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Journal ArticleDOI

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

01 Apr 2007-Multidiscipline Modeling in Materials and Structures (Emerald Group Publishing Limited)-Vol. 3, Iss: 4, pp 461-476
Abstract: 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.
Topics: Finite element method (56%), Beam (structure) (54%), Buckling (52%), Magneto (51%), Vibration (51%)
Citations
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Journal ArticleDOI
23 Mar 2016-Applied Physics A
Abstract: 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.

131 citations


Journal ArticleDOI
Abstract: In this article, a nonlocal geometrically nonlinear beam model is developed for magneto-electro-thermo-elastic (METE) nanobeams subjected to external electric voltage, external magnetic potential and uniform temperature rise. The effects of transverse shear deformation, rotary inertia and geometric nonlinearity are taken into account through using the Timoshenko beam theory together with von Karman’s hypothesis. Also, the size-dependent nonlinear forced vibration behavior of METE nanobeams under different model parameters is studied based on an efficient numerical solution procedure. The governing equations and boundary conditions are obtained on the basis of Hamilton’s principle which are then discretized via the generalized differential quadrature (GDQ) method. A numerical Galerkin procedure is employed to derive the Duffing-type equations. The resulting equations are discretized on time domain using a set of time differential matrix operators that are defined based on the derivatives of a periodic base function. The pseudo arc-length continuation algorithm is finally applied to obtain the response curves of METE nanobeams with different types of end conditions. In the numerical results, the influences of temperature change, nonlocal parameter, external electric voltage and external magnetic potential on the nonlinear forced vibration behavior of METE nanobeams are explored. It is shown that the hardening-type response of nanobeams intensifies as the nonlocal parameter increases. In addition, the effects of external magnetic potential and electric voltage on the response curves are significant especially for simply-supported nanobeams.

124 citations


Journal ArticleDOI
Abstract: 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.

102 citations


Cites background from "Buckling and Vibration Analysis of ..."

  • ...[4] researched linear buckling and free vibration behavior of layered and multiphase magneto‐electro‐elastic (MEE) beam under thermal environment....

    [...]


Journal ArticleDOI
Abstract: In this article, buckling behavior of nonlocal magneto-electro-elastic functionally graded (MEE-FG) beams is investigated based on a higher-order beam model. Material properties of smart nanobeam are supposed to change continuously throughout the thickness based on the power-law model. Eringen's nonlocal elasticity theory is adopted to capture the small size effects. Nonlocal governing equations of MEE-FG nanobeam are obtained employing Hamilton's principle and they are solved using the Navier solution. Numerical results are presented to indicate the effects of magnetic potential, electric voltage, nonlocal parameter and material composition on buckling behavior of MEE-FG nanobeams. Therefore, the present study makes the first attempt in analyzing the buckling responses of higher-order shear deformable (HOSD) MEE-FG nanobeams.

86 citations


Journal ArticleDOI
01 Jun 2016-
Abstract: This paper investigates the buckling behavior of shear deformable piezoelectric (FGP) nanoscale beams made of functionally graded (FG) materials embedded in Winkler-Pasternak elastic medium and subjected to an electro-magnetic field. Magneto-electro-elastic (MEE) properties of piezoelectric nanobeam are supposed to be graded continuously in the thickness direction based on power-law model. To consider the small size effects, Eringen\'s nonlocal elasticity theory is adopted. Employing Hamilton\'s principle, the nonlocal governing equations of the embedded piezoelectric nanobeams are obtained. A Navier-type analytical solution is applied to anticipate the accurate buckling response of the FGP nanobeams subjected to electro-magnetic fields. To demonstrate the influences of various parameters such as, magnetic potential, external electric voltage, power-law index, nonlocal parameter, elastic foundation and slenderness ratio on the critical buckling loads of the size-dependent MEE-FG nanobeams, several numerical results are provided. Due to the shortage of same results in the literature, it is expected that the results of the present study will be instrumental for design of size-dependent MEE-FG nanobeams.

73 citations


Cites background from "Buckling and Vibration Analysis of ..."

  • ...Rahmani and Jandaghian (2015) studied buckling of functionally graded nanobeams based on a nonlocal third-order shear deformation theory....

