A. Asnafi - Assistant Professor, Hydro-Aeronautical Research Center, Shiraz University, Shiraz

Recognition of the critical speed of axially moving plates plays an essential role in nonlinear behavior investigation of such systems. Many researches could be found in literature that have tried to recognize such instabilities for both linear and nonlinear axially moving elastic or viscoelastic plates via numerical procedures. Considering random motion, as it can be seen in many industrial and practical problems, for an axially moving viscoelastic plate having large deformations and trying to investigate its instability by analytical approach are the main new goals of this paper. Since the evolution of mean, variance, statistical moments and any other characteristics of a stochastic variable can be evaluated from its probability density function, it plays an essential role in studying these problems. In this paper, using the Fokker-Planck- Kolmlgorov equation which is an almost ancient partial differential equation to compute the probability density function for a random process, a novel method to investigate the nonlinear behavior of axially moving Kelvin type viscoelastic plates is presented. The results evaluated analytically can also indicate when the instability or bifurcation occurs. To validate the method, the results are also compared with the numerical ones

Axially moving plates, Random vibration, Nonlinear vibration, Viscoelastic plates, FPK equation