集中载荷作用下不同边界条件的弯曲厚矩形板的受迫振动

运用边界积分法研究了四边简支、两对边固定另两对边简支、四边固定三种复杂边界条件下厚矩形板的受迫振动问题,求解过程清晰,从而给出了受迫振动控制方程和挠曲面方程。通过在Matlab平台上进行数值计算,得出了图表形式的计算结果,并与有限元模拟值进行对照。研究表明,边界积分法用于求解厚矩形板的受迫振动问题的准确性,本文推导的控制方程和挠曲面方程的正确性,进而对工程实际中的各种相关问题具有一定的现实意义,也为求解此类问题提供了一种新途径,可以直接运用到工程实际中。

Forced vibration of bending thick rectangular plates with different boundary conditions under concentrated load

The boundary integral method is used to study the forced vibration of thick rectangular plates under three complex boundary conditions,namely,simply supported on four sides,fixed two opposite sides and simply supported on two opposite sides,and fixed on four sides.The solution process is clear,and the governing equations of forced vibration and the equations of the flexural surface are given.Through numerical calculation on the Matlab platform,the calculation results in the form of charts are obtained,and compared with the finite element simulation results.From the comparison of these results the accuracy of applying the boundary integral method to solve the forced vibration problem of thick rectangular plates and the correctness of the derived governing equations and the flexural surface equations can be seen.It has certain practical significance for various related problems in engineering practice,and provides a new way for solving such problems,which can be directly applied to engineering practice.