Dissertations / Theses on the topic 'Dynamic Stiffness Method (DSM)'

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.

The subject of acoustic fatigue first came to prominence with the advent of using jet engines on commercial aircraft in the 1950’s. Despite the period of time which has elapsed since then and the work carried out to help develop our understanding of the response of structures subject to high intensity noise, acoustic fatigue problems still occur. The novel contributions which this thesis makes to knowledge in the area have been in the application of the dynamic stiffness method which has been used to predict stress and strain response due to acoustic loading. The dynamic stiffness method can under certain circumstances provide very accurate results for natural frequency and displacement. Indeed for certain configurations it can provide exact solutions. It is largely independent of the number of degrees of freedom necessary to give an accurate result unlike the finite element method. The thesis documents how the dynamic stiffness method can offer a very favourable alternative to available analysis techniques. An alternative method of formulating the dynamic stiffness method is presented and is further extended to the analysis of orthotropic plates. The response of actual structures is discussed and previously unpublished data is also presented.

 The aim of this thesis was to evaluate the use of dynamic excitation as a method for stiffness and strength grading of wet side boards of narrow dimensions. The need for such an investigation has previously been identified in an ongoing research project in which the possibility to use side boards as lamellae in wet glued glulam beams is investigated.

     The assessment of the dynamic excitation method was carried out by means of experimental work and measurements.. The approach was quantitative in the sense that the data was collected through experiments performed on a rather large population and that the results were analyzed using statistical methods.

     To investigate the effect of moisture content on stiffness of narrow dimension, side boards, the stiffness was measured in three states:

• - in wet state, before splitting the boards,
• - in wet state, after splitting the boards, and
• - in dry state (splitted boards).

     The conclusion, after calculations and analysis of all the results, was that the natural frequency and stiffness of wet boards could, with a high degree of reliability, be predicted by use of the dynamic excitation method. There was a strong correlation in stiffness between wet state split boards and dry state split boards, with a coefficient of determination of 0.93.

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.

Thesis (M.S.)--University of Akron, Dept. of Physics, 2009.
"August, 2009." Title from electronic thesis title page (viewed 10/21/2009) Advisor, Jutta Luettmer-Strathmann; Committee members, Alper Buldum, Ben Yu-Kuang Hu; Department Chair, Robert R. Mallik; Dean of the College, Chand Midha; Dean of the Graduate School, George R. Newkome. Includes bibliographical references.

Micromagnetics is a continuum mechanics theory of magnetic materials widely used in industry and academia. In this thesis we describe a complete numerical method, with a number of novel components, for the computational solution of dynamic micromagnetic problems by solving the Landau-Lifshitz-Gilbert (LLG) equation. In particular we focus on the use of the implicit midpoint rule (IMR), a time integration scheme which conserves several important properties of the LLG equation. We use the finite element method for spatial discretisation, and use nodal quadrature schemes to retain the conservation properties of IMR despite the weak-form approach. We introduce a novel, generally-applicable adaptive time step selection algorithm for the IMR. The resulting scheme selects error-appropriate time steps for a variety of problems, including the semi-discretised LLG equation. We also show that it retains the conservation properties of the fixed step IMR for the LLG equation. We demonstrate how hybrid FEM/BEM magnetostatic calculations can be coupled to the LLG equation in a monolithic manner. This allows the coupled solver to maintain all properties of the standard time integration scheme, in particular stability properties and the energy conservation property of IMR. We also develop a preconditioned Krylov solver for the coupled system which can efficiently solve the monolithic system provided that an effective preconditioner for the LLG sub-problem is available. Finally we investigate the effect of the spatial discretisation on the comparative effectiveness of implicit and explicit time integration schemes (i.e. the stiffness). We find that explicit methods are more efficient for simple problems, but for the fine spatial discretisations required in a number of more complex cases implicit schemes become orders of magnitude more efficient.

