点阵夹芯圆柱壳自由振动分析的波有限元方法

A Wave Finite Element Method for Free Vibration Analysis of Lattice Core Sandwich Cylindrical Shells

针对点阵夹芯圆柱壳的自由振动分析发展了波有限元法.首先基于自由波的传播规律,建立了点阵夹芯圆柱壳胞元的二维波有限元控制方程,相比于全尺寸有限元模型,显著缩减了控制方程的自由度规模;其次,基于Neumann级数推导了约束动刚度矩阵求逆的显式表达式,不仅可以提高计算效率,而且使得固有频率从控制方程中分离出来,从而将点阵夹芯圆柱壳的固有频率求解转化为单个胞元自由度规模的二次特征值问题;最后,根据结构振动模态与自由波的关系,给出了圆柱壳轴向和周向的波传播参数的表达式,进而求得点阵夹芯圆柱壳的固有频率和模态.数值算例考虑了多种边界条件下的点阵夹芯圆柱壳自由振动问题,验证了该方法的正确性和高效性.

A wave finite element method was developed for the free vibration analysis of lattice core sandwich cylindrical shells.Firstly,based on the propagation law of free waves,governing equations for a core element of the lattice core sandwich cylindrical shell was established.Compared with the full-scale finite element mod-el,degrees of freedom of the governing equations for a core element are significantly reduced.Secondly,an ex-plicit expression for the inverse of the constrained dynamic stiffness matrix was derived based on the Neumann series,which not only improves computation efficiency but also separates the natural frequency from the gover-ning equations,thereby transforming the natural frequency solution of the lattice core sandwich cylindrical shell into a quadratic eigenvalue problem of a core element.Finally,according to the relationship between the struc-tural vibration mode and the free wave,the expressions of the axial and circumferential wave propagation pa-rameters of the cylindrical shell were given,and the natural frequencies and modes of the lattice core sandwich cylindrical shell were obtained.Numerical examples of the free vibration analysis on a lattice core sandwich cy-lindrical shell under different boundary conditions verify the validity and efficiency of the proposed method.