具有广义力场损伤粘弹性梁-柱的广义变分原理及应用  

Generalized Variational Principle of Generalized Force Fields for Viscoelastic Beam-Column with Voids

作　　者：盛冬发[1] 程昌钧[2] 

机构地区：[1]福建工程学院机电及自动化工程系,福州350014 [2]上海大学力学系上海市应用数学与力学研究所,上海200072

出　　处：《力学季刊》2006年第2期247-254,共8页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金资助项目(50278051);福建省自然科学基金资助项目(Z0511045);福建省教育厅科技项目(JA05310);江西省高校科技项目(赣教技字[2005]17号)

摘　　要：本文从考虑损伤的粘弹性材料的卷积型本构关系出发,建立了在小变形下损伤粘弹性梁-柱的控制方程。提出了以卷积形式表示的梁-柱弯曲问题的泛函,并给出了损伤粘弹性梁-柱的广义变分原理。应用这个广义变分原理,可分别给出梁-柱位移和损伤满足的基本方程,以及相应的初始条件和边界条件。应用Galerkin截断和非线性动力学的数值分析方法,分析了两端简支损伤粘弹性梁柱的动力学行为,给出了不同的材料参数对系统响应的影响。According to the constitutive model expressed by convolution method for viscoelastic solids with damage, the generalized motion equations of viscoelastic beam column with damage were derived under small deformation. The convolution type functional was offered for the bending of viscoelastic beam column with damage and the generalized variational principle of viscoelastic beam column with damage was presented. By using the generalized variational principle, the motion equations of displacement and the damage variables were obtained, and the initial and boundary conditions were obtained also. Applying the Galerkin method and the numerical methods in nonlinear dynamics, the dynamical behavior of a simple supported beam-column was investigated. The influences of material parameter on the dynamical behaviors of the beam-column were investigated.

关 键 词：损伤粘弹性固体 梁-柱 广义变分原理 GALERKIN方法 非线性动力学 

分 类 号：O345[理学—固体力学]