Effect of the Viscoelastic Foundations on the Free Vibration of Functionally Graded Plates

Khetib, Mounia; Abbad, Hichem; Elmeiche, N.; Mechab, Ismail

doi:10.1142/s0219455419501360

Cited by 12 publications

(2 citation statements)

References 46 publications

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“…Fernandes and Pouget (2001) presented an efficient two-dimensional approach for piezoelectric plates in the framework of the linear theory of piezoelectricity using a variational method. Based on higher-order shear deformation theory and using the principle of virtual displacements, Khetib et al (2019) studied the vibration behavior of an FGM plate resting on a viscoelastic Winkler-Pasternak foundation. Based on concepts of Boltzmann and Volterra, Sofiyev, Zerin, and Kuruoglu (2020) investigated free vibrations and the dynamic stability of an FGM viscoelastic plate under a compressive load and resting on elastic foundations using the Galerkin and Laplace integral transform.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers

Feri

Krommer

Alibeigloo

2021

Mechanics Based Design of Structures and Machines

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The three-dimensional bending behavior of a viscoelastic functionally graded material (FGM) layer embedded between piezoelectric layers and subjected to an electric field as well as a uniform transverse pressure is studied. An analytical solution is computed for a simply supported viscoelastic smart FGM plate using the state space technique along the thickness direction and a Fourier expansion along the in-plane coordinates. The governing differential equations in the time domain are transformed to the Laplace domain, solved in the Laplace domain, and transformed back to the time domain using the inverse Laplace transform. In the present study, the relaxation modulus of the FGM layer is assumed in the form of a Prony series, and it varies according to the power law in the thickness direction. The validity of the proposed approach is assessed by comparison of the numerical results of the approach with those of published works in the literature. The effects of geometric dimensions, electromechanical loads, and relaxation time constant on the behavior of the smart plate are investigated.

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Section: Introductionmentioning

confidence: 99%

Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers

Feri

Krommer

Alibeigloo

2021

Mechanics Based Design of Structures and Machines

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“…The effects of the foundation parameters on the free and forced vibration of the plate are discussed. Also, many researchers have considered the three-parameter viscoelastic Pasternak model in their analysis to include the effect of the shear modulus of the foundation (Khetib et al 2019;Hashemi et al 2015aHashemi et al , 2015b. Zamani et al (2017) analyzed the transient response of the viscoelastic laminated composite plates on the viscoelastic Pasternak foundation.…”

Section: Introductionmentioning

confidence: 99%

On the transient response of plates on fractionally damped viscoelastic foundation

Praharaj

Datta

2020

Comp. Appl. Math.

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This work underlines the importance of the application of fractional-order derivative damping model in the modelling of the viscoelastic foundation, by demonstrating the effect of various orders of the fractional derivative on the dynamic response of plates resting on the viscoelastic foundation, subjected to concentrated step load. The foundation of the plate is modelled as a fractionally-damped Kelvin-Voigt model. Modal superposition method and Triangular strip matrix approach are used to solve the partial fractional differential equations of motion. The influence of (a) fractional-order derivative, (b) foundation stiffness, and (c) foundation damping viscosity parameter on the dynamic response of the plate are investigated. Theoretical results show that with the increase in the order of derivative, the damping of the system increases, which leads to decreased dynamic response. The results obtained from the fractional-order damping model and integer-order damping model are compared. The results are verified with literature and numerical results (ANSYS).

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Analytical Solution of the Problem of Free Vibrations of a Plate Lying on a Variable Elastic Foundation

Surianinov

Krutii²,

Osadchiy³

et al. 2022

Mechanisms and Machine Science

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Effect of the Viscoelastic Foundations on the Free Vibration of Functionally Graded Plates

Cited by 12 publications

References 46 publications

Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers

Three-dimensional static analysis of a viscoelastic rectangular functionally graded material plate embedded between piezoelectric sensor and actuator layers

On the transient response of plates on fractionally damped viscoelastic foundation

Analytical Solution of the Problem of Free Vibrations of a Plate Lying on a Variable Elastic Foundation

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