Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation

Abstract

This work is devoted to the free vibration nonlocal analysis of an elastic three-layered nanoplate with exponentially graded graphene sheet core and piezomagnetic face-sheets. The rectangular elastic three-layered nanoplate is resting on Pasternak’s foundation. Material properties of the core are supposed to vary along the thickness direction based on the exponential function. The governing equations of motion are derived from Hamilton’s principle based on first-order shear deformation theory. In addition, Eringen’s nonlocal piezo-magneto-elasticity theory is used to consider size effects. The analytical solution is presented to solve seven governing equations of motion using Navier’s solution. Eventually, the natural frequency is scrutinized for different side length ratio, nonlocal parameter, inhomogeneity parameter, and parameters of foundation numerically. The comparison with various references is performed for validation of our analytical results.

Properties of multifunctional composite materials based on nanomaterials: a review

“…The study performs a comparative assessment between the proposed theory and other approaches for varying geometric corrugations and non-local parameters. Are et al 139 developed non-local constitutive relations for piezomagnetic face-sheets and exponentially graded core. The FSDT-based Hamilton's principle was used to derive the governing equations.…”

New hybrid approach for free vibration and stability analyses of axially functionally graded Euler-Bernoulli beams with variable cross-section resting on uniform Winkler-Pasternak foundation

“…Thus, the variation of minor axis moment of inertia and cross-sectional area in the local coordinate are described as follows: The non-uniformity parameter (α) can change from zero (prismatic beam) to a range of [-2 to -0.1] for non-uniform beams. Exponential variation of geometrical and/or material properties is regarded as one of the most special states of members that few numerical methods such as differential transformation method, generalized differential quadrature, method finite element method, and power series approach can solve its governing differential equation (Mohanty et al, 2012;Li et al, 2013Li et al, , 2018Ebrahimi and Mokhtari, 2015;Wang et al, 2016;Khaniki and Rajasekaran, 2018;Arefi et al, 2018;Soltani and Asgarian, 2019). Regarding the power series method for solving the linear differential equation, all variable coefficients should be represented in a polynomial form.…”

Size-dependent bending behavior of three-layered doubly curved shells: Modified couple stress formulation

“…Strain energy of three-layered small scale doubly curved piezoelectric shell based on couple stress formulation for isotropic core and integrated piezoelectric layers considering piezoelectric effect are defined based on the relation U=12∫​(σiεi+miχi−DiEi)dV [4,6]. Substitution of components of strain, curvature, and electric field into above equations and definition of resultant component, the variation of strain energy is defined as in which the resultant components are defined in Appendix 2.…”

“…Size-dependent analysis was performed using micro length scale parameter associated with modified couple stress theory. Size-dependent free vibration analysis of three-layered exponentially graded nanoplate with piezomagnetic face-sheets resting on Pasternak’s foundation was studied based on nonlocal elasticity theory and first-order shear deformation theory [6]. Free vibration analysis of laminated composite doubly curved shells was studied by Chandrashekhara [7] based on first-order shear deformation theory.…”