Stochastic P-bifurcation analysis of a fractional smooth and discontinuous oscillator via the generalized cell mapping method |
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Institution: | 1. Block 32 Ghim Moh Link, #25-298, 271032, Singapore;2. Cranfield University, United Kingdom;1. Department of Applied Mathematics, Northwestern Polytechnical University, Xi''an, 710072, PR China;2. State Key Laboratory for Strength and Vibration of Mechanical Structures, Xi''an Jiaotong University, Xi''an,710049, PR China |
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Abstract: | The smooth and discontinuous oscillator with fractional derivative damping under combined harmonic and random excitations is investigated in this paper. The short memory principle is introduced so that the evolution process of the oscillator with fractional derivative damping can be described by the Markov chain. Then the stochastic generalized cell mapping method is used to obtain the steady-state probability density functions of the response. The stochastic response and bifurcation of the oscillator with fractional derivative damping are discussed in detail. We found that both the smoothness parameter, the noise intensity, the amplitude and frequency of the harmonic force can induce the occurrence of stochastic P-bifurcation in the system. Monte Carlo simulation verifies the effectiveness of the method we adopt in the paper. |
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Keywords: | Stochastic P-bifurcation Smooth and discontinuous oscillator Fractional derivative damping Short memory principle Generalized cell mapping method |
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