扁球壳和扁锥壳的轴对称非线性热弹耦合振动

Thermoelastically Coupled Axisymmetric Nonlinear Vibration of Shallow Spherical and Conical Shells

假设温度场与应变场相互耦合,研究了旋转扁薄球壳和锥壳的轴对称非线性热弹振动问题· 基于vonK rm n理论和热弹性理论,导出了本问题的全部控制方程及其简化形式· 应用Galerkin技术进行时空变量分离后,得到了一个关于时间的非线性常微分方程组· 根据方程的特点,分别用多尺度法和正则摄动法求得了壳体振动的频率与振幅间特征关系和振幅衰减规律的一次近似解析解,并讨论了壳体几何参数。

The problem of axisymmetric nonlinear vibration for shallow thin spherical and conical shells when temperature and strain fields are coupled is studied. Based on the large deflection theories of von Krmn and the theory of thermoelasticity, the whole governing equations and their simplified type are derived. The time-spatial variables are separated by Galerkin's technique, thus reducing the governing equations to a system of time-dependent nonlinear ordinary differential equation. By means of regular perturbation method and multiple-scales method, the first order approximate analytical solution for characteristic relation of frequency vs amplitude parameters along with the decay rate of amplitude are obtained, and the effects of different geometric parameters and coupling factors as well as boundary conditions on thermoelastically coupled nonlinear vibration behaviors are discussed.