Nonlinear vibration of thin shallow conic shells under combined action of peripheral moment and transverse loads

Abstract

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.