含裂纹的抛物线型变厚度粘弹性板在随从力下的稳定性  

The Stability of Viscoelastic Plate with Parabolicly Varying Thickness and Crack Subjected to Follower Force

作　　者：王砚[1] 王忠民[1] 阮苗[1,2] 

机构地区：[1]西安理工大学机械与精密仪器工程学院,理学院,陕西西安710048 [2]长安大学理学院,陕西西安710064

出　　处：《西安理工大学学报》2008年第2期153-157,共5页Journal of Xi'an University of Technology

基　　金：陕西省自然科学基础研究计划资助项目(2005A18);西安理工大学优秀博士学位论文研究基金资助项目

摘　　要：研究了含裂纹的抛物线型变厚度粘弹性矩形板在切向均布随从力作用下的稳定性。对抛物线型变厚度裂纹Kelvin-Voigt模型粘弹性板的运动微分方程,用微分求积法建立其复特征值方程,求解了对边简支对边固支的含裂纹抛物线型变厚度粘弹性矩形板的广义特征值问题。数值计算表明,裂纹的存在会降低系统的稳定性,薄板的厚度比对在随从力作用下含裂纹的抛物线型变厚度粘弹性矩形板的临界荷载有很大影响。The stability of the cracked visoelastic rectangular plate with parabolicly varying thickness subjected to uniforuly distributed tangential follower force is investigated. The complex eigenvalue equations of the cracked viscoelastic plate constituted by Kelvin-Voigt model with parabolicly varying thickness are derived by the differential quadrature method. The general eigenvalue problems of the cracked viscoelastic varying thickness plate with two opposite edges simply supported and other two edges clamped boundary conditions are calculated. Numerical results show that existence of the crack can reduce the stability of system. The thickness ratio has a great influence on the critical loads of the cracked viscoelastic plate with parabolicly varying thickness subjected to follower force.

关 键 词：粘弹性板 抛物线型变厚度 裂纹 均布随从力 稳定性 

分 类 号：O32[理学—一般力学与力学基础]