herein this is described and analyt- ical expressions for the jump frequencies are also provided. The isolation properties of an HSLDS isolation system are evaluated in terms of the transmissibility and its performance is compared with that of an equivalent linear system. It is shown that the HSLDS has a higher isolation capability.

Railway track stiffness (vertical track load divided by track deflection) is a basic parameter oftrack design which influences the bearing capacity, the dynamic behaviour of passing vehiclesand, in particular, track geometry quality and the life of track components. Track stiffness is abroad topic and in this thesis some aspects are treated comprehensively. In the introductionpart of the thesis, track stiffness and track stiffness measurements are put in their propercontext of track maintenance and condition assessment. The first aspect is measurement of track stiffness. During the course of this project, Banverkethas developed a new device for measurement of dynamic track stiffness called RSMV(Rolling Stiffness Measurement Vehicle). The RSMV is capable of exciting the trackdynamically through two oscillating masses above one wheelset. The dynamic stiffness is acomplex-valued quantity where magnitude is the direct relation between applied load anddeflection (kN/mm) and phase is a measure of deflection-delay by comparison with force. Thephase has partial relationship with damping properties and ground vibration. The RSMVrepeatability is convincing and both overall measurements at higher speeds (up to 50 km/h)and detailed investigations (below 10 km/h) can be performed. The measurement systemdevelopment is described in Paper A and B. The second aspect is evaluation of track stiffness measurements along the track from a trackengineering perspective. Actual values of stiffness as well as variations along the track areimportant, but cannot always answer maintenance and design related questions alone. InPaper D track stiffness is studied in combination with measurements of track geometryquality (longitudinal level) and ground penetrating radar (GPR). The different measurementsare complementary and a more reliable condition assessment is possible by the combinedanalysis. The relation between soft soils and dynamic track stiffness measurements is studiedin Paper C. Soft soils are easily found and quantified by stiffness measurements, in particularif the soft layer is in the upper part of the substructure. There are also possibilities to directlyrelate substructure properties to track stiffness measurements. Environmental vibrations areoften related to soft soils and partly covered in Paper C. One explanation of the excitationmechanism of train induced environmental vibrations is short waved irregular supportconditions. This is described in Paper E, where track stiffness was evinced to have normalvariations of 2 – 10 % between adjacent sleepers and variations up to 30 % were found. Anindicative way of finding irregular support conditions is by means of filtering longitudinallevel, which is also described in the paper. Train-track interaction simulation is used in PaperH to study track stiffness influence on track performance. Various parameters of trackperformance are considered, e.g. rail sectional moment, rail displacement, forces at wheel-railinterface and on sleepers, and vehicle accelerations. Determining optimal track stiffness froman engineering perspective is an important task as it impacts all listed parameters. The third aspect, efficient maintenance, is only partially covered. As track stiffness relates toother condition data when studied from a maintenance perspective, vertical geometricaldefects (longitudinal level and corrugation/roughness) are studied in paper F. The generalmagnitude dependency of wavelength is revealed and ways of handling this in conditionassessment are proposed. Also a methodology for automated analysis of a large set ofcondition data is proposed in Paper G. A case study where dynamic track stiffness,longitudinal level and ground penetrating radar are considered manifests the importance oftrack stiffness measurements, particularly for soil/embankment related issues.
QC 20100623

