Transverse free vibration analysis of a rotating rectangular plate made of viscoelastic material with fractional derivative

The transverse free vibration of a rotating viscoelastic rectangular plate described by fractional derivative constitutive relation was studied. Based on the plane problem of the plate, the Kelvin - Voigt two-dimensional constitutive relation with fractional derivative was obtained from the Kelvin - Voigt three-dimensional constitutive equation with fractional derivative. The differential equation of the motion for the rotating rectangular plate made of viscoelastic material with fractional derivative was established with the Hamilton principle. A differential quadrature method was used to discretize the differential equations of the motion and boundary conditions, and the complex eigen-equation of the system was obtained. The effects of fractional derivative order, width to length ratio, radius to length ratio and thickness to length ratio on the imaginary part of dimensionless complex frequency of the system were analyzed. Results show that with the increase of the rotational angular speed, the imaginary part (natural frequency) of the first three order dimensionless complex frequencies increases; with the increase of the fractional derivative order, the imaginary part of dimensionless complex frequency decreases; and the effect of each parameter on the third order imaginary part of the complex frequency is greater than the first and second orders. © 2023 Chinese Vibration Engineering Society. All rights reserved.