In this Dissertation, we develop, and provide proof of principle for, parameter identification techniques for structural systems that can be described in terms of one or two nonlinear normal modes. We model the dynamics of these modes by second-order ordinary-differential equations based on the principles of mechanics, past experience, and engineering judgment. We perform a number of separate experiments on a two-mass structure using several different types of excitation. For the linear tests, the theoretical system response is known in closed-form. For the nonlinear test, we use the method of multiple scales to determine second-order uniform expansions of the model equations and hence determine the approximations to responses of the structure. Then, we estimate the linear and nonlinear parameters by regressive fits between the theoretically and experimentally obtained response relations. We report deviations and agreements between model and experiment. / Ph. D.

The vibration control of composite beams and plates subjected to a travelling load is studied in this dissertation. By comparing the controlled as well as uncontrolled responses of classical and refined structural models, the influence of several important composite structure properties which are not included in the classical structural model is revealed. The modal control approach is employed to suppress the structural vibration. In modal control, the control is effected by controlling the modes of the system. The control law is obtained by using the optimal control theory. Comparison of two variants of the modal control approach, the coupled modal control (CMC) and independent modal-space control (IMSC), is made. The results are found to be in agreement with those obtained by previous investigators. The differences between the controlled responses as well as actuator outputs that are predicted by the classical and the refined structural models are outlined in this work. In conclusion, it is found that, when performing the structural analysis and control system design for a composite structure, the classical structural models (such as the Euler-Bernoulli beam and Kirchhoff plate) yield erroneous conclusions concerning the performance of the actual structural system. Furthermore, transverse shear deformation, anisotropy, damping, and the parameters associated with the travelling load are shown to have great influence on the controlled as well as uncontrolled responses of the composite structure. / Ph. D.

This study compares energy minimization with direct stiffness for linear structural analysis. The energy minimization approach locates the generalized displacement vector by minimizing the total potential energy of the structure being analyzed. From the survey of variable metric and conjugate gradient algorithms included in this study, the Davidon-Fletcher-Powell variable metric algorithm and the FletcherReeves conjugate gradient algorithm were chosen to minimize the total potential energy. A description of both algorithms is presented. The direct stiffness method assembles the equilibrium equations of the structure being analyzed. These equations are solved by Gaussian elimination to determine the generalized displacement vector. Computer codes have been written for the energy minimization and direct stiffness methods. The comparison was based on computational effort, in terms of computer time, required for analysis. The results of this study show energy minimization is not competitive with direct stiffness for linear structural analysis. As the problem size increases by degree of freedom the direct stiffness method rapidly increases in superiority over the energy minimization method. / Master of Science

The precise and detailed characterization of the dynamic response of structures has become increasingly important in recent years. As a consequence, the accuracy of experimental data, which is often used to validate and update finite element models, has become extremely important. However, as researchers have attempted to identify and quantify sources of error in the experimental modal analysis (EMA) process, an important potential error source has been largely overlooked. Instabilities in the dynamic response of structures due to small variations in test environmental conditions may result in significant errors in experimental and analytical results, leading to erroneous and/or misleading conclusions. This thesis presents an experimental and analytical investigation of the effects of ambient temperature variations on the dynamic characteristics of a thin, square steel plate. The modal properties of the plate with two different boundary conditions and at temperatures above and below standard room temperature are examined. In addition, an analytical model is developed accounting for the effects of temperature-dependent material properties. Results indicate that natural frequencies and damping are significantly affected by changes in temperature. In the case of the natural frequency variations, the temperature-dependence of Young's modulus is the dominant factor, but boundary condition effects may also be important. Also, FRF magnitudes at spectral lines close to the resonances are very sensitive to temperature. Finally, only minor variations in the plate response shapes are observed, although significant changes in the imaginary component of the velocity field are evident. / Master of Science

In order to perform structural optimization and/or modification on a structure, an analytical model which sufficiently describes the behavior of the structure must be developed. Analytical models can be generated for almost any structure, but such a model will generally not effectively predict the behavior of the structure unless the model is somehow reconciled with experimental data taken from the structure. Additionally, the model must also be complete, i.e., it must not only model the structure but also model any suspension system used to support the structure. If the suspension is not included in the model, any attempt to reconcile the model with experimental data will result in a incorrect model. Using this incorrect model to perform structural modification cannot be expected to give correct results. In this thesis, an approach for estimating the effects of a suspension system on the flexural vibration of a structure is developed. These effects are treated mathematically as variations in boundary conditions. Topics discussed include formulation of an analytical model that includes suspension effects, experimental methods for acquiring mode shapes which exhibit these effects, and reconciliation techniques for matching analytical mode shapes to experimental mode shapes to determine the effective boundary conditions. / Master of Science