Cette thèse contribue à l'analyse des raideurs statique et dynamique des robots parallèles à câbles dans un objectif d'amélioration de la précision de positionnement statique et de la précision de suivi de trajectoire. Les modélisations statique et dynamique proposées des câbles considèrent l'effet du poids du câble sur son profil et l'effet de masse du câble sur la dynamique de ce dernier. Sur la base du modèle statique de câble proposé, l'erreur de pose statique au niveau de l'organe terminal du robot est définie et sa variation en fonction de la charge externe appliquée est utilisée pour évaluer la raideur statique globale de la structure. Un nouveau modèle dynamique vibratoire de robots à câbles est proposé en considérant le couplage de la dynamique des câbles avec les vibrations de l'organe terminal. Des validations expérimentales sont réalisées sur des prototypes de robots à câbles. Une série d'expériences de statique, d'analyses modales, d'analyses en régime libre et de suivi de trajectoire sont réalisées. Les modèles statiques et dynamiques proposés sont confirmés. Les dynamiques des câbles et du robot ainsi que leur couplage sont discutées montrant la pertinence des modèles développés pour l’amélioration des performances des robots à câbles en termes de design et le contrôle. Outre l'analyse des raideurs statique et dynamique, les modèles proposés sont appliqués dans l'amélioration du calcul de la distribution des efforts dans les câbles des robots redondants. Une nouvelle méthode de calcul de la distribution des efforts dans les câbles basée sur la détermination de la limite inférieure des forces dans les câbles est présentée. La prise en compte de la dépendance à la position dans l'espace de travail permet de limiter les efforts dans les câbles et ainsi d'améliorer l'efficience des robots d'un point de vue énergétique
This thesis contributes to the analysis of the static and dynamic stiffness of cable-driven parallel robots (CDPRs) aiming to improve the static positioning accuracy and the trajectory tracking accuracy. The proposed static and dynamic cable modeling considers the effect of cable weight on the cable profile and the effect of cable mass on the cable dynamics. Based on the static cable model, the static pose error of the end-effector is defined and the variation of the end-effector pose error with the external load is used to evaluate the static stiffness of CDPRs. A new dynamic model of CDPRs is proposed with considering the coupling of the cable dynamics and the end-effector vibrations. Experimental validations are carried out on CDPR prototypes. Static experiments, modal experiments, free vibration experiments and trajectory experiments are performed. The proposed static and dynamic models are verified. Cable dynamics, robot dynamics and their coupling are discussed. Results show the relevance of the proposed models on improving the performances of CDPRs in terms of design and control. Besides stiffness analysis, the proposed models are applied on the force distribution of redundant actuated CDPRs. A new method on the calculation of the cable forces is proposed, where the determination of the lower-boundary of the cable forces is presented. The consideration of the pose-dependence of the lower force boundary can minimize the cable forces and improve the energy efficiency of CDPRs

This thesis deals with computational modelling of rubber damper using Finite element method (FEM). This thesis includes experimental measurement of material properties of rubber subjected to static and dynamic loading and their implementation into viscoelastic and hyperelastic material models with respect to given task. Dependance of dynamic stiffness on loading frequency obtained from the simulation is validated with experimental measurement. In the end the difference between results is investigated and possible causes of that are introduced.

Measurements and predictions of railway-induced vibrations are becoming a necessity in today’s society where land scarcity causes buildings to be put close to railway traffic. The short distances mean an increased risk of the indoor vibration and noise disturbances experienced by residents. In short, the scope of the project is to investigate the transmission loss and vibration level decrease across various junction geometries. The junctions are modelled in both the Finite Element Method (FEM) and the Dynamic Stiffness Method (DSM). Resonances are avoided when possible by using semi-infinite building components. A two-dimensional model that included Timoshenko beams was set up by Wijkmark [1] and solved using the variational formulation of the DSM by Finnveden [2]. The model is efficient and user-friendly but there is no easy way to adjust the junction geometry since the depths of the walls and the floor slabs are the same. From that study, the current topic was formulated. The results presented in this paper indicate that both the Euler-Bernoulli DS model and the three-dimensional FE model have good potential in describing the vibration transmission across the different junction geometries. The two modelling types show more similar results in the analyses of the bending wave attenuation than in the analyses of the quasilongitudinal wave attenuation. One of the probable causes is that the set length of the Perfectly Matched Layers (PML) is not sufficient at such low frequencies. Larger PMLs require bigger geometries that lead to an increase of the computational time. The other proposed reason is the fact that bending waves are created above the asymmetrical junction when the lower beam is excited by a vertical harmonic force. The flexural displacements are neglected in those cases. The results however, were good enough to be satisfactory. Three junction models were investigated and the attenuation is the highest for both wave types in the case with a beam pair attached to the “middle” of an infinite plate. The attenuation is the second highest across the edge of a semi-infinite plate and the lowest across a junction corner of a semi-infinite plate. As part of the suggested future work, the wave transmission between beam and plate needs to be investigated when Timoshenko beams are included in the DS model. In the Euler-Bernoulli beam theory the cross-section remains perpendicular to the beam axis, which is different to the behaviour of solid elements in FEM.

