面内平动板横向振动研究进展  

ADVANCE IN TRANSVERSE VIBRATIONS OF IN-PLANE TRANSLATING PLATES

作　　者：唐有绮[1] 陈立群[2,3] 

机构地区：[1]上海应用技术学院机械工程学院,上海201418 [2]上海市应用数学和力学研究所,上海200072 [3]上海大学力学系,上海200444

出　　处：《固体力学学报》2015年第2期93-104,共12页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(11202135);国家自然科学基金重点项目(11232009);上海市重点学科建设项目(S30106);上海高校青年教师培养资助计划(ZZyyy12035)资助

摘　　要：面内平动板的力学行为正日益引起研究者的关注.由于面内平动板的力学性能取决于横向、轴向和侧向三个方向非线性耦合演化的结果,发展相应的多尺度数值模拟方法已成为该领域研究工作的一个热点方向.论文综述了面内平动板横向振动的研究进展,讨论了所研究问题的数学模型,建立了可整合板任意本构关系的统一的动力学方程,总结了面内平动板的模态分析、线性参数振动、非线性自由振动、非线性参数振动和受迫振动的研究进展,介绍了目前研究中近似解析方法和数值方法的应用情况.最后总结现阶段的研究成果,并提出该研究方向今后尚待深入研究的若干重要问题.Mechanical behavior of the in-plane translating plates is increasingly attracted the attention of researchers. Due to the transverse vibration for a restriction on the application of practical engineering systems,the developments of the corresponding approximate analytical methods and numerical methods have become a hot spot of the research in the field. This paper surveys main advances in the study on the transverse vibrations of in-plane translating plates. The review focuses mainly on the achievements in the fundamental studies of the mathematical model of the research questions, the dynamic equations, modal analysis, linear parametric vibration, nonlinear free vibration, nonlinear parametric vibration and forced vi- bration,as well as the approximate analytical methods and numerical methods. Finally,the paper summarizes current research achievements and addresses some open problems for future investigations.

关 键 词：面内平动板 横向振动 能量方法 近似解析方法 数值方法 

分 类 号：O327[理学—一般力学与力学基础]