• CN:11-2187/TH
  • ISSN:0577-6686

机械工程学报 ›› 2016, Vol. 52 ›› Issue (13): 87-93.doi: 10.3901/JME.2016.13.087

• 机械动力学 • 上一篇    下一篇

求解运动激励结构动态响应的固定边界-模态叠加法*

刚宪约, 李丽君, 柴山, 李双   

  1. 山东理工大学交通与车辆工程学院 淄博 255049
  • 出版日期:2016-07-05 发布日期:2016-07-05
  • 作者简介:

    刚宪约,男,1977年出生,博士,副教授。主要研究方向为结构动力学。

    E-mail:gangxianyue@sdut.edu.cn

    李丽君(通信作者),女,1977年出生,博士,副教授。主要研究方向为振动噪声控制方法。

    E-mail:lilijun@sdut.edu.cn

  • 基金资助:
    * 国家自然科学基金(51505261)和山东省自然科学基金(ZR2014AL010)资助项目; 20150913收到初稿,20160511收到修改稿;

Fixed Boundary Mode Superposition Method for the Dynamic Analysis of Base Motion Excited Structures

GANG Xianyue, LI Lijun, CHAI Shan, LI Shuang   

  1. School of Transportation and Vehicle Engineering, Shandong University of Technology, Zibo 255049
  • Online:2016-07-05 Published:2016-07-05

摘要:

针对运动激励下结构动态响应的模态叠加法求解问题,在分析传统的大质量法、大刚度法的局限性的基础上,提出一种新的运动激励转化方法——固定边界-模态叠加法:基于响应等效和约束反力动力平衡原理,将运动激励转化为其作用单元的等效节点载荷,并在运动激励自由度上施加固定约束,进而可以采用一般的力激励模态叠加算法进行结构动态响应计算。固定边界转化方法没有改变原有结构的固有振动特性,在理论上是精确的,克服了大质量法、大刚度法需要补充新的单元修改有限元模型和人为选择参数的缺点,并且可以通过局部有限元网格细化,提高转换载荷矢量近似计算的精度。通过一个平面应力结构的频率响应分析和一辆轻型货车三维板壳模型的瞬态响应分析验证了固定边界-模态叠加法的有效性。

关键词: 固定边界, 模态叠加, 转换载荷矢量, 运动激励

Abstract:

The mode superposition method is an effective way to solve the dynamic response problem of force excited linear structures. But this method cannot be used directly for base motion excited structures in several commercial CAE softwares, such as MSC.Nastran, ANSYS, etc. The large mass method and large stiffness method, which transfer these structures to force excited structures, are two commonly preprocessing procedures for the mode superposition method. However, additional elements should be added to the original finite element model and the physical parameters of these elements are chosen arbitrarily in these two methods, and the natural vibration characteristics are changed slightly. A new fixed boundary mode superposition method is proposed to transfer the base motion excited degree of freedoms (DOFs) to fixed boundary DOFs, transfer the base motion excitation to the equivalent loads of nodes which lie in the same elements with the base motion excited DOFs, and then solve the dynamic response problem with the traditional mode superposition procedure. The natural vibration characteristics of the original base motion excited model are not changed in the fixed boundary transfer model, and no additional elements need to be added and no arbitrary parameters need to be selected. Furthermore, the transfer load vector can be calculated more precisely by refining the local elements at base motion excited DOFs. Finally, the performance of the proposed fixed boundary mode superposition method is illustrated by solving the frequency response problem of a plane stress structure and the transient response problem of the shell element model of a light truck.

Key words: fixed boundary, mode superposition, transfer load vector, base motion excited