Large amplitude free vibration study of non-uniform plates with in-plane material inhomogeneity

Proceedings of the Institution of Mechanical Engineers, Part L:

Azam

2021

In the present work, effect of hygrothermal environment on vibration and buckling behavior of embedded functionally graded elliptical plate under uniform in plane compression is studied. The properties of elliptical plate vary in transverse direction following power law. The functionally graded elliptical plate is considered to be resting on the Winkler–Pasternak elastic foundation. The governing equations are derived using the principle of virtual work and solved by employing the Rayleigh–Ritz method. The algebraic polynomials are employed to satisfy the different boundary constraints. The advantage of the presented mathematical model over the previously reported methods is that it eliminates the constraints regarding edge conditions, and it is simple and computationally fast. The inclusive results depicting the effect of various parameters namely, material property exponents, foundation parameters, aspect ratio on mechanical and thermomechanical buckling, and natural frequency of embedded functionally graded elliptical plate in a hygrothermal environment are reported after the test of convergence and extensive comparisons. The study shows that increase in foundation moduli lead to an increase in natural frequency and buckling parameter. Furthermore, it is noticed that the temperature and moisture concentration remarkably affect the buckling and vibration behavior of functionally graded elliptical plate.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Buckling and free vibration characteristics of embedded inhomogeneous functionally graded elliptical plate in hygrothermal environment

Proceedings of the Institution of Mechanical Engineers, Part L:

Azam

2021

“…Sixteen natural frequencies were obtained for different taper ratio and boundary conditions. Kumar et al 34 investigated the free vibration of non-uniform plate with considering the geometric nonlinearity. The formulation based on non-linear strain-displacement relation was developed for the simply supported plate.…”

Section: Introductionmentioning

confidence: 99%

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

Kumar

Proceedings of the Institution of Mechanical Engineers, Part L:

Saran

et al. 2020

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.

“…However, the last method is cumbersome as it requires a large set of trigonometric terms and a high number of iterations. Kumar et al 18 analyzed the vibration response of a plate with in-plane material inhomogeneity using the energy method and nonlinear strain-displacement relations. Saidi et al 19 used Navier equations to solve classical elastostatic and elastodynamic problems of plates.…”

Section: Introductionmentioning

confidence: 99%

“…Kumar et al. 18 analyzed the vibration response of a plate with in-plane material inhomogeneity using the energy method and nonlinear strain–displacement relations. Saidi et al.…”

Section: Introductionmentioning

confidence: 99%

Size-dependent natural frequencies of functionally graded plate with out of plane material inhomogeneity using Eringen’s theory of nonlocal elasticity

Proceedings of the Institution of Mechanical Engineers, Part L:

Azam

Ranjan

2019

Nonlocal effect is one of the critical reasons which cause an extraordinary vibration response in small-scale structures. In the present work, vibration characteristics of functionally graded nonlocal plate are studied using Eringen’s nonlocal classical elasticity theory. A computationally efficient numerical method has been proposed in this study by reformulating the classical plate theory and Rayleigh–Ritz method using nonlocal differential relationship of Eringen’s theory in conjugation with algebraic polynomial displacement functions. The reformulated method helps to evaluate the natural frequencies of functionally graded nonlocal plates subjected to all possible combinations of edge conditions. The material properties are assumed to vary through the thickness of the plate following the power law. The computed results of natural frequencies are first tested for convergence and then validated with the published one. A parametric study has been thoroughly conducted focusing on the effects of aspect ratio, nonlocal parameter, material property index and Young’s modulus ratio on the natural frequency parameters of the functionally graded nonlocal plate. It has been observed that the material property index and aspect ratio affect the vibration behaviour of the functionally graded plate. The study also establishes that nonlocal effect has a pronounced influence on the higher modes of vibration of functionally graded plate. 3D mode shapes of functionally graded material nonlocal plate have also been reported.