The Localized Boundary Type Methods For Numerical Analysis Of Free Vibration And Inverse Cauchy Problems

Problems in practical engineering are often described by partial differential equations.How to set relevant boundary conditions according to specific engineering problems and reasonably use relevant methods to obtain the solutions of partial differential equations is an important research direction in today’s scientific development.Due to the complexity of boundary conditions,it is often difficult to obtain analytical solutions that satisfy engineering problems.But with the rapid development of computer numerical simulation technology,numerical solutions provide the possibility to solve many engineering problems.The traditional numerical simulation method in engineering is mainly the finite element method.However,the traditional meshless method,like the finite element method,is based on the interpolation theory,and it is difficult to deal with the vibration problem of high frequency and high waves.The boundary-type numerical simulation methods based on relevant analytic functions,such as boundary element,basic solution method,boundary node method,etc.,can satisfy the governing equations of vibration problems,and have good results for such problems,especially in the case of high frequency and high waves..Since boundary-type methods often generate full-rank matrices,it is difficult to solve large-scale problems in engineering.In this paper,a novel localized boundary method will be used to simulate and analyze the vibration problem of plate structures.This kind of new calculation method adopts the basic solution or general solution as the basis function,and uses the virtual point interpolation technology to analyze the large-scale engineering structural components.Compared with the traditional boundary method,the localized boundary method has greatly improved the calculation speed,and compared with other regional methods,the calculation accuracy has been greatly improved.It is a new type of algorithm between the two.It is very suitable for solving vibration problems.Based on this kind of method,this paper solves the free vibration of the plate and the related Cauchy inverse calculation problems,discusses the structural vibration of the plate and a new solution method for the Cauchy inverse calculation problem,and studies the plate’s in-depth analysis based on the newly developed numerical model.Vibration characteristics,analyze the possible impact of plate vibration problems on actual engineering.