一类非线性发展方程组的定解问题

将不可压缩的广义neo-Hookean材料组成的超弹性圆柱壳径向对称运动的数学模型归结为一类非线性发展方程组的初边值问题.利用材料的不可压缩条件和边界条件求得了描述圆柱壳内表面径向运动的二阶非线性常微分方程.给出了微分方程的周期解(即圆柱壳的内表面产生非线性周期振动)的存在条件,讨论了材料参数和结构参数对方程的周期解的影响,并给出了相应的数值模拟.

Qualitative Solution Problems of a Class of Nonlinear Evolution Equations

The radial symmetric motion of a hyper-elastic cylindrical shell composed of the incompressible generalized neo-Hookean material was described as an initial and boundary value problem of a class of nonlinear evolution equations.A second-order nonlinear ordinary differential equation that describes the motion about the radial direction of the inner-surface of the shell was obtained by using the incompressibility constraint and boundary conditions.Existence conditions of periodic solution of the differential equation(i.e,the inner-surface of cylindrical shell producing nonlinear periodic oscillation) are presented.The effects of material and structure parameters on the periodic solution of the equation are discussed,and the corresponding numerical simulations are also carried out.