Exact Solution for Free Vibration and Buckling of Sandwich S-FGM Plates on Pasternak Elastic Foundation with Various Boundary Conditions

Singh, S. J.; Harsha, S. P.

doi:10.1142/s0219455419500287

Cited by 49 publications

(19 citation statements)

References 53 publications

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“…Shen and Wang 15 reported the small to large amplitude vibration of rectangular FGM plates using Mori-Tanaka and Voigt model for effective determination of properties in the thickness direction. Singh and Harsha 16 investigated the vibration and buckling characteristics of sandwich plates made of FGM resting on an elastic foundation.…”

Section: Introductionmentioning

confidence: 99%

“…Galerkin-Vlasov's method for free vibration analysis of tapered FGM plate is not available in the literature. The available literature on Galerkin-Vlasov's method 16,[37][38][39] is limited to the analysis of uniform plate. In most of the research, tapered plate is formulated based on first-order shear deformation theory (FSDT) or some polynomial-based higher order shear deformation theory (HSDT) which is unable to capture the realistic responses of the plate.…”

Section: Introductionmentioning

confidence: 99%

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Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

Kumar

Singh

Saran

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part L:

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The present paper investigates the free vibration analysis for functionally graded material plates of linearly varying thickness. A non-polynomial higher order shear deformation theory is used, which is based on inverse hyperbolic shape function for the tapered FGM plate. Three different types of material gradation laws, specifically: a power (P-FGM), exponential (E-FGM), and sigmoid law (S-FGM) are used to calculate the property variation in the thickness direction of FGM plate. The variational principle has been applied to derive the governing differential equation for the plates. Non-dimensional frequencies have been evaluated by considering the semi-analytical approach viz. Galerkin-Vlasov’s method. The accuracy of the preceding formulation has been validated through numerical examples consisting of constant thickness and tapered (variable thickness) plates. The findings obtained by this method are found to be in close agreement with the published results. Parametric studies are then explored for different geometric parameters like taper ratio and boundary conditions. It is deduced that the frequency parameter is maximum for S-FGM tapered plate as compared to E- and P-FGM tapered plate. Consequently, it is concluded that the S-FGM tapered plate is suitable for those engineering structures that are subjected to huge excitations to avoid resonance conditions. In addition, it is found that the taper ratio is significantly affected by the type of constraints on the edges of the tapered FGM plate. Some novel results for FGM plate with variable thickness are also computed that can be used as benchmark results for future reference.

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

Kumar

Singh

Saran

et al. 2020

Proceedings of the Institution of Mechanical Engineers, Part L:

View full text Add to dashboard Cite

show abstract

“…The advantages of S-FGM plate over P-FGM plate lie in the fact that the former provides more strength and stiffness under the same working conditions [23][24][25][26]. Duc and Cong [23] analyzed the perfect rectangular and sandwich circular [24,25] S-FGM plate for nonlinear dynamic analysis.…”

Section: Introductionmentioning

confidence: 99%

“…It was found that the dynamic response of S-FGM plate can be controlled by varying various parameters such as volume fraction, elastic foundation, imperfection, and geometrical parameters. Recently, Singh and Harsha [26] presented a study for the first time for free vibration and buckling analysis of symmetric and asymmetric sandwich S-FGM plate resting on elastic foundation with different boundary conditions. New modified sigmoid functions are developed and used for sandwich plate keeping in mind the smooth variation of constituent material across the thickness of the plate.…”

Section: Introductionmentioning

confidence: 99%

“…Till now, very limited studies have been reported on sandwich S-FGM plates due to the complexity of constituent distribution. The advantages of S-FGM plate over other common FGM models lie in the fact that the former provides more strength and stiffness under the same working conditions [23][24][25][26]. Also, the stress concentrations occur at the interfaces in case of P-and E-FGM plate where the material is continuous but rapidly changing [37] and to avoid this Chung and Chi [38] proposed model consisting of two-power law function known as S-FGM.…”

Section: Introductionmentioning

confidence: 99%

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Analysis of porosity effect on free vibration and buckling responses for sandwich sigmoid function based functionally graded material plate resting on Pasternak foundation using Galerkin Vlasov’s method

Singh

Harsha

2020

Jnl of Sandwich Structures & Materials

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The objective of the present paper is to study the effect of porosity on vibration and buckling responses for sandwich plate supported with different boundary conditions at the edges. The formulation is performed for recently developed sandwich plate using new modified sigmoid function based functionally graded material plate of different symmetric and asymmetric configurations. Three different types of porosity are considered viz. even, uneven but symmetric, and uneven but non-symmetric. A new uneven non-symmetric porosity model is used in which micro-voids are varied in accordance with material property variation in the thickness direction in order to capture the accurate distribution of voids on the plate. The variational principle is employed to derive equilibrium equations. A closed form solution is obtained using the assumed solution with shape functions satisfying the edge boundary conditions using Galerkin Vlasov's method. Free vibration

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Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

et al. 2023

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In this article, various non‐polynomial higher‐order shear deformation theories are applied for the first time to analyze the free vibration and transient responses of plates with functionally graded material (FGM) supported on an elastic foundation. The shear deformation theories account for the non‐linear variation of the transverse shear strains with various warping functions, namely trigonometric, inverse hyperbolic, and inverse trigonometric ones. These models also inherently satisfy the traction‐free boundary conditions of transverse shear stresses at the top and bottom surfaces of the plates and do not require any shear correction factor. A two‐parameter model, namely Winkler‐Pasternak's elastic foundation model, is utilized to develop the interaction between the FGM plates and the elastic medium. The governing equations of motion are obtained using Hamilton's principle and solved analytically using Navier's solution scheme. Furthermore, the transient responses of the plates are obtained using Newmark's average acceleration method. The applicability of the present theories is established by solving several numerical problems and validating the results with the solutions available in the literature. The effects of various parameters like span‐thickness ratios, aspect ratios, gradation coefficients, mechanical loads, and foundation stiffness on the fundamental frequencies and the transient responses of the plates are thoroughly investigated. The comparison of the results reveals the efficiency of the non‐polynomial functions, and the capability of efficient prediction of the structural responses of the FGM plates at a similar computational cost compared to established models in the literature. Furthermore, the results show that the stiffness of the elastic foundation can tweak the stiffness characteristics of the FGM plate resulting in significant changes in the natural frequencies and more controlled displacement‐time responses.

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Exact Solution for Free Vibration and Buckling of Sandwich S-FGM Plates on Pasternak Elastic Foundation with Various Boundary Conditions

Cited by 49 publications

References 53 publications

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

Exact solution for free vibration analysis of linearly varying thickness FGM plate using Galerkin-Vlasov’s method

Analysis of porosity effect on free vibration and buckling responses for sandwich sigmoid function based functionally graded material plate resting on Pasternak foundation using Galerkin Vlasov’s method

Assessment of non‐polynomial shear deformation theories for the free vibration and transient analysis of plates with functionally‐graded materials supported on an elastic foundation

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