Nonlinear vibration of corrugated shallow shells under uniform load |
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Authors: | Yuan Hong Liu Ren-huai |
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Institution: | Institute of Applied Mechanics, Jinan University, Guangzhou 510632, P. R. China |
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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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Keywords: | corrugated shells spherical shells Green's function integral equation nonlinear vibration |
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