Free vibration of an infinite magneto-electro-elastic cylinder

Buchanan, George R.

doi:10.1016/s0022-460x(03)00357-2

Cited by 89 publications

(71 citation statements)

References 8 publications

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“…The constitutive equations for the magneto-electro-elastic medium relating stress σ j , electric displacement D j and magnetic induction B j to strain S k , electric field E k and magnetic field H k , exhibiting linear coupling between magnetic, electric and elastic field can be written as [Buchanan 2003]:…”

Section: Constitutive Equationsmentioning

confidence: 99%

“…Wang and Zhong [2003] studied the finitely long magneto-electroelastic circular cylindrical shell under pressure and temperature changes using power series expansion method together with the Fourier series expansion method. Free vibrations studies of the magnetoelectro-elastic cylindrical shell have been carried out by various authors [Buchanan 2003;Bhangale and Ganesan 2005;Annigeri et al 2006]. The transient responses of the inelastic shells of revolution using finite difference solution techniques in time and space has been presented by Philip [1972].…”

Section: Introductionmentioning

confidence: 99%

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Transient response of magneto-electro-elastic simply supported cylinder using finite element

Daga

Ganesan

Shankar

2008

JOMMS

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The transient response of a simply supported layered cylinder made of a three-phase magneto-elecroelastic (MEE) composite, consisting of an elastic matrix reinforced with piezoelectric and piezomagnetic fiber has been studied by developing a semianalytical finite element method employing fourth-order Runge-Kutta method. Numerical results are presented for different volume fractions of piezomagnetic fiber in a three-phase MEE material with simply supported boundary conditions. A study of the transient responses of (PZT)-epoxy mixed component (PECP), (Terfenol-D)-epoxy mixed components (MSCP), barium titanate (BaTiO 3 ) and a two phase magneto-electro-elastic layered cylinder, under simply supported boundary conditions has also been presented. A comparison between the elastic and the coupled responses of the MEE cylinder is presented as well. Ansys 8.1 is used to validate the present code for the response of cylinder made of PECP and MSCP materials.

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Section: Constitutive Equationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Transient response of magneto-electro-elastic simply supported cylinder using finite element

Daga

Ganesan

Shankar

2008

JOMMS

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“…Phoenix et al analysed the static and dynamic behaviors of coupled MEE plates using FEM with the Reissner mixed variational theorem [14]. Buchanan used FEM to study the free vibrations of infinite magnetoelectroelastic cylinders [15]. However, these FEMs overestimated the stiffness of solid structures and were limited by low accuracy.…”

Section: Introductionmentioning

confidence: 99%

An Inhomogeneous Cell‐Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

Cai

Meng

Wang

2018

Shock and Vibration

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To overcome the overstiffness and imprecise magnetoelectroelastic coupling effects of finite element method (FEM), we present an inhomogeneous cell-based smoothed FEM (ICS-FEM) of functionally graded magnetoelectroelastic (FGMEE) structures. Then the ICS-FEM formulations for free vibration calculation of FGMEE structures were deduced. In FGMEE structures, the true parameters at the Gaussian integration point were adopted directly to replace the homogenization in an element. The ICS-FEM provides a continuous system with a close-to-exact stiffness, which could be automatically and more easily generated for complicated domains, thus significantly decreasing the numerical error. To verify the accuracy and trustworthiness of ICS-FEM, we investigated several numerical examples and found that ICS-FEM simulated more accurately than the standard FEM. Also the effects of various equivalent stiffness matrices and the gradient function on the inherent frequency of FGMEE beams were studied.

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Section: Introductionmentioning

confidence: 99%

Untitled

2008

JOMMS

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See inside back cover or http://www.jomms.org for submission guidelines.Regular subscription rate: $500 a year.Subscriptions, requests for back issues, and changes of address should be sent to Mathematical Sciences Publishers, 798 Evans Hall, Department of Mathematics, University of California, Berkeley, CA 94720-3840. ELASTIC CONSTANTS AND THERMAL EXPANSION AVERAGES OF A NONTEXTURED POLYCRYSTAL ROLAND DEWITThis paper gives expressions for the overall average elastic constants and thermal expansion coefficients of a polycrystal in terms of its single crystal components. The polycrystal is assumed to be statistically homogeneous, isotropic, and perfectly disordered. Upper and lower bounds for the averages are easily found by assuming a uniform strain or stress. The upper bound follows from Voigt's assumption that the total strain is uniform within the polycrystal while the lower bound follows from Reuss' original assumption that the stress is uniform. A self-consistent estimate for the averages can be found if it is assumed that the overall response of the polycrystal is the same as the average response of each crystallite. The derivation method is based on Eshelby's theory of inclusions and inhomogeneities. We define an equivalent inclusion, which gives an expression for the strain disturbance of the inhomogeneity when external fields are applied. The equivalent inclusion is then used to represent the crystallites. For the self-consistent model the average response of the grains has to be the same as the overall response of the material, or the average strain disturbance must vanish. The result is an implicit equation for the average polycrystal elastic constants and an explicit equation for the average thermal expansion coefficients. For the particular case of cubic symmetry the results can be reduced to a cubic equation for the selfconsistent shear modulus. For lower symmetry crystals it is best to calculate the self-consistent bulk and shear modulus numerically. IntroductionA polycrystal, whose properties vary in a complicated fashion from point to point over a small microscopic length scale, may appear on average to be uniform or perhaps, more generally, its properties appear to vary smoothly. The determination of such overall properties from the properties and geometrical arrangement of the constituent monocrystal grains is our aim. In the simplest case the polycrystal is assumed to be statistically homogeneous, isotropic, and perfectly disordered. General expressions for averages can then be derived. Many different properties can be averaged, such as dielectric constants, diffusivity, elastic constants, electrical conductivity, magnetic permeability, magnetostriction, piezoelectric constants, thermal conductivity, or thermal expansion. In this paper we treat the elastic constants, which have already received more attention than most other physical properties, and the thermal expansion. Elastic constants are fundamental physical data needed for the characterization of materials. In addition to their fundam...

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Free vibration of an infinite magneto-electro-elastic cylinder

Cited by 89 publications

References 8 publications

Transient response of magneto-electro-elastic simply supported cylinder using finite element

Transient response of magneto-electro-elastic simply supported cylinder using finite element

An Inhomogeneous Cell‐Based Smoothed Finite Element Method for Free Vibration Calculation of Functionally Graded Magnetoelectroelastic Structures

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