Influence of visco-Pasternak foundation parameters on the bending and vibrational behavior of thick isotropic plates

Abstract

Introduction/purpose: This study primarily aims to investigate the effect of viscoelastic Pasternak foundation parameters on the bending and free vibrational behavior of simply supported thick isotropic plates using a two-variable high-order shear deformation theory (HSDT). The theory adopted in this study uses a limited number of unknowns and avoids the use of shear correction factors to ensure zero transverse shear stresses at the surface of the plates, which is not the case with other higher-order theories that generally involve four or five unknowns. In addition, the stress and displacement responses are analyzed under uniformly distributed loads (UDLs) and sinusoidally distributed loads (SDLs). Moreover, natural frequencies corresponding to both bending and thickness-shear modes are provided to demonstrate the accuracy of the proposed model in predicting the dynamic behavior of simply supported isotropic square and rectangular plates. Methods: The main contribution of this work lies in the integration of the effects of elastic foundation parameters and damping coefficients on the bending and vibration responses of simply supported thick isotropic plates, using a refined two-variable high-order shear deformation theory. In addition, the formulation of the displacement field introduces a number of undetermined integral terms, hence reducing the number of unknowns. The governing equations are derived using Hamilton's principle. Moreover, Navier's method is utilized to determine the analytical solutions for simply supported plates, while natural frequencies are calculated by solving the corresponding eigenvalue problem. Results: The analytical results are validated against several established higher-order shear deformation theories (ESDT, HSDT, TSDT), the first-order shear deformation theory (FSDT), and the classical plate theory (CPT). The findings show excellent agreement when viscoelastic and foundation effects are not taken into account. It is important to emphasize that when these effects are considered, the results show increased plate stiffness, leading to lower deflections and higher natural frequencies. Conclusion: The proposed theory provides results in close agreement with those obtained from existing models. It also clearly highlights the significant influence of viscoelastic foundation parameters on both the static and dynamic behavior of isotropic plates.