VIBRATION EQUATIONS OF A RECTANGULAR ORTHOTROPIC VISCOELASTIC PLATE WITH ATTACHED MASSES BASED ON THE TIMOSHENKO HYPOTHESIS

This paper investigates the derivation of governing equations for both free and forced vibrations of a rectangular orthotropic viscoelastic plate carrying attached masses. The formulation is based on the Timoshenko plate theory. The equations are obtained using an energy-based approach, specifically the Hamilton–Ostrogradsky principle. As a result, a system of integro-differential equations describing the coupled dynamics of the plate and the attached masses is derived.