Analysis of steady responses for a frictional oscillator based on the Harmonic Balance-Alternating Frequency/Time Domain Method
KANG Jiahao1,XU Chao1,LI Dongwu1,REN Huaiyu2
1.School of Astronautics, Northwestern Polytechenical University, Xi’an 710072, China;
2.China Academy of Launch Vehicle Technology, Beijing 100076, China
Abstract:Complex contact and frictional behaviors appear on the interface of jointed structures in vibration environment. When subjected to different tangential excitation, the interface may have different frictional behaviors: micro-slip and macro-slip. Solving the steady-state response of frictional oscillator considering micro/macro-slip accurately and efficiently is of great significance to the design and optimization of jointed structures. Using the continuous spring-slider model (Iwan model) to describe the cross-scale frictional behavior on the jointed surface, and combing multiple harmonic balance method and alternating frequency/time domain method to solve the steady-state response of single/multi-degree of freedom friction oscillators. Results showed that the method has high accuracy and higher computational efficiency than conventional numerical integration method. The higher the truncated harmonic order, the more accurate the frictional restoring force is. The frequency response analysis showed that the friction nonlinearity results in nonlinear phenomena of stiffness softening and harmonic resonance for the amplitude-frequency response.
康佳豪1,徐超1,李东武1,任怀宇2. 基于谐波平衡-时频转换法的摩擦振子稳态响应分析[J]. 振动与冲击, 2020, 39(12): 170-176.
KANG Jiahao1,XU Chao1,LI Dongwu1,REN Huaiyu2. Analysis of steady responses for a frictional oscillator based on the Harmonic Balance-Alternating Frequency/Time Domain Method. JOURNAL OF VIBRATION AND SHOCK, 2020, 39(12): 170-176.
[1] Papangelo A, Ciavarella M. Effect of normal load variation on the frictional behavior of a simple Coulomb frictional oscillator[J]. Journal of Sound and Vibration, 2015, 348: 282-293.
[2] 王本利,张相盟,卫洪涛. 基于谐波平衡法的含Iwan模型干摩擦振子非线性振动[J]. 航空动力学报, 2013, 28(1):1-9.
WANG Ben-li, ZHANG Xiang-meng, WEI Hong-tao. Harmonic balance method for nonlinear vibration of dry friction oscillator with Iwan model [J]. Journal of Aerospace Power, 2013, 28(1):1-9.
[3] 阎俊, 徐超. 谐波激励下多尺度粘滑干摩擦系统混沌[J]. 振动与冲击, 2014, 33(14):195-200.
YAN Jun, XU Chao. Chaotic motion of dry friction systems with multi-scale stick-slip characteristics [J]. Journal of Vibration and Shock, 2014, 33(14):195-200.
[4] 李东武,徐超.考虑法向载荷变化的Iwan模型及其特性分析[J].哈尔滨工业大学学报,2017,49(10):138-144.
Li Dong-wu, Xu Chao. Iwan model considering variable normal load and its characteristic analysis. Journal of Harbin Institute of Technology, 2017,49(10):138-144.
[5] 徐超,李东武,陈学前,王东. 考虑法向载荷变化的微滑摩擦系统振动分析[J]. 振动与冲击, 2017, 36(13): 122-127.
Xu Chao, Li Dong-wu, Chen Xue-qian,Wang Dong. Vibration analysis of a micro-slip frictional system considering variable normal load. JOURNAL OF VIBRATION AND SHOCK, 2017, 36(13): 122-127.
[6] Krack M, Gross J. Harmonic Balance for Nonlinear Vibration Problems[M]. Springer, 2019.
[7] Cameron T M, Griffin J H. An Alternating Frequency/Time Domain Method for Calculating the Steady–State Response of Nonlinear Dynamic Systems[J]. Journal of Applied Mechanics, 1989, 56(1):149-154.
[8] Petrov E P, Ewins D J. Analytical formulation of friction interface elements for analysis of nonlinear multi-harmonic vibrations of bladed disks [J]. Journal of Turbomachinery, 2003, 125(2): 364-371.
[9] 李洪亮. 球轴承—不对中转子系统的非线性振动特性研究[D].哈尔滨工业大学,2017.
LI Hong-liang. Research on nonlinear vibration characteristics of ball bearing-misaligned rotor system[D]. Harbin Institute of Technology, 2017.
[10] 李琳,刘久周,李超.干摩擦阻尼器对宽频多阶次激励减振效果分析[J].航空动力学报,2016,31(09):2171-2180.
LI Lin, LIU Jiu-zhou, LI Chao. Analysis on damping effect of dry friction damper under wideband multi-harmonic excitation[J]. Journal of Aerospace Power, 2016,31(09):2171-2180.
[11] 刘天源,谢永慧,张荻.干摩擦阻尼叶片的高保真有限元模型振动特性研究[J].噪声与振动控制,2018,38(S1):92-95.
LIU Tian-yuan, XIE Yong-hui, ZHANG Di. Investigation of Vibration Characteristics for Dry Friction Damped Blades with High-fidelity Finite Element Model. Noise and Vibration Control, 2018,38(S1):92-95.
[12] Süß D, Willner K. Investigation of a jointed friction oscillator using the multiharmonic balance method[J]. Mechanical Systems and Signal Processing, 2015, 52: 73-87.
[13] 李东武, 徐超. 基于时频域交替法的迟滞非线性振动系统的稳态响应分析[J]. 动力学与控制学报, 2016, 14(3):217-222.
LI Dong-wu, XU Chao. Alternating time/frequency domain method for calculating the steady-state response of hysteresis nonlinear vibration systems[J]. Journal of Dynamics and Control, 2016, 14(3):217-222.
[14] 张智勇. 球轴承—转子系统变柔度振动的分岔与滞后行为[D].哈尔滨工业大学,2015.
ZHANG Zhi-yong. Bifurcation and hysteresis of varying compliance vibrations of a ball bearing-rotor system[D]. Harbin Institute of Technology, 2015.
[15] 李琳,刘久周,李超.航空发动机中的干摩擦阻尼器及其设计技术研究进展[J].航空动力学报,2016,31(10):2305-2317.
LI Lin, LIU Jiu-zhou, LI Chao. Review of the dry friction damper in aero-engine and their design technologies [J]. Journal of Aerospace Power, 2016,31(10):2305-2317.
[16] Wang J H, Chen W K. Investigation of the Vibration of a Blade With Friction Damper by HBM[C]. Structures and Dynamics. 1992:V005T14A003.Gaul L, Lenz J. Nonlinear dynamics of structures assembled by bolted joints[J]. Acta Mechanics Sinica, 1997, 125(1):169-181.
[17] Iwan W D. A Distributed-Element Model for Hysteresis and Its Steady-State Dynamic Response[J]. Trans.asme J.of Appl.mech, 1966, 88(4):893.
[18] The Mechanics of Jointed Structures: Recent Research and Open Challenges for Developing Predictive Models for Structural Dynamics[M]. Springer, 2017.
[19] Yamauchi S. Nonlinear vibration of flexible rotors(1st report, development of a new numerical calculation technique)[J]. Nippon Kikai Gakkai Ronbunshu C Hen/transactions of the Japan Society of Mechanical Engineers Part C, 1983, 49(446):1862-1868.