Large-Amplitude Vibration of Imperfect Rectangular, Circular and Laminated Plate with Viscous Damping

Large-amplitude vibration of thin plates and shells has been critical design issues for many engineering structures. The increasingly more stringent safety requirements and the discovery of new materials with amazingly superior properties have further focused the attention of research on this area. This thesis deals with the vibration problem of rectangular, circular and angle-ply composite plates. This vibration can be triggered by an initial vibration amplitude, or an initial velocity, or both. Four types of boundary conditions including simply supported and clamped combined with in-plane movable/immovable are considered. To solve the differential equation generated from the vibration problem, Lindstedt\u27s perturbation technique and Runge-Kutta method are applied. In previous works, this problem was solved by Lindstedt\u27s Perturbation Technique. This technique can lead to a quick approximate solution. Yet based on mathematical assumptions, the solution will no longer be accurate for large amplitude vibration, especially when a significant amount of imperfection is considered. Thus Runge-Kutta method is introduced to solve this problem numerically. The comparison between both methods has shown the validity of the Lindstedt\u27s Perturbation Technique is generally within half plate thickness. For a structure with a sufficiently large geometric imperfection, the vibration can be represented as a well-known backbone curve transforming from soften-spring to harden-spring. By parameter variation, the effects of imperfection, damping ratio, boundary conditions, wave numbers, young\u27s modulus and a dozen more related properties are studied. Other interesting research results such as the dynamic failure caused by out-of-bound vibration and the change of vibration mode due to damping are also revealed