The current study presents a vibration investigation of a laminated plate considering a viscoelastic core with embedded magnetostrictive layers. The simply-supported plate is supported via Pasternak’s substrate medium. Based on different plate theories and employing Hamilton’s principle, the system of governing differential equations is derived. The mechanical properties of the viscoelastic core are described depend on the time varies based on Kelvin–Voigt model. Actuating magnetostrictive layers are utilized to control the vibration damping process of the system with the assistance of feedback and constant gain distributed control. The analytical solution is obtained to investigate the influence of half wave numbers, thickness ratios, core thickness, aspect ratios, lamination schemes, elastic foundation parameters, damping coefficient, feedback coefficient magnitude, magnetostrictive layers location, on the vibrational behavior of laminated plate. Some observations about the vibration damping process of the present plate are displayed. The results refer to that the vibration suppression rate depends on the thickness of the plate, the feedback control value, the foundation constants, and the viscoelastic structural damping significantly. Moreover, the study can be providing benchmark tests to validate future contributions on the viscoelastic smart structural issues and developing the design of smart viscoelastic structures and control of their vibrations.
