Abstract
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 is investigated. The nonlinear partial differential equations of shallow shell are reduced to the nonlinear integral-differential equations by the method of Green’s function. To solve the integral-differential equations, expansion method is used to obtain Green’s function. Then the integral-differential equations are reduced to the form with degenerate core by expanding Green’s function as series of characteristic function. Therefore, the integral-differential equations become nonlinear ordinary differential equations with regard to time. The amplitude-frequency response under harmonic force is obtained by considering single mode vibration. As a numerical example, forced vibration phenomena of shallow spherical shells with sinusoidal corrugation are studied. The obtained solutions are available for reference to design of corrugated shells
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Yuan, H., Liu, Rh. Nonlinear vibration of corrugated shallow shells under uniform load. Appl Math Mech 28, 573–580 (2007). https://doi.org/10.1007/s10483-007-0502-1
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DOI: https://doi.org/10.1007/s10483-007-0502-1