Sensitivity analysis based on Lanczos algorithm in structural dynamics

IntroductionTheproblemforcomputingeigenpairderivativeshasoccupiedmanyresearchersinthepastseveraldecades.SurveypaperbyAdelmanandHaftka[1]isanexcellentintroductiontothetopicandalsoindicatevariousdisciplinesofapplications.Thereasonwhysomanypeopleareinterestedinthisproblemisthatsensitivitiesplayaveryimportantroleinstructuraldynamics,optimalanalysisandcontrolsystemdesign ,andmayalsobeanexpensiveandtime_consumingtask.Researchonsensitivityofmultipleeigenvalueshasbeenanareaofsignificantinterestinrece…     

Homotopy solution of the inverse generalized eigenvalue problems in structural dynamics

The structural dynamics problems, such as structural design, parameter identification and model correction, are considered as a kind of the inverse generalized eigenvalue problems mathematically. The inverse eigenvalue problems are nonlinear. In general, they could be transformed into nonlinear equations to solve. The structural dynamics inverse problems were treated as quasi multiplicative inverse eigenalue problems which were solved by homotopy method for nonlinear equations. This method had no requirements for initial value essentially because of the homotopy path to solution. Numerical examples were presented to illustrate the homotopy method.     

结构动力学逆特征值问题的同伦解法

将结构动力学反问题视为拟乘法逆特征值问题,利用求解非线性方程组的同伦方法来解决结构动力学逆特征值问题,这种方法由于沿同伦路径求解,对初值的选取没有本质的要求,算例说明了这种方法是可行的．     

基于Lanczos方法的结构动力学灵敏度分析

利用数学理论得到结构动力学重特征值的灵敏度表达式,从而解决了奇异性问题.然后,为降低计算工作量,基于Lanczos方法得到降阶的结构系统,从而得到降阶的灵敏度分析近似解.用一个算例证明的方法正确性.