Information about dynamic tire properties has always been important for drivers of wheel driven vehicles. With the increasing amount of systems in modern vehicles designed to measure and control the behavior of the vehicle information regarding dynamic tire properties has grown even more important.

In this thesis a number of methods for modeling and estimating dynamic tire properties have been implemented and evaluated. The more general issue of estimating model parameters in linear and non-linear vehicle models is also addressed.

We conclude that the slope of the tire slip curve seems to dependent on the stiffness of the road surface and introduce the term combined stiffness. We also show that it is possible to estimate both longitudinal and lateral combined stiffness using only standard vehicle sensors.

The theoretical study of this thesis deals with different approaches that can be used to optimize the topology of various structures. Main attributes and principles which they are based on of individual methods are discussed. The first point of the practical part is to design the model for computational analysis of stand and other machining centre parts based on real machine TOS FU. Afterwards, the model is analyzed to determine the dynamic characteristic of the machine. Subsequently, several changes of the stand design are performed in order to improve the dynamic behavior. Eventually, new stand kernel is designed which aims to enhance these dynamic characteristic. This model is analyzed again and the results are compared with the original form of the machining centre.

Stiffness identification of an impacted constraint is the main issue discussed in this thesis. Primarily, a change of stability (bifurcation) is used to determine the dynamical stiffness of an impacted beam for a piecewise-linear impact oscillator. Detailed one- and two-parameter bifurcation analyses of this impacting system are carried out by means of experiments and numerical methods. Particularly, the two-parameter numerical continuation of the obtained codimension-one bifurcation (period-doubling bifurcation, or fold bifurcation) indicates a strong monotonic correlation between the stiffness of the impacted beam and the frequency at which this bifurcation appears. In addition to the bifurcation techniques, another method for stiffness identification is analysis of impact duration. To accurately detect impact durations from numerical or experimental signals, nonlinear time series methods are utilised. Two impacting systems, including the piecewise-linear impact oscillator and a drillbit-rock vibro-impact system, are studied to demonstrate this proposed method. For either system, the impact duration is relatively constant when the response of oscillator is a period-one one-impact motion, and it is approximated as a half of the natural period of the oscillator-constraint system. When the mass of oscillator is constant, for an impacted constraint with a certain stiffness, the higher the stiffness, the lower the impact duration. This monotonic correlation provides another mechanism to estimate the stiffness of the impacted constraint. Based on the developed two dynamical methods for stiffness identification, a control algorithm for parameter adjustment of the axial vibration for rotary-percussive drilling applications is designed. This control algorithm aims to maintain the optimal drilling state under the varying formations. By this way, the efficiency of rotary-percussive drilling is expected to be promoted.

