构造纵向功能梯度梁的单模态逆问题  

Single Mode Inverse Problems of Construction Axially Functionally Graded Beams

作　　者：王其申[1] 吴磊[1] 章礼华[1] 何敏[1] 

机构地区：[1]安庆师范学院物理与电气工程学院,安徽安庆246133

出　　处：《安庆师范学院学报（自然科学版）》2013年第3期73-79,共7页Journal of Anqing Teachers College(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10772001)资助

摘　　要：文献报道了采用半逆解法研究非匀质材料纵向功能梯度梁的单模态逆问题,具体讨论了当梁的横截面积为定值而材料线密度或抗弯刚度为已知多项式时,如何求解梁的多项式型抗弯刚度系数或材料线密度的条件和方法,及所得轴向抗弯刚度系数的正值性。这些研究成果获得了学界的高度重视,但也存在某些不足。本文就此研究成果做一回顾,指出存在的问题,展望今后的研究方向。By using the semi - inverse solving methods, I. Elishakoff and Lei Wu et al. have researched the single mode in- verse problems for axially functionally graded inhomogeneous beams before. They discussed the conditions and methods about re- constructing the axial flexure stiffness coefficients or linear density function when the cress - section area is constant and the linear density function or axial flexure stiffness coefficient is given polynomial. Lei Wu et al. have discussed the positivity problem of oh- mined flexure stiffness coefficient also. These researched achievements obtained scientist＇ s sufficient attention but have some defi- ciencies also. Based on these cases, we review the obtained achievements and point out being problems in this paper. And we ex- pect this researched direction also.

关 键 词：纵向功能梯度梁 半逆解法 密度函数 抗弯刚度 单模态 

分 类 号：O327[理学—一般力学与力学基础]