1999
DOI: 10.1007/s004660050380
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Nonlinear forced vibration analysis of the rectangular plates by the Fourier series method

Abstract: In this paper the Fourier series method is introduced to obtain the solution for the displacement response of rectangular plates subjected to a blast loading. Applying the Fourier series method, the von Karman nonlinear equations of plates are transformed into Duf®ng type nonlinear ordinary differential equations and then solved by adopting the Lindstedt-Poincar'e perturbation method. The complete analysis of square plates was carried out for all-clamped edge conditions. The results of de¯ection history and st… Show more

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Cited by 10 publications
(5 citation statements)
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“…A direct numerical integration method applied to the resulting Duffing equation has been used by Singh et al [36] to analyze the forced vibration of antisymmetric rectangular cross-ply plates. The Fourier series has been used by Teng et al [37] to study the non-linear forced vibration of rectangular plates. A semi-analytical method, based on the multi-mode analysis and continuation procedures, has been developed and applied to forced vibrations of beams at large amplitudes [38,39].…”
Section: Introductionmentioning
confidence: 99%
“…A direct numerical integration method applied to the resulting Duffing equation has been used by Singh et al [36] to analyze the forced vibration of antisymmetric rectangular cross-ply plates. The Fourier series has been used by Teng et al [37] to study the non-linear forced vibration of rectangular plates. A semi-analytical method, based on the multi-mode analysis and continuation procedures, has been developed and applied to forced vibrations of beams at large amplitudes [38,39].…”
Section: Introductionmentioning
confidence: 99%
“…where F is the Airy stress function, m is the mass of the plate, 4 ∇ is the biharmonic operator, h refers to the plate thickness, p is the external transverse load per unit area, (.…”
Section: Dynamic Modelling Of the Smart Platementioning
confidence: 99%
“…Remark 3. For detailed derivation for dynamics of a simply supported plate considering axial stretching due to large deflection, the reader is referred to [3,4].…”
Section: Dynamic Modelling Of the Smart Platementioning
confidence: 99%
See 1 more Smart Citation
“…From the " Nonlinear forced vibration analysis of the rectangular plates by the Fourier series method " published by Teng, TL in 1999 [27], it is known that to establish the double Fourier series equation, it is necessary to make all items on the left and right sides of the equation equal.…”
Section: Expression Of Equations Of Motionmentioning
confidence: 99%