Forced vibration of a fractional-order single degree-of-freedom oscillator with clearance

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Journal of Vibration and Shock ›› 2020, Vol. 39 ›› Issue (14) : 251-256.

NIU Jiangchuan1,2, ZHAO Zhishuang2, XING Haijun1,2, SHEN Yongjun1,2

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Abstract

The forced vibration of a single degree-of-freedom piecewise linear oscillator with a clearance and a fractional-order derivative term was investigated.The approximate analytical solution for its primary resonance was obtained by the Krylov-Bogoliubov-Mitropoisky (KBM) asymptotic method.The primary resonance of the piecewise linear system was analyzed, and a unified expression of the fractional-order differential term was obtained, where the fractional order was restricted in 0 to 2.The effects of the fractional-order differential term on the dynamic characteristics of the piecewise system were expressed as an equivalent linear damping and an equivalent linear stiffness, while that of the clearance was an equivalent nonlinear stiffness.The expression of the amplitude-frequency response of the primary resonance was obtained, and the stability condition of the system was also achieved.The approximate analytical solutions and numerical solutions of the primary resonance amplitude-frequency responses were compared, which shows both are in good agreement.The effects of the fractional-order term and clearance on the amplitude-frequency response of the primary resonance were analyzed in detail.It concludes that the KBM asymptotic method is an effective method to analyze the dynamics of fractional-order piecewise smooth systems.

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fractional-order derivative / approximate analytical solution / Krylov-Bogoliubov-Mitropoisky (KBM) asymptotic method / primary resonance

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NIU Jiangchuan1,2, ZHAO Zhishuang2, XING Haijun1,2, SHEN Yongjun1,2. Forced vibration of a fractional-order single degree-of-freedom oscillator with clearance[J]. Journal of Vibration and Shock, 2020, 39(14): 251-256

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