Applied To The Boundary Integral Method To Solve The Natural Frequency Of Bending Thick Tectangular Plates

Thick plate has wide application value in the field of modern science and technology. The flat raft foundation in building structures, the beamless floor and the transfer floor in high-rise building can be seen as thick plate. In addition, the protection door of civil air defense basement, bridge plate and carrieraircraft deck can also be seen as thick plate. Thick plate has more important role than thin plate, and when destroyed, the impact is much greater than that of thin plate. So it has practical value for the research of thick plate. The accurate solution of the natural frequency can avoid the damage caused by structural resonance. But the classical thin plate theory without considering the transverse shear deformation is no longer suitable for thick plate calculation. So a new way to calculate natural frequency of thick rectangular plate is presented in this paper.This paper is based on the Reissner theory which is the earliest theory of thick plates considering shear deformation and compression deformation. The control equation and boundary condition of the Reissner thick plate theory are derived by Reissner theory. This paper applies the boundary integral method to solve the natural frequency of thick rectangular plate based on thick plate theory. This paper firstly presents the quasi basic system of thick rectangular plate and get the basic solution. Then this paper applies the boundary integral between the quasi basic system and the actual system, derives the natural frequency equation of thick plate with six kinds of boundary conditions, respectively, two opposite edges is simply supported one edges is fixed and the other edges is free, two opposite edges is simply supported and other two opposite edges fixed, three edges simply supported one edges is fixed, two opposite edges is simply supported and other two opposite edges free, four edges simply supported, three edges simply supported one edges is free. The natural frequency of different vibration modes are calculated by Matlab software, and the results are compared with the results of the ANSYS structural analysis. Then it can be seen that the accuracy of natural frequency equation. It’s a new method to solve the natural frequency of thick plates.