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In this paper, the dynamic response of a simply supported sandwich plate with viscoelastic transversely flexible core is investigated, analytically using three-layered sandwich plate theory. Hamilton’s principle is employed to obtain governing equations of motion. Also, GHM (Golla–Hughes–McTavish) method is used to model the Frequency-Dependent Material properties of viscoelastic core. Modal superposition method is used to convert partial differential equations of motion to ordinary differential equations with time varying coefficients. Newmark approach is applied to solve the ordinary differential equations, numerically. Results of dynamic analysis in the present model are validated by the results published in the literatures. The natural frequencies and modal loss factors of the sandwich plate are extracted at 30°C and 90°C and effects of geometrical parameters are discussed. The advantages of the GHM model over the classical models such as Kelvin–Voigt are illustrated. The obtained results show that GHM model presents a more accurate description of transient response of the sandwich plate with viscoelastic core by considering the frequency dependency behavior of viscoelastic material. Core flexibility causes a difference between deflection of lower and upper surfaces, so that the three-layered sandwich theory will lead to more exact results with a remarkable deviation from the high-order single-layered theory.

A buckling analysis of temperature-dependent embedded plates reinforced by single-walled carbon nanotubes (SWCNTs) subjected to a magnetic field is investigated. The SWCNTs are distributed as uniform (UD) and three types of functionally graded nanotubes (FG), in which the material properties of the nano-composite plate are estimated based on the mixture rule. The surrounding temperature-dependent elastic medium is simulated as Pasternak foundation. Based on the orthotropic Mindlin plate theory, the governing equations are derived using Hamilton's principle. The buckling load of the structure is calculated based on an exact solution by the Navier method. The influences of elastic medium, magnetic field, temperature and distribution type, and volume fractions of SWCNT are shown on the buckling of the plate. Results indicate that CNT distribution close to the top and bottom are more efficient than that distributed near the mid-plane for increasing the stiffness of the plates.