Assessing effects of parameters of viscoelastic foundation on the dynamic response of functionally graded plates using a novel HSDT theory

Frahlia, Hamid; Bennai, Riadh; Nebab, Mokhtar; Atmane, Hassen Ait; Tounsi, Abdelouahed

doi:10.1080/15376494.2022.2062632

Cited by 23 publications

(4 citation statements)

References 75 publications

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“…Using the four-unknown plate theory with an improved trigonometric shear deformation function, Bounouara et al 56 investigated the vibration behavior of FG sandwich plates placed on the visco-Pasternak foundation, where the Galerkin technique was utilized in solving the governing equations. Frahlia et al 57 studied the vibrational response of the FG plate with a viscoelastic foundation, where the damping effect was represented by one additional term in the Winkler–Pasternak model. Based on the quasi-3D HSDT, Li et al 58 performed the free vibration analysis of FGM plates with different kinds of elastic foundations, such as Winkler, Pasternak, and Kerr foundation models.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic analysis of auxetic-FGM sandwich plates resting on a Kerr elastic substrate under blast loading

Dang,

Nguyen,

Tran

et al. 2024

Proceedings of the Institution of Mechanical Engineers, Part C:

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This study examines the nonlinear dynamic response of sandwich plates placed on the Kerr elastic substrate under blast loading. The plate is composed of an auxetic honeycomb core and functionally graded material (FGM) coating layers. The volume fraction of FGM is determined following the power-law model (P-FGM). The equations of motion of the plate are formulated by using the first-order shear deformation theory (FSDT) in conjunction with the use of the Airy stress function. The Runge-Kutta scheme, with the assistance of the Galerkin technique, is utilized in the present study to obtain numerical results for the nonlinear dynamic response of the plate. After verifying the proposed solution, the influences of material characteristics, blast loading, elastic substrate, and geometry parameters on the free vibration and nonlinear dynamic behavior of the plate are investigated comprehensively. The results show that negative Poisson’s ratio has a significant effect on the linear and nonlinear vibration characteristics of the auxetic-FGM sandwich plate.

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Section: Introductionmentioning

confidence: 99%

Nonlinear dynamic analysis of auxetic-FGM sandwich plates resting on a Kerr elastic substrate under blast loading

Dang,

Nguyen,

Tran

et al. 2024

Proceedings of the Institution of Mechanical Engineers, Part C:

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“…Frahlia et al [36] examined the vibration response of a functionally graded plate resting on a viscoelastic foundation. Alazwari and Zenkour [37] developed a quasi-3D refined theory for the linear vibration of functionally graded plates resting on visco-Winkler-Pasternak foundations.…”

Section: Introductionmentioning

confidence: 99%

On the Solution of Dynamic Stability Problem of Functionally Graded Viscoelastic Plates with Different Initial Conditions in Viscoelastic Media

Sofiyev

2023

Mathematics

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The widespread use of structural elements consisting of functionally graded (FG) materials in advanced technologies has led to extensive research. Due to the difficulties encountered during modeling and problem solving, the number of studies on the dynamic behavior of structural elements made of FG viscoelastic materials is quite limited compared to the number examining FG elastic materials. This study is one of the first attempts to solve the dynamical problem by the mathematical modeling of functionally graded viscoelastic plates (FG-VE-Ps) and viscoelastic media together with different initial conditions. FG-VE-Ps on viscoelastic foundations (VE-Fs) are assumed to be under compressive edge load in the longitudinal direction. The governing equations for FG-VE-Ps on VE-Fs are derived using Boltzmann and Volterra concepts. The problem is reduced to the solution of integro-differential equation system using the Galerkin method. Then, by performing Laplace transforms, new analytical expressions for the time-dependent deflection function and critical time at different initial conditions are found. The loss of stability of FG-VE-Ps on VE-Fs is modeled to cover three time-varying ranges: the first is the range in which the deflection function decreases; the second is the transition interval; the third is the increase range of deflection function, which leads to the loss of stability. The time corresponding to the sharp increase of the deflection function is defined as the critical time, and is determined both theoretically and numerically. The results are compared with the results obtained by various methods to confirm their accuracy. Finally, the effects of VE-Fs, VE material properties, and FG profiles on the critical time behavior of plates are studied numerically.

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“…A lot of research in the fabrication and analysis of functionally graded structures is going on. Studies on static and dynamic analysis on FGM plates have been performed by authors using methods such as higher-order shear deformation theory [37][38][39], and sinusoidal shear deformation [40] to name a few.…”

Section: Introductionmentioning

confidence: 99%

Deformation and stress analysis of rotating functionally graded hollow cylindrical body for variable heat generation

Sahu¹,

Sondhi²,

Bhowmick³

et al. 2022

Res. Eng. Struct. Mater.

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In the present study, one-dimensional steady-state temperature variation with variable heat generation was considered and thermo-mechanical stress and deformation analysis on a hollow functionally graded cylinder were then performed. A governing differential equation with a variable coefficient is solved using Navier's equation by applying thermal and mechanical boundary conditions. The effect of internal pressure and temperature, rotation, gravity, and heat generation, and their combined effect such as rotation and heat generation, gravity and heat generation, rotation, gravity, and heat generation were studied in a cylindrical body. The gradation properties varied radially as per power-law variation. The grading parameter ranging between -2 to 3, changes the material properties in the radial direction. A critical grading index was identified that lowers the induced stresses and hence an improvement in the performance of functionally graded cylinders can be obtained under the influence of a combination of loads. The validation of the results was carried out with published literature.

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Assessing effects of parameters of viscoelastic foundation on the dynamic response of functionally graded plates using a novel HSDT theory

Cited by 23 publications

References 75 publications

Nonlinear dynamic analysis of auxetic-FGM sandwich plates resting on a Kerr elastic substrate under blast loading

Nonlinear dynamic analysis of auxetic-FGM sandwich plates resting on a Kerr elastic substrate under blast loading

On the Solution of Dynamic Stability Problem of Functionally Graded Viscoelastic Plates with Different Initial Conditions in Viscoelastic Media

Deformation and stress analysis of rotating functionally graded hollow cylindrical body for variable heat generation

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