Vibration-based energy harvesting using piezoelectric materials have been investigated by several research groups with the aim of harvesting maximum energy and providing power to low-powered wireless electronic systems for their entire operational life. The electromechanical coupling effect introduced by the piezoelectric vibration energy harvesting (PVEH) mechanism presents modelling challenges. For this reason, there has been a continuous effort to develop different modelling techniques to describe the PVEH mechanism and its effects on the dynamics of the system. The overall aims of this thesis are twofold: (1) a thorough theoretical and experimental analysis of a PVEH beam or assembly of beams; (2) an in-depth analytical and experimental investigation of the novel concept of a dual function piezoelectric vibration energy harvester beam/tuned vibration absorber (PVEH/TVA) or 'electromechanical TVA' and its potential application to vibration control. The salient novel contributions of this thesis can be summarised as follows: (i) An in-depth experimental validation of a PVEH beam model based on the analytical modal analysis method (AMAM), with the investigations conducted over a wider frequency range than previously tested. (ii) The precise identification of the electrical loads that harvest maximum power and that induce maximum electrical damping. (iii) A thorough investigation of the influence of mechanical damping on PVEH beams. (iv) A procedure for the exact modelling of PVEH beams, and assemblies of such beams, using the dynamic stiffness matrix (DSM) method. (v) A procedure to enhance the power output from a PVEH beam through the application of a tip rotational restraint and the use of segmented electrodes. (vi) The theoretical basis for the novel concept of a dual function PVEH beam/TVA, and its realisation and experimental validation for a prototype device. A thorough experimental validation of a cantilever piezoelectric bimorph energy harvester without a tip mass is presented under random excitation. The study provided a deep insight into the effect of PVEH on the dynamics of the system for variations in electrical load. An alternative modelling technique to AMAM, based on the DSM, is introduced for PVEH beams. Unlike AMAM, the DSM is exact, since it is based on the exact solution to the bending wave equation. It also readily lends itself to the modelling of beams with different boundary conditions or assemblies of beams of different crosssections. AMAM is shown to converge to DSM if a sufficiency of modes is used. Finally, an in-depth theoretical and experimental investigation of a prototype PVEHbeam/TVA device is presented. This device comprises a pair of bimorphs shunted by R-L-C circuitry and can be used as a tuned mass damper (TMD) to attenuate a vibration mode of a generic structure. The optimal damping required by this TMD is generated by the PVEH effect of the bimorphs. Such a device combines the advantages of conventional mechanical and electrical TVAs, overcoming their relative disadvantages. The results demonstrate that the ideal degree of attenuation can be achieved by the proposed device through appropriate tuning of the circuitry, thereby presenting the prospect of a novel class of 'electromechanical' tuned vibration absorbers.

Concrete is commonly used as a primary construction material for tall building construction. Load bearing components such as columns and walls in concrete buildings are subjected to instantaneous and long term axial shortening caused by the time dependent effects of "shrinkage", "creep" and "elastic" deformations. Reinforcing steel content, variable concrete modulus, volume to surface area ratio of the elements and environmental conditions govern axial shortening. The impact of differential axial shortening among columns and core shear walls escalate with increasing building height. Differential axial shortening of gravity loaded elements in geometrically complex and irregular buildings result in permanent distortion and deflection of the structural frame which have a significant impact on building envelopes, building services, secondary systems and the life time serviceability and performance of a building. Existing numerical methods commonly used in design to quantify axial shortening are mainly based on elastic analytical techniques and therefore unable to capture the complexity of non-linear time dependent effect. Ambient measurements of axial shortening using vibrating wire, external mechanical strain, and electronic strain gauges are methods that are available to verify pre-estimated values from the design stage. Installing these gauges permanently embedded in or on the surface of concrete components for continuous measurements during and after construction with adequate protection is uneconomical, inconvenient and unreliable. Therefore such methods are rarely if ever used in actual practice of building construction. This research project has developed a rigorous numerical procedure that encompasses linear and non-linear time dependent phenomena for prediction of axial shortening of reinforced concrete structural components at design stage. This procedure takes into consideration (i) construction sequence, (ii) time varying values of Young's Modulus of reinforced concrete and (iii) creep and shrinkage models that account for variability resulting from environmental effects. The capabilities of the procedure are illustrated through examples. In order to update previous predictions of axial shortening during the construction and service stages of the building, this research has also developed a vibration based procedure using ambient measurements. This procedure takes into consideration the changes in vibration characteristic of structure during and after construction. The application of this procedure is illustrated through numerical examples which also highlight the features. The vibration based procedure can also be used as a tool to assess structural health/performance of key structural components in the building during construction and service life.

