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 $\mathrm{BaTi}{O}_3$ and piezomagnetic material $\mathrm{CoF}{e}_2{O}_4$ 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.

In this paper, the nonlinear dynamics of a piezoelectric beam under simultaneous parametric and external excitation is studied. The energy sensor considered is composed of a substrate and a piezoelectric layer used as a vibratory sensor located in the middle of the beam. The model thus constituted takes into account the electromechanical nonlinearities. Based on the Galerkin’s method, a strongly coupled nonlinear system is obtained. The multiple scales method is used to determine the analytical expressions of the deflection of the beam, the output voltage generated by the piezoelectric patch and the power harvested around the resonant frequency of the structure. The nonlinear characteristics of the energy harvester are explored under parametric and direct excitations. Analytical formulations of the deflection and the output voltage have been provided leading to investigate new insights into the effects of certain parameters such as the electromechanical coupling coefficient, the thickness and width of the elastic beam and the piezoelectric patch. In particular the position of the piezoelectric patch on the performance of the energy harvester is studied. The results show that for large values of the damping coefficient and thickness, the frequency-amplitude response curves of the energy harvester decrease. On the other hand, the frequency response curves of the displacement and voltage increase for large values of the excitation width and amplitude. We also note the fact that the length ratio influences not only the vibration amplitudes but also the output voltage. The deflection amplitudes and the output voltage obtained by the elaborated second-order multiple scale method are higher than those obtained by the first order, these results show the importance of nonlinearities in the dynamic study of vibrational energy harvesting systems by piezoelectric materials.

Methodological approaches based on the nonlocal beam theory, differential quadrature and internal random coefficients methods are elaborated for parameters uncertainty effects on the dynamic behavior of viscoelastic Carbon NanoTubes (CNT) conveying viscous fluid. The general polynomial chaos and the superposition principle are used and several random parameters that may follow various distribution laws are considered. A selecting procedure of the most influencing random parameters on the dynamic behavior of CNT is given. The space and multimodal time domains are formulated and frequency and time responses are investigated. Effects of various random parameters on free and forced random vibrations are investigated.