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

The present work describes the finite element (FE) modeling and dynamic response of lightweight, deployable shelters (tent) to large external blast loads. Flexible shelters have been used as temporary storage places for housing equipments, vehicles etc. TEMPER Tents, Small Shelter System have been widely used by Air Force and Army, for various field applications. These shelters have pressurized Collective Protection System (CPS), liner, fitted to the frame structure, which can provide protection against explosives and other harmful agents. Presently, these shelter systems are being tested for the force protection standards against the explosions like air-blast. In the field tests carried out by Air Force Research Laboratory, it was revealed that the liner fitted inside the tent was damaged due to the air blast explosion at some distant from the structure, with major damage being on the back side of the tent. The damage comprised of tearing of liner and separation of zip seals. To investigate the failure, a computational approach, due to its simplicity and ability to solve the complex problems, is used. The response of any structural form to dynamic loading condition is very difficult to predict due to its dependence on multiple factors like the duration of the loading, peak load, shape of the pulse, the impulse energy, boundary conditions and material properties etc. And dynamic analysis of shell structures pose even much greater challenge. Obtaining solution analytically presents a very difficult preposition when nonlinearity is considered. Therefore, the numerical approach is sought which provide simplicity and comparable accuracy. A 3D finite element model has been developed, consisting of fabric skin supported over the frames based on two approaches. ANSYS has been used for obtaining the dynamic response of shelter against the blast loads. In the first approach, the shell is considered as a membrane away from its boundaries, in which the stress couple is neglected in its interior region. In the second approach, stress coupling is neglected over the whole region. Three models were developed using Shell 63, Shell 181 and Shell 41. Shell 63 element supports both the membrane only and membrane-bending combined options and include stress stiffening and large deflection capabilities. Shell 181 include all these options as Shell 63 does and also, accounts for the follower loads. Shell 41 is a membrane element and does not include any bending stiffness. This element also include stress stiffening and large deflection capabilities. A nonlinear static analysis is performed for a simple plate model using the elements, Shell 41 and Shell 63. The membrane dominated behavior is observed for the shell model as the pressure load is increased. It is also observed that the higher value of Young's modulus (E) increases the stresses significantly. Transient analysis is a method of determining the structural response due to time dependent loading conditions. The full method has been used for performing the nonlinear transient analysis. Its more expensive in terms of computation involved but it takes into account all types of nonlinearities such as plasticity, large deflection and large strain etc. Implicit approach has been used where Newmark method along with the Newton-Raphson method has been used for the nonlinear analysis. Dynamic response comprising of displacement-time history and dynamic stresses has been obtained. From the displacement response, it is observed that the first movement of the back wall is out of the tent in contrast to the other sides whose first movement is into the tent. Dynamic stresses showed fluctuations in the region when the blast is acting on the structure and in the initial free vibration zone. A parametric study is performed to provide insight into the design criteria. It is observed that the mass could be an effective means of reducing the peak responses. As the value of the Young's Modulus (E) is increased, the peak displacements are reduced resulting from the increase in stiffness. The increased stiffness lead to reduced transmitted peak pressure and reduced value of maximum strain. But a disproportionate increase lead to higher stresses which could result in failure. Therefore, a high modulus value should be avoided. / Master of Science

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

A weakly nonlinear system under simultaneous sinusoidal external and parametric excitations is investigated. Quadratic and cubic nonlinearities are present in the governing equations. A general perturbation analysis, the Method of Multiple Scales (MMS), is performed for numerous resonance frequencies. Emphasis is initially placed on the response of the system under parametric excitation alone. The nonresonant external and parametric excitations are then considered. Finally, responses involving both parametric and external excitations are considered. The excitation frequencies are assumed to be from the same source. . When the frequency of the_parametric and external excitations are different (λ≠Ω), many of the different resonances investigated have solvability conditions similar to those found in two preliminary works performed by Mook, Plaut and HaQuang. When the frequencies are nearly equal, numerous steady-state response curves are shown. Unlike the linear analysis, the frequency-response curves show many multi-valued responses. In some instances, as many as five amplitudes exist for a given frequency. Three are stable and two are unstable. In addition, multi-modal responses were found to exist under a single-mode excitation. This result is unique since no internal resonance was considered. For certain values of the coefficient of the nonlinear restoring forces, stable bimodal steady states were observed. In order to verify some of the theoretical results obtained by MMS, a sixth-order Runge Kutta procedure was performed on the original governing equation. The numerically integrated results and the approximate solution of MMS show excellent agreement when the parameter ε is sufficiently small. However, when ε is sufficiently large, the MMS approximate solution breaks down. Interesting phenomena, such as periodic doubling and chaos, are observed. / Ph. D. / incomplete_metadata

This study concerns the active damping of structural vibrations through the application of various forms of velocity feedback control. Active damping will be required for large space structures which are performance-sensitive to motion or inaccurate pointing. Several control forms, including modal-space active damping and direct rate feedback, are analyzed theoretically, and three laboratory models are described. A previous, unsuccessful attempt at control is reviewed and explained. The remaining control forms developed in the theoretical section were implemented successfully and the results compare favorably with theoretical predictions. Each control form is analyzed relative to its own merits and in comparison with other methods. An important point is the stability assured by a dual (colocated) configuration. of velocity sensors and control force actuators. Modal-space active damping is shown to be an effective control method with predictable performance in controlled modes and beneficial spillover into residual (non-controlled) modes. / Ph. D. / incomplete_metadata