Size-dependent free vibration and dynamic analyses of piezo-electro-magnetic sandwich nanoplates resting on viscoelastic foundation (original) (raw)
Related papers
Applied Physics A, 2017
Magneto-electro-thermo-mechanical bending and free vibration analysis of a sandwich microplate using strain gradient theory is expressed in this paper. The sandwich plate is made of a core and two integrated piezomagnetic face sheets. The structure is subjected to electric and magnetic potentials, thermal loadings, and resting on Pasternak's foundation. Electromagnetic equations are developed by considering the variation form of Hamilton's principle. The effects of important parameters of this problem such as applied electric and magnetic potentials, direct and shear parameter of foundation, three microlength-scale parameters, and two parameters of temperature rising are investigated on the vibration and bending results of problem.
Acta Mechanica, 2016
Thermo-electro-mechanical transient analysis of a sandwich nanoplate is studied in this paper. The sandwich nanoplate consists of a Kelvin-Voigt viscoelastic nanoplate and two integrated piezoelectric face sheets resting on a visco-Pasternak foundation. The sandwich nanoplate is subjected to thermal and mechanical loads, and the piezoelectric face sheets are subjected to an applied electric potential. Two-variable sinusoidal shear deformation plate theory is used for the description of the displacement components. The governing equations of motion are derived using Hamilton's principle by calculation of strain and kinetic energies and energy due to external forces. The natural frequencies of the sandwich nanoplate are calculated in terms of three parameters of foundation, structural viscoelastic damping parameter and excitation frequency. Also, bending results of the problem in terms of the parameters of the temperature loadings are presented.
Mechanics Research Communications, 2017
Highlights Thermo-electro-magneto-mechanical bending analysis of a sandwich nanoplate is presented based on the Kirchhoff plate theory and nonlocal theory. The sandwich nanoplate includes an elastic nano-core and two piezomagnetic face-sheets actuated by applied electric and magnetic potentials. The governing equations for the electro-magneto-mechanical bending are derived in terms of the displacement components and electric and magnetic potentials. The effects of the nonlocal parameter, temperature rise, applied electric and magnetic potentials on the bending behaviors of sandwich nanoplates are investigated.
Surface effects on scale-dependent vibration behavior of flexoelectric sandwich nanobeams
2019
This paper infer the transient vibration of piezoelectric sandwich nanobeams, In present work, the flexoelectric effect on the mechanical properties of vibration piezoelectric sandwich nanobeam with different boundary conditions is investigated. According to the Nonlocal elasticity theory in nanostructures, the flexoelectricity is believed to be authentic for such size-dependent properties. The governing equations are derived by Hamilton*$39;s principle and boundary condition solved by Galerkin-based solution. This research develops a nonlocal flexoelectric sandwich nanobeam supported by Winkler-Pasternak foundation. The results of this work indicate that natural frequencies of a sandwich nanobeam increase by increasing the Winkler and Pasternak elastic constant. Also, increasing the nonlocal parameter at a constant length decreases the natural frequencies. By increasing the length to thickness ratio (L/h) of nanobeam, the nonlocal frequencies reduce.
Journal of Intelligent Material Systems and Structures, 2017
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.
Mechanics of Advanced Materials and Structures, 2018
In this article, two-variable sinusoidal shear deformation theory, nonlocal piezoelasticity relations incorporating with concept of neutral surface are employed for free vibration analysis of a sandwich nano-plate. Due to using the functionally graded materials, the concept of neutral surface must be employed through formulation of the problem. A parametric study is performed to show how natural frequencies of sandwich nano-plate are changed in terms of nonlocal parameter, non-dimensional geometric parameters and in-homogeneous index. Before presentation of full numerical results, a comparison with a valid reference is performed to confirm our formulations and corresponding numerical results.
Microsystem Technologies, 2018
In this present work the critical loading of magneto-electro-viscoelastic-hygro-thermal (MEVHT) piezoelectric nanoplates embedded in a viscoelastic foundation are investigated. Via two variable shear deformation plate theory displacement are obtained. The governing equations of nonlocal viscoelastic nanoplate are driven by using Hamilton's principle and solved by an analytical solution. A parametric study is presented to examine the effect of the nonlocal parameter, hygro-thermomagneto-electro-mechanical loadings and aspect ratio on the critical loading of MEVHT nanoplates. It is found that the critical loading is quite important to the mechanical loading, electric loading and magnetic loading, while it is insensitive to the hygro-thermal loading.
Size-dependent vibration and bending analyses of the piezomagnetic three-layer nanobeams
Applied Physics A, 2017
Nonlocal parameter ∇ 2 Laplacian operator , Electric and magnetic potentials xx , xz Stress components xx , xz Strain components C ijkl Stiffness coefficients e ijk Piezoelectric constants q ijk Piezomagnetic coefficients E k Electric field H k Magnetic field N ij , M ij Force and moment resultants D i ,B i Electric displacement and magnetic induction resultants T Kinetic energy U Strain energy k 1 , k 2 Parameters of Pasternak's foundation W External works K, J, P Stiffness, damping, and mass matrices F Force matrix L Length of beam Natural frequencies q Transverse loads U, Θ, W, Ψ, Φ Amplitude of unknown functions 0 , 0 Applied electric and magnetic potentials
Composites Part B: Engineering, 2018
This article investigates the effect of the magnetic field on the thermomechanical buckling and vibration of viscoelastic sandwich nanobeams in humid environment. The nanoscale beam is composed of a homogeneous core integrated with two functionally graded (FG) carbon nanotube (CNT) reinforced face sheets. The present sandwich nanobeam is subjected to in-plane compressive load as well as in-plane axial magnetic field and embedded in visco-Pasternak substrate that contains Kelvin-Voigt viscoelastic layer and Pasternak shear layer. The motion equations for the deformable sandwich nanobeam are deduced based on a shear and normal deformations beam theory incorporated with the modified couple stress theory that captures the size effect by involving a material length scale parameter. The present results are verified by comparing them with the previously published ones. Moreover, parametric studies have been performed to illustrate the impacts of material parameter, viscoelastic damping for the structure and the foundation, the magnetic field parameter, humidity concentration and other parameters on the buckling load and frequency of the FGCNT reinforced viscoelastic sandwich nanobeams.