扁薄锥壳在周边弯矩和横向载荷共同作用下的非线性振动

从问题的变分方程和协调方程出发，选取扁锥壳中心最大振幅为摄动参数，采用摄动变分法，对周边简支的扁薄锥壳在周边弯矩和横向载荷共同作用下的非线性振动问题进行了求解，一次近似得到了扁薄锥壳在静载荷作用下的线性固有频率，二次近似得到了扁薄锥壳在静载荷作用下的精确度较高的非线性固有频率．并给出了小变形时固有频率与周边弯矩、横向载荷、振幅以及锥底角之间非线性关系的三次近似解析表达式，数值结果的图形反映了在一定范围内固有频率和各参数之间非线性关系的复杂性和规律性。

Nonlinear Vibration of Thin Shallow Conic Shells Under Combined Action of Peripheral Moment and Transverse Loads

Based on the variation and harmonic equations and by taking the maximum amplitude of the shell center as the perturbation parameter,nonlinear vibration of thin shallow conic shells under combined action of peripheral moment and transverse loads was solved.The linear natural frequency can be got by the first_order approximation and the more accurate nonlinear frequency is got by the second_order approximation under the action of static loads.Meanwhile the third_order approximate analytic expression is given for describing the nonlinear relation between nature frequency and peripheral moment,transverse loads,amplitude,base angle under the small deformation.Within some range,the complex and regularity of the nonlinear relation can be directly observed from the numeric results.