Transient response of sandwich plate with transversely flexible and viscoelastic frequency-dependent material core based on a three-layered theory

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 degrees C and 90 degrees 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.