Analytical study of shock response in circular plates on fractional viscoelastic foundations

Abstract

Viscoelastic materials play a vital role in engineering applications due to their ability to absorb mechanical shocks and enhance structural resilience. This study presents an analytical investigation into the dynamic response of a circular plate resting on a viscoelastic foundation subjected to base shock excitation. Both free and clamped boundary conditions are considered to assess their influence on system behavior. The viscoelastic foundation is modeled using a fractional-order Kelvin–Voigt framework, allowing for a more accurate representation of damping characteristics. The Galerkin method is applied to solve the governing equations, enabling the computation of natural frequencies and shock transmissibility. Results reveal a strong dependence of the system’s dynamic response on the fractional derivative order (α), with natural frequencies increasing up to α = 0.8, followed by a decline. The findings also demonstrate the critical impact of boundary conditions on transmitted acceleration and highlight the importance of using appropriate evaluation methods—such as the Square Root of the Sum of Squares (SRSS)—to interpret shock responses accurately. This study provides valuable insights into the design and analysis of structures subjected to transient dynamic loads and contributes to the development of more effective shock isolation strategies.