Wavelet Numerical Method And Its Application In Nonlinear Analysis Of Thin Plate Structures

Circular thin plates are widely used in various engineering structures,especially in the circular parts of aerospace,storage tanks and sensors,such as aircraft skin,storage tank bottom,elastic diaphragm in pressure instrument,etc.Because of the small stiffness of them,the vibration of large amplitude is easy to occur under the external excitation,which seriously affects the effectiveness of the whole system,service safety,service life and comfort,and must be studied.However,because of its violation of the small deformation hypothesis of linear theory,it presents obvious nonlinear characteristics,namely geometric nonlinearity,which makes it very difficult to study.The large deflection bending problem of thin plate,which is a typical example,from the establishment of the basic equation to getting the convergence solution,spanned nearly a century.For the nonlinear vibration of circular thin plate,especially the strongly nonlinear vibration problem,there is still lack of very effective method.For the nonlinear vibration of circular thin plate,the numerical method most commonly used is finite element method(FEM).However,in the process of its solution,the finite element stiffness matrix is explicitly dependent on the discrete-time format.This increases the amount of calculation,because the stiffness matrix needs to be updated at each step.At the same time,due to the accumulated error in the process of time integration,it may lead to large deviation of the structural stiffness matrix,resulting in the long time tracking results disappeared,and even the wrong approximate solution.In view of this,this paper intends to explore a set of high precision wavelet algorithm to analyze the nonlinear behavior of circular thin plate.The main contents of this paper contain:(1)The approximation formula of arbitrary L2 function on a finite interval(Lagrange extension)based on generalized Coiflets wavelet is deduced,the quantitative error analysis is given,and the derivation process and calculation results of several kinds of connection coefficients often encountered in the process of solving differential equations by Wavelet-Galerkin method are given.(2)A wavelet solution scheme for solving the large deflection problem of the center elastic constraint plate is established,and compared with the previous results,it is found that the accuracy of the results obtained by the multiple multiplication connection coefficients is higher.(3)The wavelet solution format for solving the axisymmetric nonlinear vibration problem is established,and the quantitative research is carried out in combination with the Newmark method,some conclusions are obtained,such as: the free vibration period is reduced to 65% of the linear vibration cycle when the center deflection reaches the thickness of plate;The response amplitude of the center of circular thin plate decreases with the increase of the exciting force frequency.