局部贴敷黏弹性阻尼层圆柱壳振动频率与阻尼有限元分析

Finite element analysis of vibration frequency and damping of cylindrical shell partially covered viscoelastic damping layer

在引入黏弹性材料复模量模型和考虑圆柱壳弹性边界的基础上,研发了有限元程序来解决考虑频率依赖性的复合圆柱壳振动频率与阻尼的非线性计算问题。创建了一种4节点24自由度复合壳单元来模拟局部贴敷黏弹性阻尼层圆柱壳的力学行为,推导了单元的刚度及质量矩阵。提出由6个弹簧组组成的周向变刚度弹性约束模型来模拟圆柱壳底部的弹性边界条件。确定了复合圆柱壳的动力学有限元方程,并描述了用特征向量增值法求解其振动频率与阻尼的迭代计算过程。对贴敷ZN-1自由阻尼层圆柱壳进行了实例计算,结果表明:该算法的计算结果与实验测试值误差最大为3.69%,另外黏弹性材料的频率依赖性对复合结构固有频率影响小于0.01%,而对模态损耗因子影响最大为109.47%。

On the basis of introducing the complex modulus model of viscoelastic materials and considering the elastic boundary of the cylindrical shell, the finite element program was developed to solve the nonlinear calculation problem of vibration frequency and damping for the composite cylindrical shell in view of the frequency dependence. A composite shell element with 4 nodes and 24 degrees of freedom was created to simulate the mechanical behavior of the cylindrical shell with partially covered viscoelastic damping layer, and the stiffness and mass matrices of the element were derived. A circumference variable stiffness elastic constraint model with 6 spring groups was proposed to simulate the elastic boundaries at the bottom of the cylindrical shell. The dynamic finite element equations of the composite cylindrical shell were determined, and the iterative calculation process of solving its vibration frequency and damping by eigenvector increment method was described. A case study for the cylindrical shell with ZN-1 free damping layer was performed and the results showed that the maximum error between the calculation results of the proposed algorithm and the experiment values was 3.69%. In addition, the frequency dependence of the viscoelastic material had an effect on the natural frequency of the composite structure of less than 0.01%, but the maximum effect on the modal loss factor was 109.47%.