具有初挠度扁柱面网壳的非线性动力学问题  

Nonlinear dynamic problem of reticulated shallow cylindric shells with the initial deformation

作　　者：韩明君[1] 邱平[1] 

机构地区：[1]兰州理工大学理学院,甘肃兰州730050

出　　处：《兰州理工大学学报》2009年第6期167-171,共5页Journal of Lanzhou University of Technology

基　　金：甘肃省自然科学基金(3ZS062-B25-021)

摘　　要：根据薄壳非线性动力学理论和网格结构拟壳法,给出矩形底面扁柱面网壳的非线性混合边值问题,在可移夹紧的边界条件下,求出扁柱面网壳的无量纲应力函数的解.利用扁柱面网壳的非线性动力学变分方程,通过Galerkin作用得到一个含二次和三次项的非线性动力学方程,在外激励情况下求Melnikov函数,给出可能发生混沌运动的条件.通过数字仿真绘出的相轨图,Poincare映射图,时程图证实混沌运动的存在;给出频率受初挠度影响的特征曲线,结果表明频率随初挠度增大而增大,且随初挠度增大而非线性增强.The nonlinear mixed boundary value problem of shallow reticulated cylindric shells with rectangular bottom was presented based on nonlinear dynamic theory of shallow shells and the method of quasi- shells of reticulated structures. The solution of dimensionless stress function of reticulated cylindric shells was found under the condition of clamped edges. By using nonlinear dynamic variational equation of the reticulated cylindric shells and Galerkin action, a nonlinear dynamic differential equation containing second- and third-order terms was derived. Melnikov function was found under external excitation and the condition of possible appearance of chaotic motion was given. The phase plane, Poincare mapping, and time history curve were drawn by using digital simulation, so that the existence of chaotic motion was verified. The characteristic curve of variation of frequency with initial deformation was also given, manifesting that the frequency nonlinearly increased with initial deformation.

关 键 词：拟壳法 扁柱壳 准确解 非线性 

分 类 号：O343.5[理学—固体力学]