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Assessment of Reuss, Tamura, and LRVE models for vibration analysis of functionally graded nanoplates

Shahsavari Davood, Karami Behrouz

Archives of Civil and Mechanical Engineering

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2022

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Vol. 22, no. 2

art. no. e92, 1--13

EN

Majority of structural analysis on functionally graded materials utilized Voigt and Mori-Tanaka micromechanical modelling. The current article is focused on free vibration response of inhomogeneous nano-size plate resting on elastic foundations against different micromechanical models (i.e., Reuss, Tamura, and LRVE). For the elastic foundation type, Winkler, Pasternak, and Kerr mediums are modelled one by one. The nanoplate is modelled based on a quasi-3D shear deformation plate theory which is in relation with general strain gradient theory by employing Hamilton principle, then the model is solved analytically via Navier solution procedure. This exact model determines fourfold coupled (stretching-axial-bending-shear) response with estimating softening-stiffness and hardening-stiffness mechanisms of nano-sized systems. Finally, numerical results are provided to represent the influence of size-dependent effects on vibrations of embedded nanoplate obtained through different micromechanical models.

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Effect of kerr foundation and in-plane forces on free vibration of fgm nanobeams with diverse distribution of porosity

Jankowski Piotr

Acta Mechanica et Automatica

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2020

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Vol. 14, no. 3

135--143

EN

In the present paper, the effect of diverse distribution of functionally graded porous material and Kerr elastic foundation on natu-ral vibrations of nanobeams subjected to in-plane forces is investigated based on the nonlocal strain gradient theory. The displacement field of the nanobeam satisfies assumptions of Reddy higher-order shear deformation beam theory. All the displacements gradients are assumed to be small, then the components of the Green-Lagrange strain tensor are linear and infinitesimal. The constitutive relations for functionally graded (FG) porous material are expressed by nonlocal and length scale parameters and power-law variation of material pa-rameters in conjunction with cosine functions. It created possibility to investigate an effect of functionally graded materials with diverse dis-tribution of porosity and volume of voids on mechanics of structures in nano scale. The Hamilton’s variational principle is utilized to derive governing equations of motion of the FG porous nanobeam. Analytical solution to formulated boundary value problem is obtained in closed-form by using Navier solution technique. Validation of obtained results and parametric study are presented in tabular and graphical form. Influence of axial tensile/compressive forces and three different types of porosity distribution as well as stiffness of Kerr foundation on natural frequencies of functionally graded nanobeam is comprehensively studied.

3

Mathematical modeling and stochastic stability analysis of viscoelastic nanobeams using higher-order nonlocal strain gradient theory

Pavlović I. R., Pavlović R., Janevski G.

Archives of Mechanics

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2019

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Vol. 71, nr 2

137--153

EN

This paper analyzes stochastic vibrations of a viscoelastic nanobeam under axial loadings. Based on the higher-order nonlocal strain gradient theory and the Liapunov functional method, bounds of the almost sure asymptotic stability of a nanobeam are obtained as a function of retardation time, variance of the stochastic force, higher-order and lower-order scale coefficients, strain gradient length scale, and intensity of the deterministic component of axial loading. Analytical results from this study are first compared with those obtained from the Monte Carlo simulation. Numerical calculations are performed for the Gaussian and harmonic non-white processes as models of axial forces.