This thesis develops a finite element based dynamic modeling method for design and analysis of compliant mechanisms which transfer input force, displacement and energy through elastic deformations. Most published analyses have largely based on quasi-static and lump-parameter models neglecting the effects of damping, torsion, complex geometry, and nonlinearity of deformable contacts. For applications such as handling of objects by the robotic hands with multiple high-damped compliant fingers, there is a need for a dynamic model capable of analyzing the flexible multibody system. This research begins with the formulation of the explicit dynamic finite element method (FEM) which takes into account the effects of damping, complex geometry and contact nonlinearity. The numerical stability is considered by evaluating the critical time step in terms of material properties and mesh quality. A general framework incorporating explicit dynamic FEM, topology optimization, modal analysis, and damping identification has been developed. Unlike previous studies commonly focusing on geometry optimization, this research considers both geometric and operating parameters for evaluation where the dynamic performance and trajectory of the multibody motion are particularly interested. The dynamic response and contact behavior of the rotating fingers acting on the fixed and moving objects are validated by comparing against published experimental results. The effectiveness of the dynamic modeling method, which relaxes the quasi-static assumption, has been demonstrated in the analyses of developing an automated transfer system involved grasping and handling objects by the compliant robotic hands. This FEM based dynamic model offers a more realistic simulation and a better understanding of the multibody motion for improving future design. It is expected that the method presented here can be applied to a spectrum of engineering applications where flexible multibody dynamics plays a significant role.

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Thesis (M. Tech.) - Central University of Technology, Free State, 2011 / The objectives of this research were to investigate and establish a procedure to determine the self-damping characteristics of transmission line conductors subjected to free and forced vibrations. The TERN and Aero-Z IEC62219-REV240609 conductor cables were the transmission line conductors that were readily available at the Vibration Research and Testing Centre (VTRC) of the University of KwaZulu-Natal (UKZN). The question to be answered was whether the self-damping characteristics of the TERN and Aero-Z IEC62219-REV240609 conductors were adequate to suppress Aeolian or wake-induced vibrations. In other words, is it necessary for external damping mechanisms to be used with these conductors? This study confirmed that the self-damping characteristics of conductors are not adequate to suppress Aeolian or wake-induced vibrations. Governing partial differential equations describing the characteristics of the catenary and parabolic cable conductors were developed to validate the experimental results. The experimental tests involved both conductors being subjected to an impulse function (a free vibration method) and also to a harmonic function (a forced vibration method). Measurements were carried out using accelerometers, and the recording equipment consisted of oscilloscopes and the PUMA system. With both the free and forced vibration methods, the damping factor of the TERN conductor was confirmed to be ζ ≤ 0.05, whereas the damping factor of the Aero-Z IEC62219-REV240609 was confirmed to be ζ ≤ 0.2. A procedure for determining the self-damping characteristics of the TERN and Aero-Z IEC62219-REV240609 conductors was developed, with the damping factor found to be ζ ≤ 0.2 for both conductors. These methods can assist in the implementation of procedural analysis of the self-damping behaviour of different types of transmission conductors and in finding the most suitable mass absorber (damper) to use in reducing the rate of failure of transmission line conductors. The results of this study can be used to improve the mathematical modelling of Aeolian and wind-induced vibrations where both self-damping properties and a mass absorber are incorporated.

Lead-lag dampers are present in most rotors to provide the required level of damping in all flight conditions. These dampers are a critical component of the rotor system, but they also represent a major source of maintenance cost. In present rotor systems, both hydraulic and elastomeric lead-lag dampers have been used. Hydraulic dampers are complex mechanical components that require hydraulic fluids and have high associated maintenance costs. Elastomeric dampers are conceptually simpler and provide a ``dry" rotor, but are rather costly. Furthermore, their damping characteristics can degrade with time without showing external signs of failure. Hence, the dampers must be replaced on a regular basis. A semi-active friction based lead-lag damper is proposed as a replacement for hydraulic and elastomeric dampers. Damping is provided by optimized energy dissipation due to frictional forces in semi-active joints. An actuator in the joint modulates the normal force that controls energy dissipation at the frictional interfaces, resulting in large hysteretic loops. Various selective damping strategies are developed and tested for a simple system containing two different frequency modes in its response, one of which needs to be damped out. The system reflects the situation encountered in rotor response where 1P excitation is present along with the potentially unstable regressive lag motion. Simulation of the system response is obtained to compare their effectiveness. Next, a control law governing the actuation in the lag damper is designed to generate the desired level of damping for performing adaptive selective damping of individual blade lag motion. Further, conceptual design of a piezoelectric friction based lag damper for a full-scale rotor is presented and various factors affecting size, design and maintenance cost, damping capacity, and power requirements of the damper are discussed. The selective semi-active damping strategy is then studied in the context of classical ground resonance problem. In view of the inherent nonlinearity in the system due to friction phenomena, multiblade transformation from rotating frame to nonrotating frame is not useful. Stability analysis of the system is performed in the rotating frame to gain an understanding of the dynamic characteristics of rotor system with attached semi-active friction based lag dampers. This investigation is extended to the ground resonance stability analysis of a comprehensive UH-60 model within the framework of finite element based multibody dynamics formulations. Simulations are conducted to study the performance of several integrated lag dampers ranging from passive to semi-active ones with varying levels of selectivity. Stability analysis is performed for a nominal range of rotor speeds using Prony's method.