The analysis of stiffened plate structures subject to complex loads such as air-blast pressure waves from external or internal explosions, water waves, collisions or simply large static loads is still considered a difficult task. The associated response is highly nonlinear and although it can be solved with currently available commercial finite element programs, the modelling requires many elements with a huge amount of input data and very expensive computer runs. Hence this type of analysis is impractical at the preliminary design stage. The present work is aimed at improving this situation by introducing a new philosophy. That is, a new formulation is developed which is capable of representing the overall response of the complete structure with reasonable accuracy but with a sacrifice in local detailed accuracy. The resulting modelling is relatively simple thereby requiring much reduced data input and run times. It now becomes feasible to carry out design oriented response analyses. Based on the above philosophy, new plate and stiffener beam finite elements are developed for the nonlinear static and dynamic analysis of stiffened plate structures. The elements are specially designed to contain all the basic modes of deformation response which occur in stiffened plates and are called super finite elements since only one plate element per bay or one beam element per span is needed to achieve engineering design level accuracy at minimum cost. Rectangular plate elements are used so that orthogonally stiffened plates can be modelled. The von Karman large deflection theory is used to model the nonlinear geometric behaviour. Material nonlinearities are modelled by von Mises yield criterion and associated flow rule using a bi-linear stress-strain law. The finite element equations are derived using the virtual work principle and the matrix quantities are evaluated by Gauss quadrature. Temporal integration is carried out using the Newmark-β method with Newton-Raphson iteration for the nonlinear equations at each time step. A computer code has been written to implement the theory and this has been applied to the static, vibration and transient analysis of unstiffened plates, beams and plates stiffened in one or two orthogonal directions. Good approximations have been obtained for both linear and nonlinear problems with only one element representations for each plate bay or beam span with significant savings in computing time and costs. The displacement and stress responses obtained from the present analysis compare well with experimental, analytical or other numerical results.
Applied Science, Faculty of
Civil Engineering, Department of
Graduate

The final objective of the present work is the accurate prediction of the dynamic stiffness behaviour of complex rubber parts using finite element simulation tools. For this purpose, it becomes necessary to perform a complex rubber compound material characterisation and modelling work; this needs two important previous steps. These steps are detailed in the present document together with a theoretical review of viscoelastic visco-elasto-plastic models for elastomers. Firstly, a new characterisation method is proposed to determine the degree of cure of rubber parts. It is known that the degree of cure of rubbers bears heavily on their mechanical properties. This method consists of the correlation of swelling results to rheometer data achieving a good agreement. Secondly, the influence of the strain rate used in static characterisation tests is studied. In this step, a new characterisation method is proposed. The latter characterisation method will be used to fit extended hyperelastic models in Finite Element Analysis (FEA) software like ANSYS. The proposed method improves the correlation of experimental data to simulation results obtained by the use of standard methods. Finally, the overlay method proposed by Austrell concerning frequency dependence of the dynamic modulus and loss angle that is known to increase more with frequency for small amplitudes than for large amplitudes is developed. The original version of the overlay method yields no difference in frequency dependence with respect to different load amplitudes. However, if the element in the viscoelastic layer of the finite element model are given different stiffness and loss properties depending on the loading amplitude level, frequency dependence is shown to be more accurate compared to experiments. The commercial finite element program Ansys is used to model an industrial metal rubber part using two layers of elements. One layer is a hyper viscoelastic layer and the other layer uses an elasto-plastic model with a multi-linear kinematic hardening rule. The model, being intended for stationary cyclic loading, shows good agreement with measurements on the harmonically loaded industrial rubber part.

Cycloidal drives are compact, high-ratio gear transmission systems used in a wide range of mechanical applications from conveyor drives to articulated robots. This research hypothesises that these drives can be successfully applied in dynamic loading situations and thereby focuses on the understanding of differences between static and dynamic loading conditions where load varies with time. New methods of studying the behaviour of these drives under static and dynamic loading circumstances were developed, leading to novel understanding and knowledge. A new model was developed to facilitate research and development on Cycloidal drives with potential benefits for manufacturing, robotics and mechanical-process-industries worldwide.