Cette thèse traite du développement d’un élément continu de plaques orthotropes, sandwichs et multicouches. La démarche consiste dans un premier temps à établir la matrice de raideur dynamique de plaques orthotropes pour des conditions aux limites naturelles à partir d’une reformulation des éléments de plaques isotropes développés au laboratoire QUARTZ (EA7393). La démarche est basée d’une part sur la décomposition des conditions aux limites libres décrite par Gorman et d’autre part sur la résolution des équations de mouvement en se basant sur les développements en séries de Levy. La matrice de raideur dynamique est ensuite obtenue par projection des déplacements et des efforts de frontières sur des bases fonctionnelles compatibles avec les opérations d’assemblage. Dans un second temps, la formulation des éléments sandwichs et multicouches est décrite par superposition des plaques orthotropes précédemment développées.Les formulations présentées prennent en compte les vibrations de flexion et les vibrations dans le plan, dites vibrations de membrane. La validation de ces éléments est menée par une confrontation systématique de réponses harmoniques non amorties avec celles obtenues par diverses modélisations éléments finis
This thesis deals with the development of a continuous element for orthotropic, sandwich and multilayer plates. This approach is based essentially on the construction of the dynamic stiffness matrix of orthotropic plates using natural boundary conditions from a reformulation of the isotropic plate elements developed in the QUARTZ laboratory (EA 7393). In order to develop the dynamic stiffness matrix of the studied element we resort on the first hand to the decomposition of free boundary conditions described by Gorman, on the second hand to the resolution of the equations of motion by using Levy series expansions. The dynamic stiffness matrix is then obtained by projecting movements and frontier efforts on functional bases compatible with assembly operations. Finally the continuous sandwich and multilayer plate element is described by superposition of continuous orthotropic plates element previously developed.The formulations presented takes into account the bending vibration and the vibration in the plane, called membrane vibration. The validation of all obtained results is conducted by a systematic comparison of undamped harmonic responses with those obtained by various finite element models

Due to their large torque-speed ratio and transmission efficiency, planetary gears are widely used in the automotive industry. However, high amplitude vibrations remain their critical weakness, which limits their usage especially when new strict noise legislations come into action. A new approach to handle the instability problems of planetary gears encountered in real industrial context is presented in this work. First, the dynamic response of a planetary gear failing to pass the noise regulations is theoretically investigated through an analytical model. The equations of motion were solved using the Spectral Iterative Method. The observed experimental results correlated well with those from the developed model. In order to limit the resonance phenomena, impacts of different macro and micro-geometry modifications were analytically investigated: quadratic teeth profile, different planets positioning, different number of teeth and number of planets. Optimum modifications were retrieved and are expected to be tested experimentally on a test bench and on the truck. Finally, the analytical model’s limits and sensitivity to different parameters were investigated in order to certify its reliability, and suggestions for improvements were presented.

The diploma thesis deals with the assembly of numerical models of classical track using the finite element method in several variants. Models are compared with results obtained on analytical models. More complex models simulate the real behavior of a track running on a railway vehicle. The purpose is created methodology of modeling the railway track for use in static and dynamic analysis.

Cette thèse s'inscrit dans la continuité des travaux de l'équipe CRONE appliqués à la suspension. Cette thèse permet de proposer une suspension CRONE qui non seulement gère le compromis Isolation vibratoire/ tenue de caisse mais également isolation vibratoire/ tenue de roue. Pour cela un critère est développé sur la tenue de roue, applicable à tous types de suspensions permettant l’analyse et le dimensionnement de la suspension pour le contrôle de roue. De plus afin de lever le dilemme entre sollicitations route et sollicitation conducteur, une stratégie pour les suspensions bi -états est proposée et appliquée sur suspension hydractive. Enfin , un travail de formalisme de l’ influence la suspension sur la dynamique véhicule fut réalisé permettant d ’enrichir la stratégie de commutation déjà développée pour agir en virage et en freinage et ainsi optimiser l’utilisation de la suspension
This thesis follows some previous work of the CRONE team applied to carsuspensions. It allows to purpose one car suspension, called CRONE car suspension, whichimproves the compromise between low frequency road filtering and car holding and thecompromise between hight frequency road filtering and wheel holding. To hold the wheel acriterium on the wheel holding is developed. This criterium can be used to analyse and tunedall kind of car suspension around the wheel pulsation. Moreover, to fight against thecompromise between the driver input and the raod input, a control laws is developed andapplied to a bi-state car suspension called hydractive car suspension. Finally, the influence ofthe car suspension tuning on the vehicle dynamic and more precisely on the ESP, ABSsystems is studied and illustrated with some first experiments

