Composite materials are increasingly finding use in structures, such as aircraft components, and thus, an accurate method of predicting response is required. Even laminated structures that are considered thin can be significantly affected by transverse shear effects, and as a result, transverse shear should not be neglected. The free vibration response of generally-laminated, thick, skew, trapezoidal plates is investigated as there appears to be a lack of information in this area. In the method developed, Chebychev polynomials are used as displacement functions in the Rayleigh-Ritz method. Various edge supports are considered, and appropriate linear and rotational springs are introduced to approximately satisfy the essential boundary conditions associated with simply-supported and clamped edges. First-order shear theory is used to account for transverse shear effects, and rotary inertia is also included.in the model. Convergence of the solution resulting from changes in spring values and number of terms in the series is investigated. The accuracy of the method is demonstrated by comparing the present method to available results for plates of various quadrilateral shape, material systems, and boundary conditions. Thick laminated plates of both symmetric and unsymmetric construction and of various planforms and boundary conditions are then presented. Cantilever, thick, skew, and trapezoidal plates are then extensively studied, and variations in natural frequencies due to geometric parameter changes, such as taper ratio, sweep angle, and value of the parameter q, are discussed. The parameter, q, is a root length multiplier which determines the length of the quarter-chord line, thus representing a measure of the span. Mode shapes for a number of plates of various planform and support conditions are included. / Master of Science

This dissertation focuses on nonlinear modal interactions in plates. Our first investigation involved the activation of a two-to-one internal resonance in the response of a metallic cantilever plate. Although the plate was excited around the frequency of its second bending mode, its response contained a contribution from its first torsional mode. The frequency ratio between the bending and torsional modes was nearly two-to-one. Next, we investigated the energy transfer from high-frequency to low-frequency modes in a cantilever graphite-epoxy composite plate (90/30/ — 30/ — 30/30/90)_s. The plate was excited around the natural frequency of its seventh (third torsional) mode. For some excitation amplitudes and frequencies, we observed the activation of a low-frequency (first bending) mode accompanied by an amplitude and phase modulation of the seventh mode. We studied combination resonances in the responses of cantilever composite plates with the layups (90/30/ — 30/ — 30/30/90)_s and (—75/75/75/ — 75/75/ — 75)_s to harmonic base excitations. We activated the combination resonance f_e≈ ω₂ + ω₇ in the (90/30/ — 30/ — 30/30/90)_s plate, where the w; are the natural frequencies of the plate and f<sub>e<sub> is the excitation frequency. In the (—75/75/75/ — 75/75/ — 75)_s plate, we activated the external combination resonance f<sub>e<sub>≈ 1/2(ω₂+ω₅) and the combination internal resonance f_e≈1/2(ω₂+ω₁₃) ≈ ω₈. We carried out an experimental-modal analysis (EMA) of a nonclassically supported plate with and without a constrained-layer damping (CLD) patch attached on its upper left-hand side surface. The natural frequencies and mode shapes were used to ascertain the effect of the CLD patch. / Ph. D.

[Truncated abstract] Shipbuilding is fast becoming a priority industry in Australia. With increasing demands to build fast vessels of lighter weight, shipbuilders are more concerned with noise and vibration problems in ships than ever. The objective of this thesis is to study the vibration response of coupled structures, in the hope that the study may shed some light in understanding the general features of ship vibration. An important feature characterizing the vibration in complex structures is the input mobility, as it describes the capacity of structures in accepting vibration energy from sources. The input mobilities of finite ribbed plate and plate/plate coupled structures are investigated analytically and experimentally in this study. It is shown that the input mobility of a finite ribbed plate is bounded by the input mobilities of the uncoupled plate and beam(s) that form the ribbed plate and is dependent upon the distance between the source location and the stiffened beam(s). Off-neutral axis loading on the beam (point force applied on the beam but away from the beam’s neutral axis) affects the input power, kinetic energy distribution in the component plates of the ribbed plate and energy flow into the plates from the beam under direct excitation ... solutions were then used to examine the validity of statistical energy analysis (SEA) in the prediction of vibration response of an L-shaped plate due to deterministic force excitations. It was found that SEA can be utilized to predict the frequency averaged vibration response and energy flow of L-shaped plates under deterministic force (moment) excitations providing that the source location is more than a quarter of wavelength away from the plate edges. Furthermore, a simple experimental method was developed in this study to evaluate the frequency dependent stiffness and damping of rubber mounts by impact test. Finally, analytical methods developed in this study were applied in the prediction of vibration response of a ship structure. It was found that input mobilities of ship hull structures due to machinery excitations are governed by the stiffness of the supporting structure to which the engine is mounted. Their frequency averaged values can be estimated from those of the mounting structure of finite or infinite extents. It was also shown that wave propagation in ship hull structures at low frequencies could be attenuated by irregularities imposed to the periodic locations of the ship frames. The vibration at higher frequencies could be controlled by modifications of the supporting structure.