Dynamic analysis of multilayered magnetoelectroelastic plates based on a pseudo-Stroh formalism and Lagrange polynomials

Abstract

In this article, a semi-analytical three-dimensional modeling of dynamic behavior of the multilayered magnetoelectroelastic plates under simply supported edges boundary conditions is derived. A combination of pseudo-Stroh formalism and the Lagrange polynomials is elaborated for the space and time response. The time domain is subdivided into small intervals that are discretised using the associated Tchybechev points. The layer-time solution is elaborated in time-dependent matrix form. The propagator matrices are used for the laminated multifunctional plates with an arbitrary number of layers. Extended-traction vectors are obtained for mechanical, electrical, and magnetic excitations. To validate the elaborated numerical procedure, the dynamic behavior of the three layered plates made of piezoelectric material [Formula: see text] and piezomagnetic material [Formula: see text] is investigated. The lower surface of the plate is assumed to be traction free, whereas the upper surface is subjected to a dynamic sinusoidal loading. The obtained results are in good agreement with the available ones based on the Layer wise and the state-space approaches. These results demonstrated that a magnetoelectric coupling coefficient is time-independent but depends strongly on the kind of imperfect interfaces and the taking sequences of the multilayered plates. Furthermore, it is established that the imperfect interfaces have a strong influence on the dynamic behavior of the laminated structures.

Multilayer Viscoelastic Media with Interface Quality Using Pseudo Stroh-Formalism: Application to Local Materials

“…Equation ( 18) is an eigenvalue problem. It is solution in mechanics has been investigated by several authors [19,20].…”

“…Moreover, when we replace the vectors and of Equation (22) in Equation (20), the elements of the column matrix are rewritten as:…”

“…Combining Equations (20)(21)(22)(23)(24), we obtain the propagation relation from the upper to the lower interface of this structure:…”

Dislocation singularities in layered magneto-electro-elastic plates

“…In particular, a strong electromagnetic coupling effect can be realized by combining piezomagnetic and piezoelectric phases, thus providing the attractive ability of storing and converting different forms of energy among magnetic, electric and mechanical energies (vanSuchtelen, 1972, van den Boomgaard et al, 1974, van Run et al, 1974. In recent years, the opportunity to investigate novel components and device designs leads to an increasing amount of theoretical and numerical studies on the response and stability of magneto-electro-elastic (MEE) multilayered composites (Alshits et al, 1992, Harshe et al, 1993, Chung and Ting, 1995, Pan, 2001, Wang and Shen, 2002, Bichurin et al, 2003, Pan and Han, 2005, Challagulla and Georgiades, 2011, Zhang et al, 2017, Ghobadi et al, 2019, Ngak et al, 2019, Ren et al, 2020, Bustamante et al, 2021, Vinyas, 2021, Yu and Kang, 2021. Due to the beneficial cumulative effects and facile layer-bylayer fabrication processes, multilayered sequences with different faults are preferably arranged in plates.…”