Lead-lag dampers are present in most rotor systems to provide the desired level of damping for all flight conditions. These dampers are critical components of the rotor system, and the performance of semi-active Coulomb-friction-based lead-lag dampers is examined for the UH-60 aircraft. The concept of adaptive damping, or “damping on demand,” is discussed for both ground resonance and forward flight. The concept of selective damping is also assessed, and shown to face many challenges. In rotorcraft flight dynamics, optimized warping twist change is a potentially enabling technology to improve overall rotorcraft performance. Research efforts in recent years have led to the application of active materials for rotorcraft blade actuation. An innovative concept is proposed wherein the typically closed section blade is cut open to create a torsionally compliant structure that acts as its own amplification device; deformation of the blade is dynamically controlled by out-of-plane warping. Full-blade warping is shown to have the potential for great design flexibility. Recent advances in rotorcraft blade design have also focused on variable-camber airfoils, particularly concepts involving “truss-core” configurations. One promising concept is the use of hexagonal chiral lattice structures in continuously deformable helicopter blades. The static behavior of passive and active chiral networks using piezoelectric actuation strategies is investigated, including under typical aerodynamic load levels. The analysis is then extended to the dynamic response of active chiral networks in unsteady aerodynamic environments.

M. Tech. : Mathematical Technology. / Attempts will be made to extend the elementary quarter-mass models (for instance Gillepse, 1992, [5]; Kiecke & Nielsen, 2000, [6] and Singiresu, 2004, [7]) of a motor vehicle suspension system to include the radial vibrations of a rubber tyre in the model. Tangential vibrations of the tyre surface were investigated by Bekker (2009, [8]) and the possible incorporation of such vibrations into a suspension model invites the possibility of future study.

New materials and new fabrication techniques in turbomachinery lead to monolithic<p>structures with extremely low damping which may be responsible for severe vibrations<p>and possible high-cycle fatigue problems. To solve this, various techniques<p>of damping enhancement are under investigation. The present work is focused on<p>piezoelectric shunt damping.<p>This thesis considers the RL shunt damping of rotationally periodic structures using<p>an array of piezoelectric patches, with an application to a bladed drum representative<p>of those used in turbomachinery. Due to the periodicity and the cyclic symmetry of<p>the structure, the blade modes occur by families with very close resonance frequencies,<p>and harmonic shape in the circumferential direction; the proposed RL shunt<p>approaches take advantage of these two features.<p>When a family of modes is targeted for damping, the piezoelectric patches are<p>shunted independently on identical RL circuits, and tuned roughly on the average<p>value of the resonance frequencies of the targeted modes. This independent<p>configuration offers a damping solution effective on the whole family of modes, but<p>it requires the use of synthetic inductors, which is a serious drawback for rotating<p>machines.<p>When a specific mode with n nodal diameters has been identified as critical and<p>is targeted for damping, one can take advantage of its harmonic shape to organize<p>the piezoelectric patches in two parallel loops. This parallel approach reduces considerably<p>the demand on the inductors of the tuned inductive shunt, as compared<p>to independent loops, and offers a practical solution for a fully passive integration<p>of the inductive shunt in a rotating structure.<p>Various methods are investigated numerically and experimentally on a cantilever<p>beam, a bladed rail, a circular plate, and a bladed drum. The influence of blade<p>mistuning is also investigated. / Doctorat en Sciences de l'ingénieur / info:eu-repo/semantics/nonPublished

The aim of the thesis is to propose active damping as a potential control strategy for chatter instability in machine tools.<p>The regenerative process theory explains chatter as a closed loop interaction between the structural dynamics and the cutting process. This is considered to be the most dominant reason behind machine tool chatter although other instability causing mechanisms exist.<p>The stability lobe diagram provides a quantitative idea of the limits of stable machining in terms of two physical parameters: the width of contact between tool and the workpiece, called the width of cut and the speed of rotation of the spindle. It is found that the minimum value of the stability limit is proportional to the structural damping ratio for turning operations. This important finding provides the motivation of influencing the structural dynamics by active damping to enhance stability limits of a machining operation.<p>A direct implementation of active damping in an industrial environment may be difficult. So an intermediate step of testing the strategy in a laboratory setup, without conducting real cutting is proposed. Two mechatronic "Hardware in the Loop" simulators for chatter in turning and milling are presented, which simulate regenerative chatter experimentally without conducting real cutting tests. A simple cantilever beam, representing the MDOF dynamics of<p>the machine tool structure constitutes the basic hardware part and the cutting process is simulated in real time on a DSP board. The values of the cutting parameters such as spindle speed and the axial width of cut can be changed on the DSP board and the closed loop interaction between the structure and the cutting process can be led to instability.<p><p>The demonstrators are then used as test beds to investigate the efficiency of active damping, as a potential chatter stabilization strategy. Active damping is easy to implement, robust and does not require a very detailed model of the structure for proper functioning, provided a collocated sensor and actuator configuration is followed. The idea of active damping is currently being implemented in the industry in various metal cutting machines as part of the European Union funded SMARTOOL project (www.smartool.org), intended to propose smart chatter control technologies in machining operations. / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

