正交各向异性扁球壳的非线性自由振动的求解

基于正交各向异性扁球壳非线性动力方程，首先应用Ｇａｌｅｒｋｉｎ法，导出了扁球壳非线性自由振动的运动微分方程，而后应用修正的Ｌｉｎｄｓｔｅｄｔ－Ｐｏｉｎｃａｒｅ法，给出了非线性固有频率和时间函数的近似解析表达式，并分析了周边弹性约束扁球壳的几何参数，正文各向异性参数，中心质量，约束条件等对系统非线性动力特性的影响，最后在较小振幅振动下，给出了扁球壳由硬弹簧特性过渡到软弹簧特性的临界拱高表达式。

Solution of Non-linear Free Vibration of Orthogonal Anisotropic Shallow Spherical Shells

Based on the non-linear dynamic equation of orthogonal anisotropic shallowspherical shells,the kinematics differential equation of non-linear free vibration of the latteris derived first with the Galerkin method.Then an approximate analytical expression fornon-linear intrinsic frequency is given with the modified Lindstedt-Poincare method.The in-fluence of the geometry of the shell with peripheric elastic restrain,orthogonal anisotropymass,restrain condition etc on the non-linear dynamic characteristics of the system is alsoanalysed.Finally,the expression for critial arch rise of the shell at the transition from theregime with hard spring characteritics to the regime with soft spring characteritics under thevibration with smaller amplitude is presented.