Nonlinear Vibration of Corrugated Shallow Shells Under Uniform Load

Based on the large deflection dynamic equations of axisymmetric shallow shells of revolution,the nonlinear forced vibration of a corrugated shallow shell under uniform load had been investigated.The nonlinear partial differential equations of shallow shell were reduced to the nonlinear integral-differential equations by using the method of Green's function.To solve the integral-differential equations,expansion method was used to obtain Green's function.Then the integral-differential equations were reduced to the form with degenerate core by expanding Green's function as series of characteristic function.Therefore,the integral-differential equations became nonlinear ordinary differential equations with regard to time.The amplitude-frequency response under harmonic force was obtained by considering single mode vibration.As a numerical example,forced vibration phenomena of shallow spherical shells with sinusoidal corrugation were studied.The obtained solutions are available for reference to design of corrugated shells.