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

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

Abstract: Free vibration studies of multiphase and layered magneto-electro-elastic beam for BaTiO3–CoFe2O4 composite is carried out. In-plane plate finite-element analysis is used to obtain the behaviour of magneto-electro-elastic beam. Studies are carried out for beams for different boundary conditions, as may be applicable in design of smart sensors/actuators. The ANSYS package is used to validate the results obtained by the computer code developed for piezoelectric (PE) beam. Plane stress condition is used for the Euler–Bernouli magneto-electro-elastic beam.

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

Abstract: Buckling and vibration analysis of functionally graded magneto-electro-thermo-elastic (FGMETE) circular cylindrical shell are carried out in the present work. The Hamilton principle, higher order shear deformation theory, constitutive equation considering coupling effect between mechanical, electric, magnetic, thermal are considered to derive the equations of motion and distribution of electrical potential, magnetic potential along the thickness direction of FGMETE circular cylindrical shell. The influences of various external loads, such as axis force, temperature difference between the bottom and top surface of shell, surface electric voltage and magnetic voltage, on the buckling response of FGMETE circular cylindrical shell are investigated. The natural frequency obtained by present method is compared with results in open literature and a good agreement is obtained.

Love waves in layered piezoelectric/piezomagnetic structures

Abstract: The propagation of Love waves in layered structures is investigated for two cases: a piezomagnetic (PM) layer on a piezoelectric (PE) half-space and the reverse configuration. The dispersion relations are obtained in explicit form. The numerical examples are provided to illustrate the variations of the phase and group velocities versus the wavenumber for the combinations of different materials. The results show that: (1) the phase and group velocities initiate at the bulk shear wave velocity of the half-space medium and approach the bulk shear wave velocity of the layer with increasing wavenumber; (2) the influence of the magnetic permeabilities of PE materials on the phase velocity can be neglected; (3) for the layered medium consisting of a PM layer and a PE half-space, the properties of PE materials have a great influence on the phase and group velocities at lower wavenumber for the lowest mode. These findings are useful for PE/PM composite media or structures in the microwave technology.

Dynamic responses of functionally graded magneto-electro-elastic shells with open-circuit surface conditions

Abstract: Three-dimensional (3D) free-vibration analysis of simply supported, doubly curved functionally graded (FG) magneto-electro-elastic shells with open-circuit surface conditions is studied using an asymptotic approach. The material properties of the FG shells are regarded as heterogeneous through the thickness coordinate. The 29 basic equations of 3D magneto-electro-elasticity are firstly reduced to a system of 10 state space vector equations in terms of 10 primary variables in elastic, electric and magnetic fields. Apart from the regular asymptotic expansion in the early paper on static analysis, the method of multiple time scales is used to eliminate the secular terms and to make the asymptotic expansion feasible. Through a straightforward derivation, we finally decompose the present 3D problem as recursive sets of two-dimensional (2D) problems with motion equations of the coupled classical shell theory (CCST). The orthonormality and solvability conditions for various order problems are derived. With these conditions, it is shown that the 3D asymptotic solutions can be obtained by repeatedly solving the CCST-type motion equations order-by-order in a systematic and hierarchic manner. The influence of the gradient index of material properties on the natural frequencies and their corresponding modal field variables of various FG piezoelectric and magneto-electro-elastic shells is presented.

Static analysis of stepped functionally graded magneto-electro-elastic plates in thermal environment: A finite element study

Abstract: In this article, a finite element (FE) formulation accounting for multiphysics response of multilayered magneto-electro-elastic (MEE) plates in the thermal environment has been presented. The equilibrium equations of motion are attained using the principle of total potential energy and coupled constitutive relations of MEE material. Maxwell’s equation of electrostatics and magnetostatics are used to model the electric and magnetic behavior. The influence of various through thickness temperature distributions on the static parameters of stepped functionally graded magneto-electro-elastic ( SFG- MEE) plates is investigated. Further, an extra attention has been devoted to evaluate the effect of product properties (pyroelectric and pyromagnetic coupling), boundary conditions and aspect ratio on the direct (displacements, electric potential and magnetic potential) and derived quantities (stresses, electric displacement, and magnetic flux density) of the SFG- MEE plate. A comparative study is also carried out to analyse the effect of stacking sequence, boundary conditions, pyroeffects, length-to-width ratio and aspect ratios of the SFG- MEE plate. The credibility of the proposed FE model is verified with the results available in the literature. It is expected that the findings in this article may be useful for accurate design and analysis of MEE structures under the thermal environment.

Exact Solution for Simply Supported and Multilayered Magneto-Electro-Elastic Plates

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.

Free vibrations of simply supported and multilayered magneto-electro-elastic plates

Abstract: Analytical solutions are derived for free vibrations of three-dimensional, linear anisotropic, magneto-electro-elastic, and multilayered rectangular plates under simply supported edge conditions. For any homogeneous layer, we construct the general solution in terms of a simple formalism that resembles the Stroh formalism, from which any physical quantities can be solved for given boundary conditions. In particular, the dispersion equation that characterizes the relationship between the natural frequency and wavenumber can be obtained in a simple form. For multilayered plates, we derive the dispersion relation in terms of the propagator matrices. The present solution includes all previous solutions, such as piezoelectric, piezomagnetic, and purely elastic solutions as special cases, and can serve as benchmarks to various thick plate theories and numerical methods used for the modelling of layered composite structures. Typical natural frequencies and mode shapes are presented for sandwich piezoelectric/piezomagnetic plates. It is shown clearly that some of the modes are purely elastic while others are fully coupled with piezoelectric/piezomagnetic quantities, with the latter depending strongly upon the material property and stacking sequence. These frequency and mode shape features could be of particular interest to the analysis and design of various “smart” sensors/actuators constructed from magneto-electro-elastic composite laminates.

Micromechanical analysis of fully coupled electro-magneto-thermo-elastic multiphase composites

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.

State vector approach to analysis of multilayered magneto-electro-elastic plates

Abstract: The state vector equations for three dimensional, orthotropic and linearly magneto-electro-elastic media are derived from the governing equations by eliminating σ x , σ y · τ xy , B x , B y , D x and D y . An efficient method is presented for analysis of multilayered magneto-electro-elastic plates. The methodology is based on the mixed formulation, in which basic unknowns are formed by collecting not only displacements, electrical potential and magnetic potential but also some of stresses, electrical displacements, and magnetic induction. As special case, simply supported and multilayered rectangular plate is analyzed under the surface loading. Numerical results are presented graphically. The procedure of numerical calculation shows that the formulation presented here is simple and direct.

Layerwise partial mixed finite element analysis of magneto-electro-elastic plates

Abstract: In this paper a partial mixed layerwise finite element model for adaptive plate structures is presented. Static analysis of magneto-electro-elastic laminated plate structures is considered. The mixed finite element formulation is obtained by considering a Reissner mixed variational principle. The mixed functional is formulated using transverse stresses, displacement components and electric and magnetic potentials as primary variables. The other fields are calculated by post-computation through constitutive equations. The numerical results obtained by the present model are in good agreement with available three-dimensional analytical solutions.