This paper discusses the sensitivity analysis of semisimple eigenvalues and associated eigen-matrix triples of regular quadratic eigenvalue problems analytically dependent on several parameters. The directional deriva...This paper discusses the sensitivity analysis of semisimple eigenvalues and associated eigen-matrix triples of regular quadratic eigenvalue problems analytically dependent on several parameters. The directional derivatives of semisimple eigenvalues are obtained. The average of semisimple eigenvalues and corresponding eigen-matrix triple are proved to be analytic, and their partial derivatives are given. On these grounds, the sensitivities of the semisimple eigenvalues and corresponding eigenvector matrices are defined.展开更多
在结构优化过程中,精确的结构参数灵敏度分析是最主要的困难之一。该文在Hamilton体系下推导了复合材料层合板特征值响应灵敏度系数的控制方程,基于BSWI(B-spline wavelet on the interval)样条小波有限元方法,利用二分法求得了四边固...在结构优化过程中,精确的结构参数灵敏度分析是最主要的困难之一。该文在Hamilton体系下推导了复合材料层合板特征值响应灵敏度系数的控制方程,基于BSWI(B-spline wavelet on the interval)样条小波有限元方法,利用二分法求得了四边固支复合材料层合板前四阶特征值对材料密度的灵敏度系数,并与有限差分法所得结果相比较,证明了该文所提出方法的可靠性。另外,该方法能够方便地拓展到复杂层合板壳结构以及智能材料层合板特征值灵敏度系数的求解问题中去。展开更多
A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the s...A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system.展开更多
在Hamilton体系下,基于区间B(B-spline wavelet on the interval)-样条小波有限元法研究压电材料特征值的灵敏度分析问题,推导压电材料特征值响应灵敏度系数的控制方程。利用二分法求得压电材料层合板前4阶特征值对材料密度的灵敏度系数...在Hamilton体系下,基于区间B(B-spline wavelet on the interval)-样条小波有限元法研究压电材料特征值的灵敏度分析问题,推导压电材料特征值响应灵敏度系数的控制方程。利用二分法求得压电材料层合板前4阶特征值对材料密度的灵敏度系数,并与有限差分法所得结果相比较,证明所提方法的可靠性。结果表明,在Hamilton体系下求解特征值的灵敏度系数是可行的。展开更多
基金Supported by Shanghai Natural Science Fund(No.15ZR1408400)
文摘This paper discusses the sensitivity analysis of semisimple eigenvalues and associated eigen-matrix triples of regular quadratic eigenvalue problems analytically dependent on several parameters. The directional derivatives of semisimple eigenvalues are obtained. The average of semisimple eigenvalues and corresponding eigen-matrix triple are proved to be analytic, and their partial derivatives are given. On these grounds, the sensitivities of the semisimple eigenvalues and corresponding eigenvector matrices are defined.
文摘在结构优化过程中,精确的结构参数灵敏度分析是最主要的困难之一。该文在Hamilton体系下推导了复合材料层合板特征值响应灵敏度系数的控制方程,基于BSWI(B-spline wavelet on the interval)样条小波有限元方法,利用二分法求得了四边固支复合材料层合板前四阶特征值对材料密度的灵敏度系数,并与有限差分法所得结果相比较,证明了该文所提出方法的可靠性。另外,该方法能够方便地拓展到复杂层合板壳结构以及智能材料层合板特征值灵敏度系数的求解问题中去。
基金Project supported by the Mathematical Tianyuan Foundation of China (No. 10626019)
文摘A procedure is presented for computing the derivatives of repeated eigenvalues and the corresponding eigenvectors of damped systems. The derivatives are calculated in terms of the eigenvalues and eigenvectors of the second-order system, and the use of rather undesirable state space representation is avoided. Hence the cost of computation is greatly reduced. The efficiency of the proposed procedure is illustrated by considering a 5-DOF non-proportionally damped system.
文摘在Hamilton体系下,基于区间B(B-spline wavelet on the interval)-样条小波有限元法研究压电材料特征值的灵敏度分析问题,推导压电材料特征值响应灵敏度系数的控制方程。利用二分法求得压电材料层合板前4阶特征值对材料密度的灵敏度系数,并与有限差分法所得结果相比较,证明所提方法的可靠性。结果表明,在Hamilton体系下求解特征值的灵敏度系数是可行的。
文摘采用特征值敏度分析与结构优化技术相结合的方法研究全侧开棚车车体结构模态问题.通过全侧开棚车车体结构模态分析,发现其车顶结构的固有频率偏低;将车顶等部件的厚度作为设计变量,对其一阶固有频率进行灵敏度分析,获到车顶内蒙皮厚度对频率最敏感,灵敏度值为0.936;以重量为约束条件、一阶固有频率最大化为目标函数,采用可行方向法对车顶部件进行动力优化设计,并将优化结果映射到整车车体模型上,进行车体结构模态分析,车体第一阶固有频率提高至5.749 Hz,第四阶固有频率提高至11.3525 Hz.
