Free vibration analysis of an axially moving multiscale composite plate including thermal effect

On the basis of the frequency-temperature equivalence principle and the elastic viscoelastic equivalence, a linear mathematical model in the form of the equilibrium state equation of the moving multiscale composite plate is derived in the complex frequency domain. To describe thermomechanical properties of the plate material, viscoelastic properties of multiscale fiber reinforced stationary composites presented in literature are taken into account. Fractional standard rheological model of the plate material as the function of reduced frequency depended on the temperature is determined. Numerical investigations of free vibrations are carried out for the 0.1 wt%, 1 wt% multiscale fiber reinforced composite plates and the neat fiber reinforced composite plate in the temperature range 35-200 degrees C. The effects of transport speed, internal damping and the volume fraction of fibers in the plate material on natural frequencies are presented. In the range of low temperatures the values of critical transport speeds of the tested plates to a small extent differ from each other and significantly decrease with the temperature increase. In higher temperatures the critical transport speeds of the tested plates differ from each other and with the temperature increase reach constant values.