    [...]

  • ...Kumaravel et al. (2007) researched linear buckling and free vibration behavior of layered Corresponding author, Professor, E-mail: febrahimy@eng.ikiu.ac.ir Farzad Ebrahimi and Mohammad Reza Barati and multiphase magneto‐electro‐elastic (MEE) beam under thermal environment....

    [...]

  • ...Rahmani and Pedram (2014) Analyzed the size effect on vibration of functionally graded nanobeams based on nonlocal Timoshenko beam theory....

    [...]


References
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Journal ArticleDOI
Abstract: Exact solutions are derived for three-dimensional, anisotropic, linearly magneto-electroelastic, simply-supported, and multilayered rectangular plates under static loadings. While the homogeneous solutions are obtained in terms of a new and simple formalism that resemble the Stroh formalism, solutions for multilayered plates are expressed in terms of the propagator matrix. The present solutions include all the previous solutions, such as piezoelectric, piezomagnetic, purely elastic solutions, as special cases, and can therefore serve as benchmarks to check various thick plate theories and numerical methods used for the modeling of layered composite structures. Typical numerical examples are presented and discussed for layered piezoelectric/piezomagnetic plates under surface and internal loads.

534 citations


Journal ArticleDOI
Jacob Aboudi1
Abstract: A homogenization micromechanical method is employed for the prediction of the effective moduli of electro-magneto-thermo-elastic composites. These include the effective elastic, piezoelectric, piezomagnetic, dielectric, magnetic permeability and electromagnetic coupling moduli, as well as the effective thermal expansion coefficients and the associated pyroelectric and pyromagnetic constants. Comparisons between the present homogenization theory, the generalized method of cells and the Mori-Tanaka predictions are given. Results are presented for fibrous and periodically bilaminated composites.

302 citations


Journal ArticleDOI
Abstract: An approximate solution for the free vibration problem of two-dimensional magneto-electro-elastic laminates is presented to determine their fundamental behavior. The laminates are composed of linear homogeneous elastic, piezoelectric, or magnetostrictive layers with perfect bonding between each interface. The solution for the elastic displacements, electric potential, and magnetic potential is obtained by combining a discrete layer approach with the Ritz method. The model developed here is not dependent on specific boundary conditions, and it is presented as an alternative to the exact or analytical approaches which are limited to a very specific set of edge conditions. The natural frequencies and through-thickness modal behavior are computed for simply supported and cantilever laminates. Solutions for the simply supported case are compared with the known exact solution for piezoelectric laminates, and excellent agreement is obtained. The present approach is also validated by comparing the natural frequencies of a two-layer cantilever plate with known analytical solution and with results obtained using commercial finite element software.

216 citations


Journal ArticleDOI
Abstract: Two independent state equations are established for transversely isotropic magneto-electro-elastic media by introducing proper stress and displacement functions. The free vibration problem of simply supported rectangular plates with general inhomogeneous (functionally graded) material properties along the thickness direction is then considered. An approximate laminate model is employed to transform the state equations with variable coefficients to the ones with constant coefficients. Two different classes of vibrations are found. In particular, the frequency of the first class is only related to the elastic property of the plate, while that of the second class is affected by the couplings among the elastic, electric and magnetic fields. Numerical results are presented and some important issues are discussed.

179 citations


Journal ArticleDOI
Abstract: Several researchers have focused on developing material properties for homogeneous magneto-electro-elastic multiphase composite materials. The candidate materials for this study are piezoelectric BaTiO 3 barium titanate as the embedded material with magnetostrictive CoFe 2 O 4 cobalt iron oxide as the matrix material. The materials are evaluated in terms of modeling the physical problem of the free vibration an infinite plate. Multiphase material properties vary depending upon the ratio of fiber material to matrix material. Actual electromagnetic materials are modeled as layered materials with the ratio of constituent materials being controlled by varying the number and thickness of layers of each material. Frequencies of vibration are compared for the layered materials versus the multiphase materials as a measure of the accurateness of the derived material constants. Multiphase material predictions for frequency agree quite well with layered materials for the problem that is studied.

116 citations