Free vibration of three-layer sandwich plate with viscoelastic core modelled with fractional theory

Abstract

In the present study, natural frequencies and damping behavior of three-layer sandwich plates with viscoelastic core modelled with fractional theory are studied. Governing equations of motion are derived using Lagrange's equation and then solved via Rayleigh-Ritz method. In the first section of the analysis, the coefficients of the fractional and classical viscoelastic models are determined utilizing the curve fitting method on existed experimental data in the literature, and the best viscoelastic model is selected for free vibration analysis of sandwich plate. The method of least squares for fitting smooth curves to experimental data is applied. The results show that the fractional Zener model gives the best fit curve to the experimental data. After that, the effects of some geometrical parameters such as length to width ratio and viscoelastic core thickness on the natural frequency and loss factor of the sandwich plate with viscoelastic core are investigated, and some conclusions are drawn.