四角点简支双稳态层合板振动特性研究  

Natural Vibration Characteristics of Bi-Stable Laminates Simply Supported at Four Corners

作　　者：周伟兵 郝育新[1] ZHOU Weibing;HAO Yuxin(Beijing Information Science and Technology University,Beijing 100192,China)

机构地区：[1]北京信息科技大学机电学院,北京100192

出　　处：《力学季刊》2021年第4期718-730,共13页Chinese Quarterly of Mechanics

基　　金：国家自然科学基金(11872127)。

摘　　要：双稳态层合板作为一种柔性可变体结构,为实现振动状态下的构型调控,将对其开展固有振动特性的研究.本文以四角点简支约束的矩形非对称铺设双稳态板作为研究对象,运用最小势能原理、一阶剪切变形理论、以及冯卡门几何非线性位移应变关系,得到双稳态板的两种稳态构型.首次给出了适合于四点简支的6参数构型函数与17参数构型函数,研究对比发现对于稳态构型采用17参数的构型函数结果相对更精确;对于应用线性位移应变关系的基于任一稳态构型下振动固有特性而言,这两种构型函数得到的结果基频相差2%,其它阶次频率相差也不大.随后采用6参数构型函数得到的稳态构型研究了几何尺寸、铺层数分别对两种稳态构型固有振动特性的影响.本研究对于进一步研究该类结构动态跳变机理具有重要意义.In order to control the configuration of the cross-ply bi-stable composite laminates which can be used in the deformable structure, the natural vibration characteristics of the composite laminates are studied. Taking the rectangular bi-stable laminates simply supported at four corners as the object of study, two stable configurations of the bi-stable laminates are obtained using the energy minimization principle, the first-order shear deformation theory(FSDT) and the von Karman nonlinear strain-displacement relationship. The 6-parameter configuration function and the 17-parameter configuration function that are applicable for the corner simply supported problem are obtained for the first time. The 17-parameter configuration function is found to be more accurate for solving the stable configuration of the bi-stable laminates. However, for the natural vibration characteristics based on the stable configuration with linear displacement-strain relationship, the results from the two configuration functions do not differ much from each other, with only 2 % relative error for the first order frequency. Then, the effects of the geometric size and the number of laminate plys on the natural vibration characteristics of the two stable configurations were investigated using the stable configurations obtained by 6-parameter configuration function. This paper is of significant meaning for further understanding of the dynamic snap mechanisms of the bi-stable laminates.

关 键 词：双稳态层合板 瑞利-里兹法 四角点简支 振动特性 

分 类 号：O31[理学—一般力学与力学基础] O32[理学—力学]