基于状态空间法的结构动力学建模与简化算法  

Structure dynamic modeling and its reduced algorithm based on state space method

作　　者：杜运东[1] 史宝军[1] 杨廷毅[1] 季加东[1] 李芳芬[1] 

机构地区：[1]山东建筑大学机电工程学院,山东济南250101

出　　处：《山东建筑大学学报》2009年第4期288-292,302,共6页Journal of Shandong Jianzhu University

基　　金：国家自然科学基金(50775132);山东省自然科学基金(Z2008F06);山东省教育厅科技计划(J07YA08)

摘　　要：介绍一种利用模态变换和状态空间理论求解多自由度系统动力学特性和动态响应的方法。该方法可以通过多个单自由度系统模态叠加得出系统的总体频率及时域响应,并可以排序各阶模态对总体响应的相对重要性;通过对各阶模态进行排序,忽略一些不太重要的模态,以对模型进行降阶处理获得简化模型。以简单的悬臂梁模型为例介绍了如何利用有限元模态分析求解模型的特征值和特征向量并建立状态空间模型,并对结构动态响应进行简化计算分析的过程。数值结果表明:该悬臂梁的降阶简化模型和全模型的结果非常接近,验证了该方法在简化计算分析过程的同时可以保证分析的准确性。In this paper, a method is introduced with modal transform and state space theory concerning solving dynamic characteristics and dynamic responses for multi-dof （degree of freedom） system. The total frequency and time domain responses of the system can be constructed by combinations of its individual modes. By ranking the relative importance of each mode to the overall responses, the less important modes could be eliminated in order to get reduced order model. Taking a cantilever beam as an example the whole process is presented including how to obtain the eigenvalues and eigenvectors by using the finite element modal analysis. The state space model is constructed and its dynamic responses is analyzed as well in this paper with the reduced model. Numerical results show that solutions of the cantilever beam with its reduced-order model are very closed to those of its full model, which indicates that the method presented in this paper can simplify the process while keeping its accuracy for structure dynamic analysis.

关 键 词：模态变换 状态空间法 动力学 模型降阶 

分 类 号：TH218[机械工程—机械制造及自动化]