The aim of this thesis is to calculate the stiffness and damping coefficients for radial hydrodynamic bearings. Cylindrical and lemon hydrodynamic bearings are considered. The solution to this problem mainly depends on the hydrodynamic pressure in the bearing. The numerical solution of the Reynolds equation is used to calculate the pressure. The effect of variable viscosity and density of the lubricant due to temperature changes is considered. The static equilibrium position of the journal centre is also solved. The stiffness and damping coefficients are determined using small amplitude journal motions about the equilibrium position. Three methods for determining these coefficients are presented. The outcome of this thesis is an algorithm for the calculation of stiffness and damping coefficients for cylindrical and lemon bearings. Results for lemon bearings are presented and comparison with the commercial software DynRot BR is made. The benefit of this thesis is the creation of an algorithm for the calculation of journal centre equilibrium position, a new way of incorporating the temperature changes in the viscosity and the density of the lubricant, and the modification of a method for calculating stiffness and damping coefficients based on experimental analogy.

碩士
國立交通大學
土木工程系所
94
To solve soil-structure interaction problem, finding the foundation impedance is an important part in using sub-structure technique. To find the impedance, finite element method is employed. The commercial program ABAQUS is used for the finite element method. Firstly, we set up an ideal finite element model and analyzed it to obtain numerical solutions. Then we compared the numerical solutions with the analytical solutions in order to examine the accuracy and convergency of the finite element method. Finally, extending the result of the convergency analysis to calculate the impedance of embedded square foundation by finite element method.

碩士
元智大學
機械工程研究所
88
In this research, critical speed analysis of asymmetric rotor systems was performed by using the dynamic stiffness method. The asymmetric rotors are different from the common symmetric rotors in that the properties at the cross sections of the rotors are not axisymmtric. The dynamic stiffness matrices of shaft elements are derived with Rayleigh beam modeling. The element matrices are assembled with the matrices of disks and bearings to form the system matrix, where the compatibility and equilibrium conditions have to be fulfilled at the joints of the elements. Synchronous critical speeds and subcritical speeds of the asymmetric rotor-bearing systems are analyzed under the effects of various conditions. Damping effects on the stability of the asymmetric rotors are also investigated.

This thesis presents a method for structural optimisation called bi-directional evolutionary structural optimisation (BESO). It is an extension of the systematic research on the evolutionary method. The basic concept of evolutionary structural optimisation (ESO) is that by slowly removing the inefficient material, the structure evolves towards an optimum. BESO extends the concept by allowing for the efficient material to be added while the inefficient material is removed. The formulation of BESO is motivated to improve the reliability and efficiency of the ESO method. The BESO method for topological optimisation of 2D continua subject to stiffness and displacement constraints is the major task of this thesis. The theoretical aspects are explored by following the optimality criteria algorithm for problems of discrete design variables. These aspects include the optimality criteria, sensitivity analysis, displacement extrapolation and evolutionary procedure. The bi-directional evolutionary procedure is incorporated with the finite element analysis to realise an automatic optimisation process. A wide range of examples are tested by using the proposed BESO procedure. Different design conditions are considered including stiffness optimisation and single or multiple displacement optimisation under single and multiple loading conditions. The solution reliability and parametric effect are further studied to improve the BESO performance. The comparison of results by BESO and ESO are attempted and the satisfactory agreement demonstrates the validity of the proposed procedure. Two major conclusions are derived from the work in this thesis. The first one is that BESO is as effective as ESO, and the second one is that BESO can be computationally more efficient in most cases.

碩士
國立臺灣大學
電機工程學研究所
102
Frozen shoulder is a functional disorder related to shoulder muscles. Among many treatment strategies, rehabilitation exercise is one of the most common and viable therapy. In this research, a new 8 degrees of freedom (DOFs) rehabilitation robot arm named NTUH-II has been developed for frozen shoulder rehabilitation in our laboratory. The robot arm is able to provide most of upper limb rehabilitation motions in passive, active, and assistive modes. There are many improvements for NTUH-II from the previous version NTUH-ARM, also developed in our laboratory such as larger shoulder flexion/extension range of motion, shoulder localization with laser tools, side-changing, and shoulder traction. This work combines knowledge from rehabilitation medicine to robotic engineering. From the nature of muscle stretching, the exponential torque-angle relationship curve can be found, and thus it is possible to model and evaluate the condition of the patient’s motion quality. The use of two parameters, stiffness and control authority, is proposed in this work. Based on these two parameters, an adjustment method of dynamic stiffness model and assistance torque gain is developed and implemented on NTUH-II. The control algorithm proposed in this research can customize the rehabilitation to meet the individual needs of frozen shoulder patients. Various experiments have been conducted on healthy subjects in National Taiwan University Hospital, and appealing performance has been observed, which validates the method proposed in this paper.

