Nonlinear vibration of circular corrugated plates

王新志,; 王林祥,; 胡小方,; Wang, Xinzhi; Wang, Linxiang; Xiao-fang, HU

doi:10.1007/bf02018549

Cited by 12 publications

(1 citation statement)

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“…In despite of very importance in both theory and application, it is quite difficult to analyze the nonlinear vibration problems of corrugated shells due to their complicated shape, too many parameters and existence of inertia force term. Based on the theory of orthotropic circular plate [18−20] , selecting the maximum amplitude in the center of the corrugated circular plate as the perturbation parameter, the nonlinear natural frequency of corrugated circular plate was solved using the perturbation variation method by Wang et al [18] . The problem of nonlinear free vibration of corrugated circular plate was solved successfully by Liu and Li utilizing Galerkin method [19] and modified iteration method [20] , and the relationship between amplitude and frequency was obtained.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of corrugated shallow shells under uniform load

袁鸿

刘人怀

2007

Appl Math Mech

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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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Section: Introductionmentioning

confidence: 99%

Nonlinear vibration of corrugated shallow shells under uniform load

袁鸿

刘人怀

2007

Appl Math Mech

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Application of the modified iteration method to nonlinear vibration of corrugated circular plates

Liu

1990

Appl Math Mech

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

2003

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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.

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Nonlinear vibration of circular corrugated plates

Cited by 12 publications

References 1 publication

Nonlinear vibration of corrugated shallow shells under uniform load

Nonlinear vibration of corrugated shallow shells under uniform load

Application of the modified iteration method to nonlinear vibration of corrugated circular plates

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

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