A Class of 2-DOF Coupled Systems With Fractional-Order Derivatives

GE Zhi-xin; CHEN Xian-jiang; CHEN Song-lin

doi:10.21656/1000-0887.370333

Volume 38 Issue 11

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GE Zhi-xin, CHEN Xian-jiang, CHEN Song-lin. A Class of 2-DOF Coupled Systems With Fractional-Order Derivatives[J]. Applied Mathematics and Mechanics, 2017, 38(11): 1300-1308. doi: 10.21656/1000-0887.370333

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A Class of 2-DOF Coupled Systems With Fractional-Order Derivatives

doi: 10.21656/1000-0887.370333

¹School of Mathematics and Physics, Anhui University of Technology, Maanshan, Anhui 243002, P.R.China;²School of Business, Anhui University of Technology, Maanshan, Anhui 243002, P.R.China

Received Date: 2016-11-01
Rev Recd Date: 2017-09-14
Publish Date: 2017-11-15

Abstract

Abstract

The vibration problems of a class of 2-DOF coupled systems with fractional-order derivatives and small perturbations were studied. First, the asymptotic solutions of the vibration equations with Riemann-Liouville fractional-order derivatives were constructed. With the multi-scale method, the solvability conditions for the asymptotic solutions to the vibration problems were obtained. Then, under the solvability conditions for the solutions, the influences of the fractional-order derivatives, their coefficients and the small parameters on the vibration were discussed, and the asymptotic solutions were also given. Finally, the stability properties of the 1st-order approximate solutions were studied. It is found that all the steady-state solutions are stable.
- multi-scale,
- fractional-order derivative,
- 2-DOF coupled system,
- solvability condition

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References(16)

References

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