Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions

Yewei ZHANG, Kefan XU, Jian ZANG, Zhiyu NI, Yunpeng ZHU, Liqun CHEN

doi:10.1007/s10483-019-2548-9

2019 , Vol. 40 >Issue 12: 1791 - 1804

DOI: https://doi.org/10.1007/s10483-019-2548-9

Articles

Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions

Expand

1. College of Aerospace Engineering, Shenyang Aerospace University, Shenyang 110136, China;
2. Department of Automatic Control and Systems Engineering, Sheffield University, Mapping Street Sheffield S1 3JD, U.K.;
3. Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China;
4. School of Mechanics and Engineering Science, Shanghai University, Shanghai 200444, China;
5. Shanghai Key Laboratory of Mechanics in Energy Engineering, Shanghai University, Shanghai 200072, China

Received date: 2019-05-14

Revised date: 2019-07-13

Online published: 2019-11-20

Supported by

Project supported by the National Natural Science Foundation of China (No. 11772205), the Scientific Research Fund of Liaoning Provincial Education Department (No. L201703), the Liaoning Revitalization Talent Program (No. XLYC1807172), and the Training Project of Liaoning Higher Education Institutions in Domestic and Overseas (No. 2018LNGXGJWPY-YB008)

Fold

Abstract

A novel vibration isolation device called the nonlinear energy sink (NES) with NiTiNOL-steel wire ropes (NiTi-ST) is applied to a whole-spacecraft system. The NiTi-ST is used to describe the damping of the NES, which is coupled with the modified Bouc-Wen model of hysteresis. The NES with NiTi-ST vibration reduction principle uses the irreversibility of targeted energy transfer (TET) to concentrate the energy locally on the nonlinear oscillator, and then dissipates it through damping in the NES with NiTi-ST. The generalized vibration transmissibility, obtained by the root mean square treatment of the harmonic response of the nonlinear output frequency response functions (NOFRFs), is first used as the evaluation index to analyze the whole-spacecraft system in the future. An optimization analysis of the impact of system responses is performed using different parameters of NES with NiTi-ST based on the transmissibility of NOFRFs. Finally, the effects of vibration suppression by varying the parameters of NiTi-ST are analyzed from the perspective of energy absorption. The results indicate that NES with NiTi-ST can reduce excessive vibration of the whole-spacecraft system, without changing its natural frequency. Moreover, the NES with NiTi-ST can be directly used in practical engineering applications.

Key words： nonlinear energy sink (NES); vibration isolation; NiTiNOL-steel wire rope (NiTi-ST); nonlinear output frequency response function (NOFRF); root mean square; transmissibility

Cite this article

Yewei ZHANG, Kefan XU, Jian ZANG, Zhiyu NI, Yunpeng ZHU, Liqun CHEN . Dynamic design of a nonlinear energy sink with NiTiNOL-steel wire ropes based on nonlinear output frequency response functions[J]. Applied Mathematics and Mechanics, 2019 , 40(12) : 1791 -1804 . DOI: 10.1007/s10483-019-2548-9

