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

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

Comparisons were made on the behavior of two full-sized reticulated domes subjected to uniform static loads only and uniform static loads with earthquake excitations. Space truss elements were used in the dome models. The stiffness matrix of the space truss element allows for the nonlinear strain-displacement behavior and the stress-strain behavior of the material is modeled with a bilinear approximation. The nonlinear solution technique is the Newton-Raphson method while the direct integration technique is the Newmark- Beta method. The joint displacements for the static and the dynamic analyses were compared for both domes along with the axial stresses in all members. The percentage increases in the axial stresses of the dynamic analyses as compared to those of the static analyses were determined. The reticulated domes used in the study were found to bet capable of withstanding the earthquake excitations when subjected to various uniform loads without failure. / Master of Science

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

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

Indiana University-Purdue University Indianapolis (IUPUI) / We study the one-parameter family of determinants $det(I-\gamma K_{PII}),\gamma\in\mathbb{R}$ of an integrable Fredholm operator $K_{PII}$ acting on the interval $(-s,s)$ whose kernel is constructed out of the $\Psi$-function associated with the Hastings-McLeod solution of the second Painlev\'e equation. In case $\gamma=1$, this Fredholm determinant describes the critical behavior of the eigenvalue gap probabilities of a random Hermitian matrix chosen from the Unitary Ensemble in the bulk double scaling limit near a quadratic zero of the limiting mean eigenvalue density. Using the Riemann-Hilbert method, we evaluate the large $s$-asymptotics of $\det(I-\gamma K_)$ for all values of the real parameter $\gamma$.