Nonlinear Vibration Analysis of Thin Laminated Rectangular Plates on Elastic Foundations

Manoj, T.; Ayyappan, M.; Krishnan, Karthik; Rao, B. Nageswara

doi:10.1002/(sici)1521-4001(200003)80:3<183::aid-zamm183>3.0.co;2-p

Cited by 18 publications

(3 citation statements)

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“…for the ratio of the amplitude-to-thickness w h max ( ) / of isotropic square plate with simply supported boundary conditions is shown in table 1. As seen, the results indicate a good agreement with other available literatures [65][66][67][68][69]. The material properties of graphene and PZT-4 are presented in appendix, which are taken from Refs.…”

Section: Validation Of the Studysupporting

confidence: 87%

Nonlinear dynamic modeling of smart graphene/piezoelectric composite nanoplates subjected to dual frequency excitation

Ebrahimi

Hosseini

2020

Eng. Res. Express

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The nonlinear frequency response of graphene/PZT/graphene nano composite subjected to multifrequency excitation is the objective of this paper. The nano composite is embedded on a visco-Pasternak foundation. Firstly, based on the nonlocal continuum theory and nonlinear von Karman strain-displacement relations, the nonlinear governing differential equation of motion is derived. Secondly, the Galerkin method is employed to transfer the partial differential equation to the ordinary differential equation. Then, the governing equation is solved based on the multiple time scales method. It is demonstrated that the multiple time scales is a useful analytical method to analyze nonlinear problems. Finally, the modulation equation under sub-harmonic and super-harmonic stimulation is studied. Emphasizing the influence of nonlinearity and dual frequency excitation, the nonlinear frequency response, phase angle and amplitude response of graphene/PZT/graphene nano composite are discussed. At the end, the numerical results are performed while the emphasis is placed on investigating the effect of nonlocal parameter, damping coefficient, multi-frequency external excitation, electric voltage load and visco-Pasternak foundation coefficients of the graphene/PZT/ graphene nano composite. The results illustrate that dual frequency excitation can intensify the nonlinear frequency response. In addition, the electric voltage as well as external excitation plays an important role in resonance phenomenon.

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Section: Validation Of the Studysupporting

confidence: 87%

Nonlinear dynamic modeling of smart graphene/piezoelectric composite nanoplates subjected to dual frequency excitation

Ebrahimi

Hosseini

2020

Eng. Res. Express

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“…Also, the material properties of graphene and PZT-4 are presented in Appendix 1, which are taken from [54,81]. Now, in order to evaluate the nonlinear numerical results, some strong researches have been used [82][83][84][85][86]. It is worth mentioning that these are identified as a benchmark and outstanding works among researches.…”

Section: Validation Of the Studymentioning

confidence: 99%

Nonlinear forced vibration of graphene/piezoelectric sandwich nanoplates subjected to a mechanical shock

Ghadiri

Hosseini

2019

Jnl of Sandwich Structures & Materials

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The nonlinear frequency response of graphene/piezoelectric sandwich nanoplates under the electric voltage exerted on piezoelectric layer and a shock force pulse is the objective of the present paper. First, using von Karman nonlinear relations, Kelvin-Voigt model, piezoelectric nonlocal elasticity theory and Hamilton's principle, the nonlinear governing differential equation of motion is derived. In the second step, to transform the partial differential equations to the ordinary differential ones, Galerkin technique is employed. Then, governing equation is solved based on multiple scale method. At the end, modulation equation of graphene/piezoelectric sandwich nanoplate is obtained. Emphasizing the effect of the electric voltage and the shock force pulse, the results for fundamental frequency response are obtained. The results emphasize that the exciting loads can cause multivaluedness in frequency response and intensify the jump phenomenon. Also, they can be effective to amplify the vibration behavior of the structure to make resonance. In addition, the thickness of piezoelectric layer plays a significant role in nonlinear frequency response.

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“…The large amplitude vibration of orthotropic plates was investigated by many scientists [3,4,8,9,11]. However most papers are devoted to research of nonlinear vibrations of plates and shallow shells with simple enough form.…”

Section: Introductionmentioning

confidence: 99%

Research of nonlinear vibrations of orthotropic plates with a complex form

Kurpa

Shmatko

Onufrienko

2006

Mathematical Problems in Engineering

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This paper deals with effects of large amplitude on the free and forced flexural vibrations of elastic orthotropic plates of arbitrary shape.R-function method (RFM) is applied to obtain the basis functions need for expansion of sought solution into Fourier series. The initial nonlinear system of differential equations with partial derivatives is reduced to system of ordinary nonlinear differential equations by Galerkin procedure. The solving-obtained system is carried out by Runge-Kutta or Galerkin methods. The numerical results for the plate of complex form and also rectangular form and different boundary conditions have been presented and compared with other known results.

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Nonlinear Vibration Analysis of Thin Laminated Rectangular Plates on Elastic Foundations

Cited by 18 publications

References 0 publications

Nonlinear dynamic modeling of smart graphene/piezoelectric composite nanoplates subjected to dual frequency excitation

Nonlinear dynamic modeling of smart graphene/piezoelectric composite nanoplates subjected to dual frequency excitation

Nonlinear forced vibration of graphene/piezoelectric sandwich nanoplates subjected to a mechanical shock

Research of nonlinear vibrations of orthotropic plates with a complex form

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