Surface effect on the biaxial buckling and free vibration of FGM nanoplate embedded in visco-Pasternak standard linear solid-type of foundation

Abstract

In this study, nonlocal elasticity theory in conjunction with Gurtin-Murdoch elasticity theory is employed to investigate biaxial buckling and free vibration behavior of nanoplate made of functionally graded material (FGM) and resting on a viscoPasternak standard linear solid-type of the foundation. The material characteristics of simply supported FGM nanoplates are assumed to be varied continuously as a power law function of the plate thickness. Hamilton's principle is implemented to derive the non-classical governing equations of motion and related boundary conditions, which analytically solved to obtain the explicit closed-form expression for complex natural frequencies and buckling loads. Finally, attention is focused on considering the influences of various parameters on variation of damped natural frequency and buckling load ratio such as nonlocal parameter, surface effects, geometric parameters, power law index and properties of visco-Pasternak foundation and it is clearly demonstrated that these factors highly affect on vibration and buckling behavior.

Sound Transmission Loss of a Honeycomb Sandwich Cylindrical Shell with Functionally Graded Porous Layers

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Nanoscale mass nanosensor based on the vibration analysis of embedded magneto-electro-elastic nanoplate made of FGMs via nonlocal Mindlin plate theory

“…Here, q refers to the transverse load per unit area of FG-MEE nanoplate due to the added nanoparticle with mass m e for eth mass in position (x e ; y e ), Pasternak elastic medium, and external loads which can be expressed as (Shen et al 2012;Hosseini et al 2016a)…”

Existence of solution in the bending of thin plates with Gurtin–Murdoch surface elasticity

“…The recent literature continues to emphasize the development of predictive models to accommodate the behavior of structures at smaller scales (for example, nanobeams and nanoplates) by incorporating the contribution of size effects to overall elastic deformation [1][2][3][4]. It is well known that, as the thickness of typical plate-and shell-type structures tends toward the nanoscale, the effects of size dependence dominate and classical theories fail to adequately predict accurate deformation fields.…”