Large amplitude response of circular plates on elastic foundations

Nath, Y.

doi:10.1016/0020-7462(82)90028-2

Cited by 30 publications

(15 citation statements)

References 7 publications

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“…The foundation is modeled in terms of Winkler parameter k f and shear parameter G f of the Pasternak model. Including the normal inertia and neglecting damping of the foundation, the distributed reaction from the elastic foundation on the plate at any instant of time t is given by [Nath (1982)]:…”

Section: Governing Equationsmentioning

confidence: 99%

“…Then, the equations for the nonlinear dynamic response of thin circular plates are written in the following dimensionless form [Nath (1982); Nath et al (1985)]:…”

Section: Governing Equationsmentioning

confidence: 99%

“…Kirkhope and Wilson [1972] adopted the method of finite element method in the vibration analysis of circular and annular plates. Alwar and Nath [1976], Nath [1982] and Nath et al [1985], in a series of papers, examined the nonlinear dynamic analysis of circular plates subjected to sinusoidal and constant step loading by the Chebyshev series and collocation method. A number of analytical and numerical studies have been conducted on the linear and nonlinear static and dynamic analysis of thin circular plates [Chia (1980); Soedel (1996); Timoshenko and Woinowski-Krieger (1959); Vlasov and Leont'ev (1966)].…”

Section: Introductionmentioning

confidence: 99%

“…The large deflection analysis of circular plates of variable thickness was studied by Benerjee [1983]. Nath [1982] presented the Chebyshev polynomials for spatial discretization and Houbolt's time marching discretization to study the dynamic analysis of circular paltes resting on elastic foundation. Reddy et al [1981] have investigated large deflections and large amplitude vibrations analysis of axisymmetric circular plates.…”

Section: Introductionmentioning

confidence: 99%

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Large Deflection Static and Dynamic Analysis of Thin Circular Plates Resting on Two-Parameter Elastic Foundation: HDQ/Fd Coupled Methodology Approaches

Cívalek

2005

Int. J. Comput. Methods

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An analysis of the geometrically nonlinear dynamics of thin circular plates on a two parameter elastic foundation is presented in this paper. The nonlinear partial differential equations obtained from von Karman's large deflection plate theory have been solved by using the harmonic differential quadrature method in the space domain and the finite difference numerical integration method in the time domain. Winkler-Pasternak foundation model is considered and the influence of stiffness of Winkler (K) and Pasternak (G) foundation on the geometrically nonlinear analysis of the circular plates has been investigated.Numerical examples demonstrate the satisfactory accuracy, efficiency and versatility of the presented approach. From the numerical computation, it can be concluded that the present coupled methodology is an efficient method for the nonlinear static and dynamic analysis of circular plates with or without an elastic medium.

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Section: Governing Equationsmentioning

confidence: 99%

“…Then, the equations for the nonlinear dynamic response of thin circular plates are written in the following dimensionless form [Nath (1982); Nath et al (1985)]:…”

Section: Governing Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Large Deflection Static and Dynamic Analysis of Thin Circular Plates Resting on Two-Parameter Elastic Foundation: HDQ/Fd Coupled Methodology Approaches

Cívalek

2005

Int. J. Comput. Methods

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“…In this study the effect of both initial deflection and initial edge displacement were considered. Additionally, Nath (1982) studied the effect of foundation parameters on the large amplitude response of orthotropic circular plates.…”

Section: Introductionmentioning

confidence: 99%

Assessment of Homotopy Perturbation Method for Study the Forced Nonlinear Vibration of Orthotropic Circular Plate on Elastic Foundation

Yazdi

2016

Lat. Am. j. solids struct.

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In this paper the nonlinear forced vibration of an orthotropic circular plate resting on Winkler, Pasternak and nonlinear Winkler foundation is investigated. Plates with edges elastically restrained against rotation and inplane displacement are analyzed and the Von-Karman geometric nonlinear equations are employed. In this study it is assumed that the plate can be subjected to any periodic distributed lateral loading with respect to time. The Galerkin method is used to obtain Duffing's equation for the central deflection. The Homotopy Perturbation Method was used to study the effects of various parameters including orthotropic parameter, elastic foundation parameters and initial deflection on frequency ratio. Highly accurate results were obtained by the application of the aforementioned method.

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Seismic design response by an alternative SRSS rule

Singh

Mehta

1983

Earthq Engng Struct Dyn

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The square root of the sum of the squares (SRSS) procedure and its modified forms are often used to obtain seismic design response. The design inputs for such procedures are usually defined in terms of pseudo velocity or acceleration response spectra. Erroneous results have been obtained with these existing SRSS procedures, especially in the calculation of responses where high frequency effects dominate. Here an alternative SRSS procedure is developed using the so‐called mode acceleration approach of structural dynamics. The design input in this procedure is defined in terms of relative acceleration and relative velocity spectra. The relative spectra can be related to pseudo spectra. For a given number of modes to be included in the analysis the new SRSS rule proposed here will reduce the error due to the so‐called ‘missing mass’ effect and predict a more accurate response value than the rules which use pseudo spectra as input, for systems either with or without dominant high frequency mode effects.

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Large amplitude response of circular plates on elastic foundations

Cited by 30 publications

References 7 publications

Large Deflection Static and Dynamic Analysis of Thin Circular Plates Resting on Two-Parameter Elastic Foundation: HDQ/Fd Coupled Methodology Approaches

Large Deflection Static and Dynamic Analysis of Thin Circular Plates Resting on Two-Parameter Elastic Foundation: HDQ/Fd Coupled Methodology Approaches

Assessment of Homotopy Perturbation Method for Study the Forced Nonlinear Vibration of Orthotropic Circular Plate on Elastic Foundation

Seismic design response by an alternative SRSS rule

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