In many environments vibration is transmitted to a person through a seat. Seats can be designed to reduce the discomfort and the injuries caused by vibration. The efficiency of a seat in reducing vibration depends on the characteristics of the vibration, the characteristics of the seat, and the characteristics of the person sitting on the seat (Griffin, 1990). This research was designed to investigate several aspects of the transmission of vertical and fore-and-aft vibration through polyurethane foams used in seat construction. The research programme was focused on two experiments. The first experiment was designed: (i) to investigate non-linearities in the seat and the human body in the vertical direction and their contributions to seat transmissibility; (ii) to compare the vertical apparent mass of the human body on rigid and soft seats; (iii) to measure and model the vertical dynamic stiffness of polyurethane foam seat cushions and investigate how the dynamic stiffness depends on vibration magnitude and subject characteristics (i.e. sitting weight, and hip breadth). The second experiment was designed: (i) to investigate the dependence of fore-and-aft seat cushion transmissibility on vibration magnitude, foam stiffness and contact with a backrest; (ii) to compare the fore-and-aft apparent masses of the human body on rigid and soft seats; (iii) to measure and model the dynamic stiffness of polyurethane foam seat cushions in the fore-and-aft direction, compare the fore-and-aft and vertical dynamic stiffness of foam, and investigate how fore-and-aft dynamic stiffness depends on subject sitting weight and hip breadth; (iv) to study the linear and non-linear effects of simultaneous vertical and fore-and-aft vibration and investigate whether single-axis transmissibility and single-axis models can be used to predict seat cushion transmissibility in multi-axis vibration environments. Fifteen subjects attended the two experiments. In the first experiment, the vertical force and vertical acceleration at the seat base and vertical acceleration at the seat-subject interface were measured during random vertical vibration excitation (0.25 to 25 Hz) at each of five vibration magnitudes (0.25 to 1.6 ms-2 r.m.s.), with four seating conditions (rigid flat seat and three foam cushions). The measurements are reported in terms of the subject apparent mass on the rigid and foam seat surfaces, and the transmissibility and dynamic stiffness of each of the foam cushions. A frequency domain model was used to identify the dynamic parameters of the foams and to investigate their dependence on subject sitting weight and hip breadth. In the second experiment, the vertical and fore-and-aft forces and accelerations at the seat base and the vertical and fore-and-aft accelerations at the seat-subject interface were measured during random vibration excitation (0.25 to 25 Hz) in fore-and-aft and vertical directions. Using three acceleration magnitudes in each direction (0, 0.25 and 1.0 ms-2 r.m.s.) eight different combinations of vertical and fore-and-aft excitation were investigated with three seating conditions (rigid flat seat and two foam cushions), with and without contact with a rigid vertical backrest. Both the human body and the foams showed nonlinear softening behaviour, which resulted in nonlinear cushion transmissibility in both the vertical and the fore-and-aft direction. The nonlinearities in vertical cushion transmissibility, expressed in terms of changes in resonance frequencies and moduli, were more dependent on human body nonlinearity than on cushion nonlinearity. The vertical apparent masses of subjects sitting on the rigid seat and on foam cushions were similar, but with an apparent increase in damping when sitting on the foams. Fore-and-aft apparent mass was strongly dependent on the use of the backrest. Fore-and-aft apparent masses on rigid and soft seats had similar shapes. The vertical and fore-and-aft dynamic stiffness of foam was found to be nonlinear with vibration magnitude and showed complex correlations with the characteristics of the human body. Foams were stiffer in the horizontal direction than in the vertical direction. Linear cross-coupling between vertical and fore-and-aft transmissibility was found: a small part of the vertical (or fore-and-aft) vibration at the seat base contributes to fore-and-aft (or vertical) vibration at the subject-seat interface. Nonlinear cross-coupling was found in seat transmissibility and foam dynamic stiffness: the softening of the seat-subject system in one axis is affected by the vibration in the perpendicular direction. The author believes that this research increased the current state of knowledge of the dynamics of the seated human body and polyurethane foams and so it represents a step forward in the understanding of the mechanisms involved in the vibration isolation provided by seats.