Two surface wave testing methods, namely, (i) the spectral analysis of surface waves (SASW), and (ii) the multi-channel analysis of surface waves (MASW), form non-destructive and non-intrusive techniques for predicting the shear wave velocity profile of different layers of ground and pavement. These field testing tools are based on the dispersive characteristics of Rayleigh waves, that is, different frequency components of the surface wave travel at different velocities in layered media. The SASW and MASW testing procedure basically comprises of three different components: (i) field measurements by employing geophones/accelerometers, (ii) generating dispersion plots, and (iii) predicting the shear wave velocity profile based on an inversion analysis. For generating the field dispersion plot, the complexities involved while doing the phase unwrapping calculations for the SASW technique, while performing the spectral calculations on the basis of two receivers’ data, makes it difficult to automate since it requires frequent manual judgment. In the present thesis, a new method, based on the sliding Fourier transform, has been introduced. The proposed method has been noted to be quite accurate, computationally economical and it generally overcomes the difficulties associated with the unwrapping of the phase difference between the two sensors’ data. In this approach, the unwrapping of the phase can be carried out without any manual intervention. As a result, an automation of the entire computational process to generate the dispersion plot becomes feasible. The method has been thoroughly validated by including a number of examples on the basis of surface wave field tests as well as synthetic test data. While obtaining the dispersion image by using the MASW method, three different transformation techniques, namely, (i) the Park’s wavefield transform, (ii) the frequency (f) -wavenumber ( ) transform and (iii) the time intercept ( -phase slowness (p) transform have been utilized for generating the multimodal dispersion plots. The performance of these three different methods has been assessed by using synthetic as well as field data records obtained from a ground site by means of 48 geophones. Two-dimensional as well as three-dimensional dispersion plots were generated. The Park’s wavefield transformation method has been found to be especially advantageous since it neither requires a very high sampling rate nor an inclusion of the zero padding of the data in a wavenumber (distance) domain. In the case of an irregular dispersive media, a proper analysis of the higher modes existing in the dispersion plots becomes essential for predicting the shear wave velocity profile of ground on the basis of surface wave tests. In such cases, the establishment of the predominant mode becomes quite significant. In the current investigation for Rayleigh wave propagation, the predominant mode has been computed by maximizing the normalized vertical displacements along the free surface. Eigenvectors computed from the thin layer approach (TLM) approach are analyzed to predict the corresponding predominant mode. It is noted that the establishment of the predominant mode becomes quite important where only two to six sensors are employed and the governing (predominant) modal dispersion curve is usually observed rather than several multiple modes which can otherwise be identified by using around 24 to 48 multiple sensors. By using the TLM, it is, however, not possible to account for the exact contribution of the elastic half space in the dynamic stiffness matrix (DSM) approach. A method is suggested to incorporate the exact contribution of the elastic half space in the TLM. The numerical formulation is finally framed as a quadratic eigenvalue problem which can be easily solved by using the subroutine polyeig in MATLAB. The dispersion plots were generated for several chosen different ground profiles. The numerical results were found to match quite well with the data available from literature. In order to address all the three different aspects of SASW and MASW techniques, a series of field tests were performed on five different ground sites. The ground vibrations were induced by means of (i) a 65 kg mass dropped freely from a height of 5 m, and (ii) by using a 20 pound sledge hammer. It was found that by using a 65 kg mass dropped from a height of 5 m, for stiffer sites, ground exploration becomes feasible even up to a depth of 50-80 m whereas for the softer sites the exploration depth is reduced to about 30 m. By using a 20 lb sledge hammer, the exploration depth is restricted to only 8-10 m due to its low impact energy. Overall, it is expected that the work reported in the thesis will furnish useful guidelines for (i) performing the SASW and MASW field tests, (ii) generating dispersion plots/images, and (iii) predicting the shear wave velocity profile of the site based on an inversion analysis.