Size-dependent vibration and bending analyses of the piezomagnetic three-layer nanobeams (original) (raw)
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Journal of Sandwich Structures & Materials, 2017
In this work, an analytical solution for bending analysis of the three-layer curved nanobeams is presented. The nanobeams are including a nanocore and two piezomagnetic face-sheets. The structure is subjected to applied electric and magnetic potentials while is resting on Pasternak's foundation. To reach more accurate results, sinusoidal shear deformation theory is employed to derive displacement field of the curved nanobeams. In addition, nonlocal electro-magneto-elasticity relations are employed to derive governing equations of bending based on the principle of virtual work. The analytical results are presented for simply supported curved nanobeam to discuss the influence of important parameters on the vibration and bending results. The important parameters are included spring and shear parameters of the foundation, applied electric and magnetic potentials, nonlocal parameter, and radius of curvature of curved nanobeam.
Acta Mechanica, 2017
The present paper develops a transient formulation for a three-layer curved nanobeam in thermomagneto-elastic environments. The sinusoidal shear deformation theory is employed to derive the displacement field of a curved nanobeam and governing equations of motion based on nonlocal elasticity formulation and Hamilton's principle. The curved nanobeam includes a nanocore and two integrated piezo-magnetic layers subjected to electric and magnetic potentials and transverse loads resting on a Pasternak foundation. The analytical solution is presented to investigate the influence of excitation frequency, nonlocal parameter and applied electric and magnetic potentials on the dynamic responses of the curved nanobeam. It can be concluded that an increase in nonlocal parameter decreases the stiffness of the curved nanobeam and consequently increases radial and transverse deflections.
Applied Physics A, 2021
A numerical investigation is performed to examine the static bending behavior of piezoelectric nanoscale beams subjected to electrical loading, considering flexoelectricity effects and different kinematic boundary conditions. The nanobeams are modeled by the Bernoulli-Euler beam theory, and the stress-driven integral nonlocal model is used in order to capture size influences. It is also considered that the nanobeams are embedded in an elastic medium. The Winkler and Pasternak elastic foundation models are used for simulating the substrate medium. Based upon Hamilton's principle and the electrical Gibbs free energy, the governing equations are derived which are then numerically solved via a finite difference-based method. Numerical results are presented to study the influences of nonlocal, flexoelectric and Winkler/Pasternak parameters on the bending response of piezoelectric nanobeams under various end conditions.
Size-dependent analysis of a sandwich curved nanobeam integrated with piezomagnetic face-sheets
Results in physics, 2017
The aim of this research is to develop nonlocal transient magneto-electro-elastic formulation of a sandwich curved nanobeam including a nano-core and two piezo-magnetic face-sheets subjected to transverse mechanical loads and applied electric and magnetic potentials rest on Pasternak's foundation. Nonlocal magneto-electro-elastic relations and Hamilton's principle are used for derivation of the governing equations of motion. The analytical solution based on Fourier solution is presented for a simply-supported sandwich curved nanobeam. The numerical results are presented to investigate influence of significant parameters such as nonlocal parameter, radius of curvature, applied electric and magnetic potentials and two parameters of Pasternak's foundation on the dynamic responses of sandwich curved nanobeam.
Journal of Sandwich Structures and Materials, 2016
This article presents a simplified three-unknown shear and normal deformations nonlocal beam theory for the bending analysis of nanobeams in thermal environment. Eringen's nonlocal constitutive equations are considered in the analysis. Governing equations are derived according to the present refined theory using Hamilton's principle. Central deflections of nanobeams under uniform and point loads are given and compared with the available ones in the literature. Additional results of displacement and stresses are presented for future comparison. The effects of nonlocality, temperature parameters, length of beam, length-to-depth ratio as well as shear and normal strains are all investigated.
