Journal
NONLINEAR DYNAMICS
Volume 78, Issue 4, Pages 2487-2499Publisher
SPRINGER
DOI: 10.1007/s11071-014-1605-9
Keywords
Viscoelastic system; Stochastic responses; Randomly disordered periodic; Real-power stiffness; Multiple scales method
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Funding
- National Natural Science Foundation of China [11372247, 11172233, 61303020]
- Program for New Century Excellent Talents in University
- Shaanxi Project for Young New Star in Science Technology
- Youth Science and Technology Research Fund of Shanxi Province [2013021018-3]
- Shanxi University [010951801005]
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The stochastic dynamic responses of viscoelastic systems with real-power exponents of stiffness term subjects to randomly disordered periodic excitations are studied. The assumed viscoelastic damping depends on the past history of motion via convolution integrals over an exponentially decaying kernel function. The multiple scales method is used to derive the stochastic different equations of modulation of amplitude and phase. The changes of the shape of resonance curves are obtained with real-power exponents of stiffness term and viscoelastic parameters, and then, the numerical simulation method was used to verify the accuracy of the theoretical analysis results. Theoretical analysis and numerical simulations show that as the intensity of the random excitation increases, the steady-state solution changes from a limit cycle to a diffused limited cycle. Under some conditions, the system may have two steady-state solutions and the phenomenon of jumps will happen to them under the random excitations.
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