黏弹性结构精细化频域动力分析方法

Fine dynamic analysis method for viscoelastic structures in frequency domain

为了解决具有强频率依赖性的黏弹性结构频域响应计算的精确性和效率较难协调的问题,提出一种改进计算方法。首先引入广义麦克斯韦模型表征黏弹性结构的频率依赖性,建立动力学方程;然后,基于实模态叠加法,并采用分步迭代法求解黏弹性结构的特征方程,获得各阶模态频率与模态损耗因子,采用多项式拟合表征各阶模态参数的频率依赖性函数;最后,将多自由度黏弹性结构频域响应的求解简化为多个进行频率依赖性函数修正的单自由度黏弹性结构频域响应的叠加。研究结果表明:本文方法计算效率较高,与传统基于应变能法相比,对强频率依赖性的黏弹性结构具有更高的精确度,与传统迭代法相比,其在非共振区间也具有较高的精确性。

An improved method was proposed to mitigate the conflict between frequency response computation accuracy and efficiency of the viscoelastic structure with obvious frequency dependence. Firstly, the equation of motion was established by introducing the generalized Maxwell model of viscoelastic materials. Then, the iterative method was used to extract the modal frequencies and damping ratios based on real modal superposition method, and the polynomial fitting was used to express the frequency-dependency function. At last, the frequency response of the multi-degree-of-freedom viscoelastic structure was simplified as a superposition of multiple single-degreeof- freedom viscoelastic structures frequency responses, which were modified by the frequency-dependency function. The results show that compared to the modal strain energy method, the proposed simplified method can obtain more accurate result of the frequency response, especially for the structure with strong frequencydependence;compared to the iterative method, it has high accuracy even in the non-resonant range.