There is a need for spinal implants that have nonlinear stiffness to provide stabilization if the spine loses stiffness through injury, degeneration, or surgery. There is also a need for spinal implants to be customizable for individual needs, and to be small enough to be unobtrusive once implanted. Past and ongoing work that defines the effects of degeneration on the torque rotation curve of a functional spinal unit (FSU) were used to produce a spinal implant which could meet these requirements. This thesis proposes contact-aided inserts to be used with the FlexSuRe™ spinal implant to create a nonlinear stiffness. Moreover, different inserts can be used to create customized behaviors. An analytical model is introduced for insert design, and the model is verified using a finite element model and tests of physical prototypes both on a tensile tester and cadaveric testing on an in-house spine tester. Testing showed the inserts are capable of creating a non-linear force-deflection curve and it was observed that the device provided increased stiffness to a spinal segment in flexion-extension and lateral-bending. This thesis further proposes that the FlexSuRe™ spinal implant can be reduced in size by joining LET joint geometries in series in a serpentine nature. An optimization procedure was performed on the new geometry and feasible designs were identified. Moreover, due to maintaining LET joint geometry, the contact-aided insert could be implemented in conjunction with this new device geometry.

This dissertation discusses the thermomechanical analyses performed on threaded fasteners and curvilinearly stiffened composite panels with internal cutouts. The former problem was analyzed using a global/local approach using the commercial finite element software ANSYS while a fully functional code using isogeometric analysis was developed from scratch for the latter. For the threaded fasteners, a global simplified 3D model is built to evaluate the deformation of the structure. A second local model reproducing accurately the threads of the fasteners is used for the accurate assessment of the stresses in the vicinity of the fasteners. The isogeometric analysis code, capable of performing static, buckling and vibration analysis on stiffened composite plates with cutouts using single patch, multiple patches and level set methods is then discussed. A novel way to achieve displacement compatibility between the panel and stiffeners interfaces is introduced. An easy way of modeling plates with complicated cutouts by using edge curves and generating a ruled NURBS surface between them is described. Influence on the critical thermal buckling load and the fundamental mode of vibration due to the presence of circular, elliptical and complicated cutouts is also investigated. Results of parametric studies are presented which show the influence of ply orientation, size and orientation of the cutout, and the position and profile of the curvilinear stiffener. The numerical examples show high reliability and efficiency when compared with other published solutions and those obtained using ABAQUS, a commercial software.
PHD

In this thesis the effect of axle load spreading through ballast and the effect of support stiffness has been investigated on short span railway bridges. Two types of bridges, simply supported bridges and bridges with integrated backwalls, have been modeled with 2D beam elements. When analyzing the load spreading effect, two types of load shapes have been considered. The first one is the load shape proposed in Eurocode where the axle load is modeled with three point loads where 50% of the axle load acts on the sleeper located underneath the wheel and 25% on the two adjacent sleepers, respectively. Therefrom the loads are further distributed through the sleepers and the ballast. The second load shape that has been studied is a triangular load shape. These two load shapes have been modeled both with different numbers of point loads and as distributed line loads to see how the dynamic response of the bridges is affected and thereby find what level of accuracy that is required to capture the full effect of the load spreading. For the bridges with integrated backwalls the supports were also modeled as springs with varying stiffness to see how the dynamic response was affected. The response was measured in terms of vertical acceleration and bending moment. From the simulations the conclusion can be drawn that the triangular load shape gives significantly lower bridge responses than the Eurocode load shape. It is further found that modeling the axle loads with point loads can give spurious acceleration peaks, which in the case of bridges with integrated backwalls often are critical. For these bridges it is necessary to enhance the accuracy of the load spread, either by increasing the number of point loads or using a distributed line load. From the spring support simulations, it can be seen that support stiffness has great influence on the dynamic response of bridges with integrated backwalls. For certain values the response is increased, whereas for other values a large reduction is obtained.

