Nonlinear Dynamics of Honeycomb Sandwich Plate with Completed Clamped Supported
|Keywords||the honeycomb sandwich plate nonlinear dynamics the homotopy method 1 internal resonance stability|
Honeycomb sandwich is a kind of special composite construction. They are used in aeronautic and astronautic engineering, as they have many advantages such as low density, high strength ratio and high stiffness ratio. It is known that the linear theory can’t solve the problems with astronautic engineering. At present, the research of the nonlinear dynamics of honeycomb sandwich plate is based on completed simple supported. In practical, it’s used in the plate with completed clamped supported. And the research of the nonlinear dynamics of honeycomb sandwich plate with completed clamped supported has still not been reported. Therefore, research on the nonlinear dynamics of honeycomb sandwich plate is significant in theory and application.The nonlinear dynamics and stability of a camped-supported rectangular honeycomb sandwich plate is studied in this thesis. The main contents of this thesis are as follows:Based on the classical plate theory and border principle of superposition, a preliminary study is conducted for the natural frequency of the honeycomb sandwich plate with completed clamped supported, all of which provides an important basis for the results of the optimal design for honeycomb sandwich plate vibration parameters.According to the classical plate theory and the large deformation, the governing equations of motion are established for the honeycomb sandwich plate subjected to the transversal excitation force by using the Hamilton’s principle. The transversal damping is taken into consideration. The method of normalization is utilized to transform the nonlinear vibration equations for the honeycomb sandwich plate to nonlinear system with single and double modes of freedom. Numerical simulation is used directly to investigate the nonlinear responses of the honeycomb sandwich plate. The results of numerical simulation demonstrate that the coupling of the lower-order and the higher-order modes has significant influence on the nonlinear responses of the honeycomb sandwich plate.A strongly cubic nonlinear forced vibration system with single and double degrees of freedom is investigated by means of homotopy analysis method(HAM). The HAM adjusts and controls progression solution convergence region and the convergence rate by the introduction of auxiliary parameters and auxiliary functions. Therefore, it opens up a new approach to the solution of analytical approximation of non-linear problems, especially suitable for strong non-linear problems.Using the HAM solves the nonlinear vibration equations of the honeycomb sandwich and analyzes the change of amplitude with excitation frequency, attenuation coefficient and vibration parameters. The case of the primary parameter resonance and the 1:3 internal resonance are considered. In addition, motion stability analysis of honeycomb sandwich system is studied in this thesis.