References

[1] REMEDIA, M., AGLIETTI, G. S., and RICHARDSON, G. Modelling the effect of electrical harness on microvibration response of structures. Acta Astronautica, 109, 88-102(2015)
[2] WILKE, P. S., JOHNSON, C. D., and FOSNESS, E. R. Payload isolation system for launch vehicles. Proceedings of SPIE-The International Society for Optical Engineering, 3045, 20-30(1997)
[3] JOHNSON, C. D. and WILKE, P. S. Protecting satellites from the dynamics of the launch environment. AIAA Space 2003 Conference and Exposition, American Institute of Aeronautics and Astronautics, Reston (2006)
[4] WANG, X. and YANG, B. T. Transient vibration control using nonlinear convergence active vibration absorber for impulse excitation. Mechanical Systems and Signal Processing, 117, 425-436(2019)
[5] YANG, X. D., AN, H. Z., QIAN, Y. J., ZHANG, W., and YAO, M. H. Elliptic motions and control of rotors suspending in active magnetic bearings. Journal of Computational and Nonlinear Dynamics, 11, 5(2016)
[6] SALVI, J., RIZZI, E., and RUSTIGHI, E. Optimum tuning of passive tuned mass dampers for the mitigation of pulse-like responses. Journal of Vibration and Acoustics, 140(6), 061014(2018)
[7] TAKEZAWA, A., MAKIHARA, K., and KOGISO, N. Layout optimization methodology of piezoelectric transducers in energy-recycling semi-active vibration control systems. Journal of Sound and Vibration, 333, 327-344(2014)
[8] GUO, Z. K., YANG, X. D., and ZHANG, W. Dynamic analysis, active and passive vibration control of double-layer hourglass lattice truss structures. Journal of Sandwich Structures and Materials (2018) https://doi.org/10.1177/1099636218784339
[9] DING, H., ZHU, M. H., and CHEN, L. Q. Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions. Applied Mathematics and Mechanics (English Edition), 40(7), 911-924(2019) https://doi.org/10.1007/s10483-019-2493-8
[10] LU, Z. Q., LI, K., DING, H., and CHEN, L. Q. Nonlinear energy harvesting based on a modified snap-through mechanism. Applied Mathematics and Mechanics (English Edition), 40(1), 167-180(2018) https://doi.org/10.1007/s10483-019-2408-9
[11] LIU, C. C. and JING, X. J. Nonlinear vibration energy harvesting with adjustable stiffness, damping and inertia. Nonlinear Dynamics, 88(1), 79-95(2017)
[12] SIAMI, A., KARIMI, H. R., and CIGADA, A. Parameter optimization of an inerter-based isolator for passive vibration control of Michelangelo's Rondanini Pietà. Mechanical Systems and Signal Processing, 98, 667-683(2018)
[13] DING, H. Steady-state responses of a belt-drive dynamical system under dual excitations. Acta Mechanica Sinica, 32(1), 156-169(2016)
[14] DING, H., HUANG, L. L., MAO, X. Y., and CHEN, L. Q. Dynamic stiffness method for free vibration of an axially moving beam with generalized boundary conditions. Applied Mathematics and Mechanics (English Edition), 38(1), 1-14(2017) https://doi.org/10.1007/s10483-016-2152-6
[15] SUN, L. L., HANSEN, C. H., and DOOLAN, C. Evaluation of the performance of a passive-active vibration isolation system. Mechanical Systems and Signal Processing, 50-51, 480-497(2015)
[16] DING, H. and ZU, J. W. Effect of one-way clutch on the nonlinear vibration of belt-drive systems with a continuous belt model. Journal of Sound and Vibration, 332(24), 6472-6487(2013)
[17] YANG, K., ZHANG, Y. W., DING, H., YANG, T. Z., LI, Y., and CHEN, L. Q. Nonlinear energy sink for whole-spacecraft vibration reduction. Journal of Vibration and Acoustics, 139(2), 021011(2017)
[18] VAKAKIS, A. F. Inducing passive nonlinear energy sinks in vibrating systems. Journal of Vibration and Acoustics, 123(3), 324-332(2001)
[19] VAKAKIS, A. F. Shock isolation through the use of nonlinear energy sinks. Journal of Vibration and Control, 9(1/2), 79-93(2003)
[20] MOTATO, E., HARIS, A., THEODOSSIADES, S., MOHAMMADPOUR, M., RAHNEJAT, H., KELLY, P., VAKAKIS, A. F., MCFARLAND, D. M., and BERGMAN, L. A. Targeted energy transfer and modal energy redistribution in automotive drivetrains. Nonlinear Dynamics, 87(1), 169-190(2016)
[21] STAROSVETSKY, Y. and GENDELMAN, O. V. Response regimes of linear oscillator coupled to nonlinear energy sink with harmonic forcing and frequency detuning. Journal of Sound and Vibration, 315(3), 746-765(2008)
[22] ZANG, J., ZHANG, Y. W., DING, H., YANG, T. Z., and CHEN, L. Q. The evaluation of a nonlinear energy sink absorber based on the transmissibility. Mechanical Systems and Signal Processing, 125, 99-122(2019)
[23] HUBBARD, S. A., MCFARLAND, D. M., BERGMAN, L. A., and VAKAKIS, A. F. Targeted energy transfer between a model flexible wing and nonlinear energy sink. Journal of Aircraft, 47(6), 1918-1931(2010)
