Vibrational Analysis of Magneto-viscoelastic Bi-directional Functionally Graded Beams Subjected to Complex Environments Based on a Novel High-Order Shear Deformation Theory

This research is focused on the dynamical examination of bi-directional functionally graded (FG) magnetostrictive viscoelastic sandwich beams with an FG core surrounded by the Kerr medium in hygro-thermal environments. The considered sandwich beam has simply supported boundary conditions and consists of two magnetostrictive layers. The mechanical characteristics of the sandwich beam are supposed to vary continuously along the length and thickness directions of the beam. A novel higher-order shear deformation theory (HSDT) is offered to consider the shear effects through the thickness direction exactly. The transverse displacement is divided into bending and shear parts to consider the shear effects accurately. Nonlinear relations are exploited to reflect the thermal and moisture loadings comprehensively. Hamilton’s axiom, as well as the Kelvin–Voigt relation, is dedicated to attaining the governing equations of motion of the system. The Navier solution technique is implemented to acquire the eigenfrequency of the sandwich beam. Parametric studies are conducted to highlight the impacts of several key factors, such as material gradation and environmental loads, on the vibrational frequency and dynamical response of the system.” Conclusion”The results demonstrated that the deflection of the beam and the damping time are reduced by enhancing the velocity feedback gain.