约束层阻尼板动力学问题的半解析解

利用条形传递函数方法(SDTFM)得到了约束层阻尼(CLD)板动力学问题的半解析解.首先对CLD板沿纵向离散成多个条形单元,基于Hamilton原理推导出条形单元的刚度矩阵和质量矩阵,仿照有限元法组集得到系统的总刚度矩阵和总质量矩阵.经Laplace变换后引入状态向量,采用分布参数传递函数方法在状态空间内建立CLD板的控制方程并进行求解.最后以对边固支和悬臂CLD板为例,得到了板的动力学特性和频响曲线,并与NASTRAN或相关文献结果进行了比较,吻合良好,验证了该方法的有效性.从推导过程和算例可以看出,该方法所需的单元数目少,获得的是半解析解,计算效率高且准确可靠.

SEMI-ANALYTICAL DYNAMICS SOLUTION OF CONSTRAINED LAYER DAMPING PLATE

The dynamic problems of constrained layer damping (CLD) plates are investigated using the striped transfer function method(SDTFM). Firstly a CLD plate is divided into a lot of strip elements in its longitudinal direction. Both the stiffness and mass matrices of a SDTFM element are derived by the Hamilton principle, and then the global stiffness and mass matrices of the system are obrained through the assembling method in finite element method. Introduced the state variables after Laplace transform, the governing equations of a CLD plate in state space are established by the distributed parameter transfer function method. Finally numerical analyses for a CLD clamped-clamped plate and a cantilever plate are performed, and the dynamic behavior and the frequency-response relationship are obtained. The good agreement with the related literatures or the results of NASTRAN shows the validity of the transfer function method. It is observed that SDTFM needs fewer elements to obtain more efficient and more accurate Semi-Analytical results.