T型耦合板结构振动特性研究

Vibration analysis of a T-coupled plate structure

以T型耦合板为研究对象,在同时考虑面内振动和面外振动条件下采用改进傅里叶级数方法(Improved Fourier Series Method,IFSM)对其自由振动特性进行了计算分析。板结构的面内振动和面外振动位移函数表示为改进傅里叶级数形式,并引入正弦傅里叶级数以解决边界的不连续或跳跃现象。将位移函数的级数展开系数作为广义坐标,采用Rayleigh-Ritz方法对其进行求解。通过对不同边界条件及耦合连接情况下T型板自由振动特性进行计算,并将之与有限元法结果相比较,验证了该方法的正确性和有效性,为耦合板结构的振动控制提供可靠的理论依据。

Here,an analytical method,the improved Fourier series method （IFSM）was presented for the free vibration analysis of a T-coupled plate with general boundary conditions.The in-plane vibration and out-of-plane vibration were taken into account via four types of coupling springs of arbitrary stiffnesses.Regardless of boundary conditions,the transverse and in-plane vibration displacement functions were taken as a new form of trigonometric expansion with accelerated convergence. The displacement functions could overcome all the relevant discontinuities of the elastic boundaries.The expansion coefficients were considered as the generalized coordinates,and they were determined using Rayleigh-Ritz method.The free vibration analysis of the T-coupled plate with various boundary and coupling conditions was performed using the proposed method.The reliability and accuracy of the proposed method were validated with the FEM results.This study provided a reliable and theoretical basis for vibration control of coupled plate structures.