Size-dependent nonlinear forced vibration analysis of magneto-electro-thermo-elastic Timoshenko nanobeams based upon the nonlocal elasticity theory

In this article, free vibration behavior of magneto–electro–thermo-elastic functionally graded nanobeams is investigated based on a higher order shear deformation beam theory. Four types of thermal loading including uniform and linear temperature change as well as heat conduction and sinusoidal temperature rise through the thickness are assumed. Magneto–electro–thermo-elastic properties of FG nanobeam are supposed to change continuously throughout the thickness based on power-law model. Via nonlocal elasticity theory of Eringen, the small size effects are adopted. Based upon Hamilton’s principle, the coupled nonlocal governing equations for higher order shear deformable METE-FG nanobeams are obtained and they are solved applying analytical solution. It is shown that the vibrational behavior of METE-FG nanobeams is significantly affected by various temperature rises, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio.

Dynamic modeling of a thermo–piezo-electrically actuated nanosize beam subjected to a magnetic field

Free vibration behaviour of multiphase and layered magneto-electro-elastic beam

The present paper examines the thermal buckling of nonlocal magneto-electro-thermo-elastic functionally graded (METE-FG) beams under various types of thermal loading namely uniform, linear and sinusoidal temperature rise and also heat conduction. The material properties of nanobeam are graded in the thickness direction according to the power-law distribution. Based on a higher order beam theory as well as Hamilton's principle, nonlocal governing equations for METE-FG nanobeam are derived and are solved using Navier type method. The small size effect is captured using Eringen's nonlocal elasticity theory. The most beneficial feature of the present beam model is to provide a parabolic variation of the transverse shear strains across the thickness direction and satisfies the zero traction boundary conditions on the top and bottom surfaces of the beam without using shear correction factors. Various numerical examples are presented investigating the influences of thermo-mechanical loadings, magnetic potential, external electric voltage, power-law index, nonlocal parameter and slenderness ratio on thermal buckling behavior of nanobeams made of METE-FG materials.

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Buckling Analysis of Smart Size-Dependent Higher Order Magneto-Electro-Thermo-Elastic Functionally Graded Nanosize Beams

Buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic circular cylindrical shells

The free vibrations of simply supported magneto-electro-elastic cylindrical shells are studied. A series solution is assumed in the circumferential and axial directions of the shell to preserve the three-dimensional character of the structure. The constitutive equations of the magneto-electro-elastic medium involving mechanical, electrical and magnetic fields are used to derive the finite element model for the system. The influence of the piezomagnetic effect on the structural frequencies of the cylindrical shell is studied. A comparison is made between a shell with a layered configuration and one with a multiphase system. The study is carried out for a typical shell with simply supported boundary conditions for different ratios of length to radius and radius to thickness to analyse the frequency behaviour.

Free vibrations of simply supported layered and multiphase magneto-electro-elastic cylindrical shells

The paper deals with the investigation of linear buckling and free vibration behavior of layered and multiphase magneto‐electro‐elastic (MEE) beam under thermal environment. The constitutive equations of magneto‐electro‐elastic materials are used to derive finite element equations involving the coupling between mechanical, electrical and magnetic fields. The finite element model has been verified with the commercial finite element package ANSYS. The influence of magneto electric coupling on critical buckling temperature is investigated between layered and multiphase magneto‐electro‐elastic beam. Furthermore, the influence of temperature rise on natural frequencies of magneto‐electro‐elastic beam with layered and different volume fraction is presented.

Buckling and Vibration Analysis of Layered and Multiphase Magneto‐Electro‐Elastic Beam Under Thermal Environment

In this paper, a three-layered electro-magneto-elastic strip is investigated under a plane stress condition using finite element procedures. Two types of thermal loading, uniform temperature rise and non-uniform temperature distribution, are used. A two-dimensional rectangular element with four nodal degrees of freedom viz. thermal displacements in the x1 and x3 directions, and electric and magnetic potentials, is used to discretize the finite element model. The uncoupled and coupled analysis is carried out for two types of stacking sequence (B/F/B and F/B/F) under fixed–fixed and fixed–simply supported boundary conditions. Steady-state analysis is carried out to study the influence of piezo and magnetic constants on displacement, electric and magnetic potential across the thickness direction. It is found that the discontinuities of normal stress σ1 occur on interfaces of two dissimilar materials across the thickness direction.

https://iopscience.iop.org/article/10.1088/0964-1726/16/2/006/pdf

N Ganesan

Papers

Free vibrations of simply supported layered and multiphase magneto-electro-elastic cylindrical shells

Buckling and Vibration Analysis of Layered and Multiphase Magneto‐Electro‐Elastic Beam Under Thermal Environment

Steady-state analysis of a three-layered electro-magneto-elastic strip in a thermal environment