Nonlinear Vibrations of Rectangular Plates

Bayles, D.J.; Lowery, R. L.; Boyd, D. E.

doi:10.1061/jsdeag.0003509

Cited by 16 publications

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“…The structures are designed to withstand static load, harmonic load, random excitation, fatigue load, etc. Although lot of research on dynamic analysis of isotropic rectangular plates [15–18] is available in literature, on FGMs, the research is scarce. In this framework, the well-known books by Amabili [19] and Duc [20] provide an in-depth knowledge on nonlinear vibration of plates and shells.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic analysis of a sandwich plate with S-FGM face sheets and homogeneous core subjected to harmonic excitation

Singh

Nataraj

Harsha

2020

Jnl of Sandwich Structures & Materials

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In the present paper, for a sandwich plate with homogeneous core, the nonlinear dynamic response is analyzed in which material properties of functionally graded facesheets are varied in accordance with sigmoid law. The sandwich plate of various configurations is presumed to be built on Pasternak foundation and subjected to harmonic load. Equilibrium and compatibility equations are derived by taking into consideration the geometrical non-linearity in von Karman sense. The Airy’s stress function and Galerkin method are used to solve geometric nonlinearity and implement the different edge conditions, respectively, for sandwich sigmoid function plate. A few numerical examples validate the accuracy of the present formulation with the results of available theory for different geometric parameters, elastic foundation, and plate configuration. A convergence study is performed to determine the number of terms in order to converge the solution, and it is deduced that considering the first four terms provides sufficient accuracy with average error less than 0.22% which is acceptable for any computation. The present paper is the first proposal to analyze the nonlinear dynamic characteristics of sandwich sigmoid function plate with homogeneous core and functionally graded material face sheets in ambient conditions. This article is also new in its assessment of the plate behavior in terms of predicting the periodicity such as periodic, quasi-periodic, chaotic, etc. and analyzing the frequency-amplitude relation. The aforementioned prediction aids researchers in active control of plates and shells under dynamic loading. It is found that core thickness in the sandwich plate reduces the effect of the nonlinearity. Also, the plate configurations 1-0-1 and 1-8-1 show the sensitive features in the dynamic response with varying aspect factors and span-to-thickness ratios.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic analysis of a sandwich plate with S-FGM face sheets and homogeneous core subjected to harmonic excitation

Singh

Nataraj

Harsha

2020

Jnl of Sandwich Structures & Materials

View full text Add to dashboard Cite

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“…They include the perturbation methods such as the method of harmonic balance, method of multiple scales, method of averaging, and the Lindstedt-Poincare method [4]. In the numerical nonlinear analyses, the finite difference method [5] and finite element method [6,7] have been popularly used.…”

Section: Introductionmentioning

confidence: 99%

Spectral Analysis Method for Nonlinear Dynamic Systems

Lee

Kim

2007

KEM

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This paper introduces a FFT-based spectral analysis method (SAM) for the nonlinear dynamic systems whose dynamic behaviors can be represented by the ordinary nonlinear differential equations. To verify the proposed SDM, a damped Duffing's equation is considered as an example nonlinear problem, and the phase diagrams obtained by the present SAM are compared with those obtained by other solution methods such as the method of multiple scales and the Runge-Kutta method.

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References

1995

Nonlinear Oscillations

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(1974). The inverse scattering transform Fourier analysis for nonlinear problems. Stud Appl. Math.. 53,249-315.588 Adams, 0. E. and R. M. Evan-Iwanowski (1973 Agrawal, B. N. (1975). Nonstationary and nonlinear vibration analysis and its application.Agrawal, B. J., and R. M. Evan-lwanowski (1973). Resonances in nonstationary, nonlinear, Ahmad, J., and H. C. Lee (1975). Nonlinear acoustic response of a cylindrical shell. J.Ahuja, R., and R. C. Duffield (1975). Parametric instability of variable crosssection beams Aks, S., and R. Carhart (1970). Renormalized perturbation theory for the weakly nonlinear

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Nonlinear Vibrations of Rectangular Plates

Cited by 16 publications

References 0 publications

Nonlinear dynamic analysis of a sandwich plate with S-FGM face sheets and homogeneous core subjected to harmonic excitation

Nonlinear dynamic analysis of a sandwich plate with S-FGM face sheets and homogeneous core subjected to harmonic excitation

Spectral Analysis Method for Nonlinear Dynamic Systems

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