Study On Nonlinear Vibration Of Circular Thin Plate And Circular Sandwich Plate

The dissertation is devoted to studying the nonlinear free vibration of elastic circular plate and circular sandwich plate. The attention is mainly focused on the nonlinear free vibration characteristics of those plates. By using modified iteration method, some new analytic methods are arrived at. Firstly, the nonlinear vibration problem of elastic circular plate is discussed, the nonlinear vibration fundamental equations of flexible circular plate, circular and annular thin plate with multistepped thickness are given under static loading. For the nonlinear vibration of flexible circular plate under static loading, following an assumed time mode approach suggested, a set of nonlinear coupling algebraic and differential eigenvalue equations are established. The approximately analytic solution is derived by use of modified iteration method. The relations of amplitude frequency-loading, and nonlinear vibration "drift" with loading and amplitude are derived, the influences of static loading on vibration characteristics are discussed under all kinds of boundary conditions. Following the method mentioned above, second-order modified iteration solutions of nonlinear vibration problem on circular and annular thin plate with multistepped thickness are obtained. Some examples are given to show the influences of geometric parameter on amplitude. By means of Hamilton principle, the fundamental equations of nonlinear vibration for circular sandwich plate are derived. In most cases, the face plates of sandwich plate are very thin, consequently, the simplified fundamental equations are given for this case. Modified iteration method is employed to solve the nonlinear differential equation, the approximately analytic solution is used to analyzed the influences of sandwich parameter on vibration characteristics. Based on the studies above, further study on nonlinear vibration of circular sandwich plate is accomplished, the nonlinear axisymmetric free vibration of circular sandwich plate considering the face plate rigidity with clamped but free to slip boundary condition are discussed in detail. Because those control equations belong to boundary layer style, the solution is more difficult, modified iteration method is generalized to solve those equations, and fine solutions are obtained. The influences of face plate bending rigidity on vibration characteristics are discussed by comparing the solutions considering the face plate bending rigidity with those solutions ignoring the face bending rigidity. Based on studies above, the nonlinear vibration problem of circular sandwich plate under static loading is studied, energy principle is employed to obtain variation control equation. Based on time mode hypothesis and variation method, the deflection and stress function are assumed as the separate form of time and space function, the time function employs the simple harmonic, the space function is unknown, substituting the mode function into variation equation of problem, the control equation of space mode and a set of algebraic equations used to solve nonlinear vibration "drift" are obtained, and the expression of space mode is obtained by using modified iteration method, the relation of amplitude frequency-loading of circular sandwich plate under uniformed loading is derived. The influences of static loading on nonlinear vibration frequency and "drift" are discussed.