On the longitudinal wave along a functionally graded magneto-electro-elastic rod

Xue, Chao‐Bin; Pan, Ernian

doi:10.1016/j.ijengsci.2012.08.004

Cited by 63 publications

(13 citation statements)

References 19 publications

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“…A local cylindrical coordinate system ( r, θ, ξ ) is also attached with its origin at O k in the source layer k . In the absence of body forces, electric charge, and magnetic monopoles, the equations of motion and the Gauss law in the MEE solid in terms of the global cylindrical coordinate system are expressed as (Xue and Pan, 2013)…”

Section: Definition Of the Problem And Basic Equationsmentioning

confidence: 99%

Time-harmonic dislocations in a multilayered transversely isotropic magneto-electro-elastic half-space

Moshtagh

Eskandari‐Ghadi

Pan

2019

Journal of Intelligent Material Systems and Structures

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Modeling layered systems with dislocations is very challenging; yet, it is important since most smart structures are made of multilayers to make best use of the combined effective property. As such, during the manufactures, defects, such as dislocations, could be introduced in the multilayers. In this article, we analytically find, for the first time, the response of three-dimensional multilayered magneto-electro-elastic systems due to time-harmonic dislocations. The dislocations are the most general, containing the elastic dislocations and discontinuity of the electric potential and/or magnetic potential over a circular region in any layer in the medium. The fully coupled partial differential equations of motion and the Gauss law for the magneto-electro-elastic materials are solved in terms of cylindrical system of vector functions, and the dual variable and position method is further introduced to treat the multilayers. Numerical examples are carried out based on the derived analytical solution to demonstrate the effects of the time-harmonic dislocations on the induced magneto-electro-elastic fields. This analytical solution is important in both electrodynamics and elastodynamics, with possible applications in material sciences and physics. The numerical results are useful in design process of smart devices made of magneto-electro-elastic solids applicable to other engineering fields like renewable energy.

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Section: Definition Of the Problem And Basic Equationsmentioning

confidence: 99%

Time-harmonic dislocations in a multilayered transversely isotropic magneto-electro-elastic half-space

Moshtagh

Eskandari‐Ghadi

Pan

2019

Journal of Intelligent Material Systems and Structures

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“…Li and Wei [14] studied the surface wave in FGPP structures, the influences of the initial stresses and the graded function variation on the dispersion curves were analyzed. The longitudinal wave in an FGPP rod was investigated by Xue and Pan [15]. By means of a nonlocal elasticity model, wave propagation in an FGPP nanorod was investigated by Arefi [16].…”

Section: Introductionmentioning

confidence: 99%

Magneto-Electric Effect on Guided Waves in Functionally Graded Piezoelectric–Piezomagnetic Fan-Shaped Cylindrical Structures

Zhang

Elmaimouni

et al. 2018

Materials

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Functionally graded piezoelectric–piezomagnetic (FGPP) material simultaneously consists of piezomagnetic and piezoelectric phases, which are able to convert energy among mechanical, electric, and magnetic fields. The magneto-electric effect on waves in FGPP fan-shaped cylindrical structures is studied by exploiting the double Legendre orthogonal polynomial method. By means of the Heaviside function, the initial conditions are brought into wave motion equations. Dispersion properties, electric and magnetic potential, and the Poynting vector are calculated. Subsequently, the effect of the graded variation and geometric size on wave characteristics is analyzed. The FGPP fan-shaped cylindrical structures are of complex geometrical shape and material inhomogeneity, so their influences on the magneto-electric effect are the focus of discussion. Results reveal that the cut-off frequencies have a negative relationship with the cross-section area of the structure. The magneto-electric effect could be adjusted via altering the geometric size of the cross-section. These results can be utilized to design and optimize piezoelectric–piezomagnetic fan-shaped transducers.

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“…As for FG torsional bars and longitudinal rods with circular cross section, there seem to be only a few studies. Examples for torsional bars are [30,31,32,33] for statics, while for axisymmetric rods one has [34,35,36,37] considering various material configurations.…”

Section: Introductionmentioning

confidence: 99%

Dynamic equations for solid isotropic radially functionally graded circular cylinders

Abadikhah

Folkow

2018

Composite Structures

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A hierarchy of dynamic equations for solid isotropic functionally graded circular cylinders is derived based on the three dimensional elastodynamic theory. The material parameters are assumed to vary in the radial direction. Using Fourier expansions in the circumferential direction and power series expansions in the radial direction, equations of motion are obtained for longitudinal, torsional, flexural and higher order motion to arbitrary Fourier and power orders. Numerical examples for eigenfrequencies and plots on mode shapes and stress distributions curves are presented for simply supported cylinders for different material distributions. The results illustrate that the present approach renders benchmark solutions provided higher order truncations are used, and act as engineering cylinder equations using low order truncation.

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On the longitudinal wave along a functionally graded magneto-electro-elastic rod

Cited by 63 publications

References 19 publications

Time-harmonic dislocations in a multilayered transversely isotropic magneto-electro-elastic half-space

Time-harmonic dislocations in a multilayered transversely isotropic magneto-electro-elastic half-space

Magneto-Electric Effect on Guided Waves in Functionally Graded Piezoelectric–Piezomagnetic Fan-Shaped Cylindrical Structures

Dynamic equations for solid isotropic radially functionally graded circular cylinders

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