YUAN Hong, LIU Ren-huai. Nonlinear Vibration of Corrugated Shallow Shells Under Uniform Load[J]. Applied Mathematics and Mechanics, 2007, 28(5): 514-520.
Citation: YUAN Hong, LIU Ren-huai. Nonlinear Vibration of Corrugated Shallow Shells Under Uniform Load[J]. Applied Mathematics and Mechanics, 2007, 28(5): 514-520.

Nonlinear Vibration of Corrugated Shallow Shells Under Uniform Load

  • Received Date: 2006-02-14
  • Rev Recd Date: 2007-03-09
  • Publish Date: 2007-05-15
  • 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.
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