Bending, Buckling and Free Vibration Analyses of Nanobeam-Substrate Medium Systems
Facta Universitatis, 2022
This study presents a newly developed size-dependent beam-substrate medium model for bending, buckling, and free-vibration analyses of nanobeams resting on elastic substrate media. The Euler-Bernoulli beam theory describes the beam-section kinematics and the Winkler-foundation model represents interaction between the beam and its underlying substrate medium. The reformulated strain-gradient elasticity theory possessing three non-classical material constants is employed to address the beam-bulk material smallscale effect. The first and second constants is associated with the strain-gradient and couplestress effects, respectively while the third constant is related to the velocity-gradient effect. The Gurtin-Murdoch surface elasticity theory is adopted to account for the surface-free energy. To obtain the system governing equation as well as corresponding boundary conditions, Hamilton's principle is called for. Three numerical simulations are presented to characterize the influences of the material small-scale effect, the surface-energy effect, and the surrounding substrate medium on bending, buckling, and free vibration responses of
Nonlinear free vibration of piezoelectric nanobeams incorporating surface effects
2014
In this study, the nonlinear free vibration of piezoelectric nanobeams incorporating surface effects (surface elasticity, surface tension, and surface density) is studied. The governing equation of the piezoelectric nanobeam is derived within the framework of Euler‐Bernoulli beam theory with the von K´ arm´ an geometric nonlinearity. In order to satisfy the balance conditions between the nanobeam bulk and its surfaces, the component of the bulk stress, zz, is assumed to vary linearly through the nanobeam thickness. An exact solution is obtained for the natural frequencies of a simply supported piezoelectric nanobeam in terms of the Jacobi elliptic functions using the free vibration mode shape of the corresponding linear problem. Then, the influences of the surface effects and the piezoelectric field on the nonlinear free vibration of nanobeams made of aluminum and silicon with positive and negative surface elasticity, respectively, have been studied for various properties of the pie...
Mechanical Response of a Piezoelectrically Sandwiched Nano-beam Based on the Nonlocal Theory
International Journal of Engineering, 2012
This article deals with the mechanical analysis of a fixed-fixed nano-beam based on nonlocal theory of elasticity. The nano-beam is sandwiched with two piezoelectric layers through its upper and lower surfaces. The electromechanical coupled equations governing the problem are derived based on nonlocal theory of elasticity considering Euler-Bernoulli beam assumptions. Also, nonlocal piezoelectricity is according to Maxwell's electrostatic equations. The piezoelectric layers are subjected to a voltage to tune the stiffness of the nano-beam. The equations are solved through step by step linearization method and Galerkin's weighted residual method. The results are compared with those of the local model. The effect of piezoelectric voltages on the non-locality of the model is investigated as well.
Vibration analysis of three-layered nanobeams based on nonlocal elasticity theory
Journal of Theoretical and Applied Mechanics, 2017
In this paper, the first investigation on free vibration analysis of three-layered nanobeams with the shear effect incorporated in the mid-layer based on the nonlocal theory and both Euler Bernoulli and Timoshenko beams theories is presented. Hamilton's formulation is applied to derive governing equations and edge conditions. In order to solve differential equations of motions and to determine natural frequencies of the proposed three-layered nanobeams with different boundary conditions, the generalized differential quadrature (GDQM) is used. The effect of the nanoscale parameter on the natural frequencies and deflection modes shapes of the three layered-nanobeams is discussed. It appears that the nonlocal effect is important for the natural frequencies of the nanobeams. The results can be pertinent to the design and application of MEMS and NEMS.
2020
The presented article investigates vibration sensitivity analysis of Nano-mechanical piezo-laminated beams with consideration of size effects. To do this, the vibration governing equation of the stepped Nano-mechanical piezo-laminated beam is firstly derived by implementation of the nonlocal elasticity theory. The nonlocal formulation is considered for both of the beam and the piezoelectric layer and the obtained equation is solved analytically. Moreover, there is a need to recognize the importance and relative effects of the beam parameters on the natural frequencies and resonant amplitudes of the nonlocal beam. Therefore, the Sobol sensitivity analysis is utilized to investigate the relative effects of geometrical and the nonlocal parameters on the natural frequencies and the resonant amplitude of the nanobeam. The obtained results show that the length and the thickness of the piezoelectric layer have prominent effects on the vibration characteristics of the beam. Moreover, it is ...