On the free vibration of orthotropic and inhomogeneous with spatial coordinates plates resting on the inhomogeneous viscoelastic foundation

The paper developed the closed-form solution for the free vibration problem of inhomogeneous orthotropic rectangular plates (IHORPs) resting on the inhomogeneous viscoelastic foundation (IHVEF). The Young's moduli and density of the orthotropic plate vary continuously with respect to three spatial coordinates, while the characteristics of the viscoelastic foundation vary depending on the in-plane coordinates. The relevant motion equation is obtained using the classical plate theory (CPT) and solved using method of separation of variables. The influences of inhomogeneity of orthotropic materials, inhomogeneity of viscoelastic and elastic foundations on the non-dimensional frequencies (NDFs) of plates are studied in detail.