The analysis of bearing systems involves the prediction of their static and dynamic characteristics. The capability to compute the dynamic characteristics for hydrodynamic bearings has been added to Bearing Design System (BRGDS), a finite element program developed by Dr. R.W. Stephenson, and the results obtained were validated. In this software, a standard finite element implementation of the Reynolds equation is used to model the land region of the bearing with pressure degrees of freedom. The assumptions of incompressible flow, constant viscosity, and no fluid inertia terms are made. The pressure solution is integrated to give the bearing load, and the stiffness and damping characteristics were calculated by a perturbation method. The static and dynamic characteristics of 60, 120 and 180 partial bearings were verified and compared for a length to diameter (L/D) ratio of 0.5. A comparison has also been obtained for the 120 bearing with L/D ratios of 0.5, 0.75 and 1.0. A 360-journal bearing was verified for an L/D ratio of 0.5 and also compared to an L/D ratio of 1.0. The results are in good agreement with other verified results. The effect of providing lubricant to the recesses has been shown for a 120 hybrid hydrostatic bearing with a single and double recess.

The primary purpose of this study was to develop a method to quantify the dynamic strain profile (DSP) of an ice hockey stick's shaft, and secondly, to use this method to assess the potential influence of player skill calibre and stick shaft properties on DSP during both the slap and wrist shots. Seventeen adult males performed a series of shots using two different stiffness ranked sticks in a laboratory setting on synthetic ice surface. These subjects were subdivided as high and low calibre players. Dependent measures included were: 1) five paired strain gauge responses along the shaft's length recorded at 10 KHz, and 2) kinematics of the puck, stick and trail arm grasping the stick recorded at 300 Hz using a Vicon MX ™ system. 2 x 2 MANOVAs were conducted for each of slap shot and wrist shot trials. The results demonstrated the feasibility of quantifying DSP such that an unambiguous rank order in maximum strain responses was obtained. Further, DSP were sensitive to both factors of player calibre and stick stiffness properties; that is, greater bend induced strains observed by high calibre player and lower stiffness sticks. Two kinematic differences relating to technique were observed: high calibre players showed less elbow flexion during the slap shot and greater wrist flexion during wrist shots. Lastly, with regards to time to maximum strain, high calibre players performed slap shots 3 to 4 times faster than the lower calibre players.
L'objectif principal de cette étude était de développer une méthode pour la quantification des différents profils de déformation dynamique de bâtons de hockey et de utiliser qu'est méthode pour examiner l'influence cinématiques du des joueurs de niveau élite et des joueurs de niveau récréatif pour les lancers frappes (SS) et des tirs du poignet (WS). Dix-sept sujets males ont donc effectué en laboratoire une série SS et de WS avec deux bâtons de hockey différent sur une surface de glace synthétique et étaient divisés en deux groupes, un pour le niveau élite et l'autre pour le niveau récréatif. Les mensures dépendantes étaient 1) la déformation du bâton a cinq étroits sur le manche du bâton à l'aide d'un système maison enregistrant à une fréquence de 10 KHz, et 2)la cinématique du bâton, de la rondelle et du membre supérieur le plus bas sur le bâton ont été enregistré à une fréquence de 300 Hz à l'aide d'un système Vicon MX ™. Deux MANOVA de forme 2x2 ont été effectuées, une pour les lancers frappés ainsi qu'une pour les lancers du poignet. Les résultats ont démontré la faisabilité de la quantification des différents profils de déformation dynamique de bâtons telle que l'ordre de classement sans ambigüité en réponse contrainte maximale a été obtenue. Des différences ont été trouvées pour la déformation aux différents capteurs à travers les niveaux d'habileté ainsi qu'à travers les bâtons. La déformation maximale était différente dépendamment du calibre et du bâton et ce pour les deux types de lancer. De plus, les joueurs de calibre récréatifs ont démontrés un délai significativement plus long entre la déformation maximal et le début du lancer pour les lancers frappés. Des différences cinématiques ont été trouvées au moins flexion du coude entre les calibres pour le niveau élite pour les lancers frappés et plus flexion pour le poignet pour les tirs du poignet pour le n