A comparison study of steady-state vibrations with single fractional-order and distributed-order derivatives

作者：Duan, Jun-Sheng^*; Cheng, Cui-Ping; Chen, Lian

来源：Open Physics, 2017, 15(1): 809-818.

DOI：10.1515/phys-2017-0095

• fractional calculus
• vibration
• distributed-order derivative
• excitation
• response

We conduct a detailed study and comparison for the one-degree-of-freedom steady-state vibrations under harmonic driving with a single fractional-order derivative and a distributed-order derivative. For each of the two vibration systems, we consider the stiffness contribution factor and damping contribution factor of the term of fractional derivatives, the amplitude and the phase difference for the response. The effects of driving frequency on these response quantities are discussed. Also the influences of the order alpha of the fractional derivative and the parameter gamma parameterizing the weight function in the distributed-order derivative are analyzed. Two cases display similar response behaviors, but the stiffness contribution factor and damping contribution factor of the distributed-order derivative are almost monotonic change with the parameter gamma, not exactly like the case of single fractional-order derivative for the order alpha. The case of the distributed-order derivative provides us more options for the weight function and parameters.

• 出版日期2017-1
• 单位上海应用技术大学