On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates

Chen, Weiqiu; Lee, Kang Yong; Ding, Hu

doi:10.1016/j.jsv.2003.10.033

Cited by 193 publications

(71 citation statements)

References 19 publications

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“…Several computational techniques were proposed to investigate the electroelastic, magnetoelastic, and electromagnetic coupling effects of smart structures, such as finite element method (FEM), mesh-free method, and scaled boundary FEM [5][6][7][8][9][10]. Bhangale and Ganesan analyzed the static behaviors of linear anisotropic FGMEE plates using semianalytical FEM and investigated the free vibration of FGMEE plates and cylindrical shells [11,12].…”

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%

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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“…Pan and colleagues [1,2] derived the static and free vibration solutions for multilayered rectangular plates under simply-supported boundary conditions by using the Stroh formulism and propagation matrix methods. By applying the state vector approach and propagation matrix method, Wang et al [3] derived the exact solution of the multilayered plate under static deformation, Chen et al [4] extended the static solution to the vibration case, and Chen et al [5] discussed the modal analysis of the multilayered plates. Combining the discrete layer approach and Ritz method, Ramirez et al [6] derived an approximate solution for the free vibration problem of two-dimensional laminate under both simply supported and fixed boundary conditions.…”

Section: Introductionmentioning

confidence: 99%

Analytical Solution for Free Vibration of Multilayered Circular Plate

Ren

Song

Han

2011

AEF

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Abstract. An analytical solution is deduced for a three-dimensional transversely isotropic axisymmetric multilayered circular plate made of piezoelectric (PE) and piezomagnetic (PM) under simply supported boundary condition. The state space vector, finite Hankel transform and propagation matrix methods are utilized together to obtain the full-field solutions for the multilayered circle plate. Numerical examples for five-layered PE/PM composites with dimensionless frequencies of the multilayered plate under simple-supported lateral boundary conditions are presented. The frequencies increase with the ratio of the thickness to radius.

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“…An approximate solution for the laminated magneto-electro-elastic two-dimensional plates has been obtained by Ramirez and co-workers [26] by combining the discrete layer approach with the Ritz method in such a way that the developed model does not depend on boundary conditions. A state-space approach has been employed to derive analytical solutions for multilayered magnetoelectro-elastic media [4,27], to study the free vibration behavior of a simply supported non-homogeneous rectangular plate [28] and to obtain the solution for the magnetoelectric thermoelasticity problem of a non-homogeneous transversely isotropic rectangular plate undergoing bending deformations [29]. In order to model general boundary condition configurations, the use of numerical methods is required.…”

Section: Introductionmentioning

confidence: 99%

An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem

Milazzo¹,

Orlando²,

Alaimo³

2009

Smart Mater. Struct.

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Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the definition of the bending moment. Moreover, the influences of the electro-mechanic, magneto-mechanic and electromagnetic coupling on the stiffness of the bimorph stem from the computation of the beam equivalent stiffness constants. Free and forced vibration analyses of both multiphase and laminated magneto-electro-elastic composite beams are carried out to check the effectiveness and reliability of the proposed analytic solution.

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On free vibration of non-homogeneous transversely isotropic magneto-electro-elastic plates

Cited by 193 publications

References 19 publications

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

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

Analytical Solution for Free Vibration of Multilayered Circular Plate

An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem

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