Bistability and stochastic jumps in an airfoil system with viscoelastic material property and random fluctuations

Abstract

The purpose of this paper is to explore analytically the influences of random fluctuations on a two-degrees-of-freedom (TDOF) airfoil model with viscoelastic terms. To begin with, a convolution integral over an exponentially decaying kernel function is employed to establish a constitutive relation of the viscoelastic material. Then the corresponding TDOF airfoil model with viscoelastic terms and random excitations is introduced. Subsequently, a theoretical analysis for the proposed airfoil model is achieved through a multiple-scale method together with a perturbation technique. All of the obtained approximate analytical solutions are verified by numerical simulation results, and a good agreement is observed. Meanwhile, we also find that both high-amplitude and low-amplitude oscillations coexist within a certain range of the excitation frequency or amplitude, which is regarded as a bi-stable behavior. In addition, effects of the viscoelastic terms and the random excitations on the system responses are investigated in detail. We uncover that the viscoelastic terms have a considerable influence on the system dynamics, which can simultaneously affect the structural damping and stiffness of the airfoil system. More interestingly, stochastic jumps between high-amplitude and low-amplitude oscillations can be induced due to random fluctuations, which are further illustrated through time history and steady-state probability density function. The jumps are considered as a transition from one probable state to another or vice versa. These results indicate that the external random fluctuations have a remarkable influence on dynamics of the TDOF airfoil model with viscoelastic material property.