The scope of this research concerns the passive damping of structural vibrations by the use of viscoelastic layers. It is motivated by the need for efficient numerical tools to deal with the medium frequency behaviour of industrial viscoelastic sandwich products. The sandwich modelling technique is based on the use of an interface element: the two deformable plates are modelled by special plate elements while the intermediate dissipative layer is modelled with interface elements. This interface element is based on the first-order shear deformation theory and assume constant peel and shear stresses in the polymer thickness. This element couples the lower and upper layers without additional degrees of freedom. The partition of unity finite element method (PUFEM) is applied to the development of enriched Mindlin plate elements. The element shape functions are obtained as the product of<p>partition of unity functions with arbitrary chosen enrichment functions. Polynomial enrichment leads to the generation of high-order polynomial shape functions and is therefore similar to a p-FEM technique. Numerical examples illustrate the use of both PUFEM Mindlin plate elements and interface elements for the simulation of viscoelastic sandwich structures. / Doctorat en sciences appliquées / info:eu-repo/semantics/nonPublished

Rubber like materials find wide applications in damping treatment of structures, vibration isolations and they appear prominently in the form of hoses in many structures such as aircraft engines. The study reported in this thesis addresses a few issues in computational modeling of vibration of structures with some of its components made up of rubber like materials. Specifically, the study explores the use of fractional derivatives in representing the constitutive laws of such material and focuses its attention on problems of parameter identification in linear time invariant systems with fractional order damping models. The thesis is divided into four chapters and two annexures. A review of literature related to mathematical modeling of damping with emphasis on fractional order derivative models is presented in chapter 1. The review covers lternatives available for modeling energy dissipation that include viscous, structural and hybrid damping models. The advantages of using fractional order derivative models in this context is pointed out and papers dealing with solution of differential equations with fractional order derivatives are reviewed. Issues related to finite element modeling and random vibration analysis of systems with fractional order damping models are also covered. The review recognizes the problems of system parameter identification based on inverse eigensensitivity and inverse FRF sensitivity as problems requiring further research. The problem of determination of derivatives of eigensolutions and FRF-s with respect to system parameters of linear time invariant systems with fractional order damping models is considered in chapter 2. The eigensolutions here are obtained as solutions of a generalized asymmetric eigenvalue problem. The order of system matrices here depends upon the mechanical degrees of freedom and also somewhat artificially on the fractional order of the derivative terms. The formulary for first and second order eigenderivatives are developed taking account of these features. This derivation also takes into account the various orthogonality relations satisfied by the complex valued eigenvectors. The system FRF-s are obtained by a straight forward inversion of the system dynamic stiffness matrix and also by using a series solution in terms of system eigensolutions. As might be expected, the two solutions lead to identical results. The first and the second order derivatives of FRF-s are obtained based on system dynamic matrix and without taking recourse to modal summation. Numerical examples that bring out various facets of eigensolutions, FRF-s and their sensitivities are presented with reference to single and multi degree freedom systems. The application sensitivity analysis developed in chapter 2 to problems of system parameter identification is considered in chapter 3. Methods based on inverse eigensensitivity and inverse FRF sensitivity are outlined. The scope of these methods cover first and second order analyses and applications to single and multi degree freedom systems. While most illustrations are based on synthetic measurement data, limited efforts are also made to implement the identification methods using laboratory measurement data. The experimental work has involved the measurement of FRF-s on a system consisting of two steel tubes connected by a rubber hose. The two system identification methods are shown to perform well especially when information on second order sensitivity are included in the analysis. The method based on inverse eigensolution is shown to become increasingly unwieldy to apply as the order of the system matrices increases while the FRF based method does not suffer from this drawback. The FRF based method also has the advantage that the prior knowledge of order of fractional order derivative terms is not needed in its implementation while such knowledge is assumed in the method based on eigensolutions. While the methods are shown to perform satisfactorily when synthetic measurement data is used, their success is not uniformly good when laboratory measurement data are employed. Chapter 4 presents a summary of contributions made in the thesis and also enlists a few suggestions for further research. Annexure I provides a précis of elementary notion of fractional order derivatives and integrals. A case study on finite element analysis of aircraft engine component made up of metallic and rubber materials is outlined in Annexure II and the study points towards possible advantages of using fractional order damping models in the study of such structures.