Hamilton体系下压电材料层合板特征值灵敏度分析

SENSITIVITY ANALYSIS OF EIGENVALUE FOR PIEZOELECTRIC IN HAMILTON SYSTEMS

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。

In the structural shape optimization （SSO） procedures,one of the main difficulties is to perform an accurate sensitivity analysis for the structural response with respect to some parameters.At present,the analytical,semi-analytical and finite difference methods are the most commonly used.In Hamilton systems,the sensitivity analysis of eigenvalue response was studied for piezoelectric laminated plates,and the governing equation of sensitivity coefficients of eigenvalue for piezoelectric laminated plates was derived based on B-spline wavelet on the interval （BSWI） wavelets element methods in the present work.So the sensitivity coefficients of eigenvalue would be obtained in Hamilton system,while it just would be gained in Lagrange system before.Sensitivity coefficients of eigenvalue of first 4 ranks with respect to density are obtained by bisection mehtod.And the numerical results of bisection mehtod are compared with that of the finite difference methods.The reliability of this eigenvalue sensitivity analysis method which based on wavelets and Hamilton systems is proved by this compare.