Journal
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION
Volume 84, Issue -, Pages -Publisher
ELSEVIER
DOI: 10.1016/j.cnsns.2020.105184
Keywords
Random airfoil model; Viscoelastic material; Multiple-scale method; Bistability and stochastic jumps
Categories
Funding
- National Natural Science Foundation of China [11772255, 11572247]
- Fundamental Research Funds for the Central Universities
- Shaanxi Project for Distinguished Young Scholars
- Research Funds for Interdisciplinary Subject, NWPU
- Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University [CX201962]
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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. (C) 2020 Elsevier B.V. All rights reserved.
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