A refined fractional viscoelastic model for vibration analysis of moderately-thick plates

In this study, a Kelvin–Voigt fractional viscoelastic model is developed based on the two-variable refined plate theory (TV-RPT) to investigate the dynamic behavior of rectangular viscoelastic plates under support movement. The TV-RPT is a novel, simple, and efficient plate theory that provides accurate results for both thin and thick plates. The steady-state condition is governed by assuming the lower limit of the integral in the Riemann-Liouville fractional derivative to be negative infinity. After deriving the governing equation, an analytical solution based on the Navier method is employed for fully simply-supported viscoelastic plates. The proposed approach is validated by comparing the natural frequencies of viscoelastic and elastic plates with existing results in the literature. Additionally, the results obtained from TV-RPT and the classical plate theory (CPT) are compared. It is observed that both theories provide similar results for thin plates. However, for thicker plates, the amplitude and frequency of vibrations for TV-RPT are smaller and larger than those for CPT, respectively. The study also investigates the effects of fractional derivative order and damping coefficient on the frequency and amplitude of vibration.