[24] HARIS, A., MOTATO, E., MOHAMMADPOUR, M., THEODOSSIADES, S., RAHNEJAT, H., MAHONY, M. O'., VAKAKIS, A. F., BERGMAN, L. A., and MCFARL, D. M. On the effect of multiple parallel nonlinear absorbers in palliation of torsional response of automotive drivetrain. International Journal of Non-Linear Mechanics, 96, 22-35(2017)
[25] LI, X., ZHANG, Y. W., DING, H., and CHEN, L. Q. Integration of a nonlinear energy sink and a piezoelectric energy harvester. Applied Mathematics and Mechanics (English Edition), 38(7), 1019-1030(2017) https://doi.org/10.1007/s10483-017-2220-6
[26] CHEN, J. E., ZHANG, W., YAO, M. H., LIU, J., and SUN, M. Vibration reduction in truss core sandwich plate with internal nonlinear energy sink. Composite Structures, 193, 180-188(2018)
[27] YANG, T. Z., LIU, T., TANG, Y., HOU, S., and LV, X. F. Enhanced targeted energy transfer for adaptive vibration suppression of pipes conveying fluid. Nonlinear Dynamics, 97, 1937-1944(2019)
[28] ZANG, J. and CHEN, L. Q. Complex dynamics of a harmonically excited structure coupled with a nonlinear energy sink. Acta Mechanica Sinica, 33(4), 801-822(2017)
[29] ZANG, J., YUAN, T. C., LU, Z. Q., ZHANG, Y. W., DING, H., and CHEN, L. Q. A lever-type nonlinear energy sink. Journal of Sound and Vibration, 437, 119-134(2018)
[30] ZHANG, Y. W., LU, Y. N., ZHANG, W., TENG, Y. Y., YANG, H. X., YANG, T. Z., and CHEN, L. Q. Nonlinear energy sink with inerter. Mechanical Systems and Signal Processing, 125, 52-64(2019)
[31] CHEN, J. E., HE, W., ZHANG, W., YAO, M. H., LIU, J., and SUN, M. Vibration suppression and higher branch responses of beam with parallel nonlinear energy sinks. Nonlinear Dynamics, 91(2), 885-904(2018)
[32] LAMARQUE, C. H. and SAVADKOOHI, A. T. Dynamical behavior of a Bouc-Wen type oscillator coupled to a nonlinear energy sink. Meccanica, 49(8), 1917-1928(2014)
[33] BOUC, R. Forced vibration of mechanical systems with hysteresis. Proceedings of the Fourth Conference on Nonlinear Oscillation, Academic, Prague (1967)
[34] BOUC, R. Modle mathmatique d'hystrsis. Acustica, 21, 16-25(1971)
[35] WEN, Y. K. Method for random vibration of hysteretic systems. Journal of the Engineering Mechanics, 102(2), 246-263(1976)
[36] GIANDOMENICO, D. M., STEFANO, P., and SALVATORE, S. Cabinet and shelter vibration isolation:numerical and experimental investigation. Engineering Letters, 22(4), 149-157(2014)
[37] CARBONI, B. and LACARBONARA, W. A new vibration absorber based on the hysteresis of multi-configuration NiTiNOL-steel wire ropes assemblies. MATEC Web of Conferences, 16, 01004(2014)
[38] CARBONI, B., LACARBONARA, W., and AURICCHIO, F. Hysteresis of multiconfiguration assemblies of nitinol and steel strands:experiments and phenomenological identification. Journal of Engineering Mechanics, 141(3), 04014135(2015)
[39] BREWICK, P. T., MASRI, S. F., CARBONI, B., and LACARBONARA, W. Data-based nonlinear identification and constitutive modeling of hysteresis in NiTiNOL and steel strands. Journal of Engineering Mechanics, 142(12), 04016107(2016)
[40] CARBONI, B. and LACARBONARA, W. Nonlinear dynamic characterization of a new hysteretic device:experiments and computations. Nonlinear Dynamics, 83(1/2), 23-39(2016)
[41] VOLTERRA, V. Theory of Functionals and of Integral and Integro-Differential Equations, Dover, New York (1932)
[42] GEORGE, D. Continuous Nonlinear Systems, MIT RLE Technical Report, U. S. A. (1959)
[43] LANG, Z. Q. and BILLINGS, S. A. Energy transfer properties of non-linear systems in the frequency domain. International Journal of Control, 78(5), 345-362(2005)
[44] PENG, Z. K., LANG, Z. Q., and BILLINGS, S. A. Linear parameter estimation for multi-degreeof-freedom nonlinear systems using nonlinear output frequency-response functions. Mechanical Systems and Signal Processing, 21(8), 3108-3122(2007)
[45] PENG, Z. K., LANG, Z. Q., and CHU, F. L. Numerical analysis of cracked beams using nonlinear output frequency response functions. Computers and Structures, 86(17/18), 1809-1818(2008)
[46] PENG, Z. K., LANG, Z. Q., WOLTERS, C., and BILLINGS, S. A. Feasibility study of structural damage detection using NARMAX modelling and nonlinear output frequency response function based analysis. Mechanical Systems and Signal Processing, 25(3), 1045-1061(2011)
[47] PENG, Z. K., LANG, Z. Q., and BILLINGS, S. A. Nonlinear parameter estimation for multidegree-of-freedom nonlinear systems using nonlinear output frequency-response functions. Mechanical Systems and Signal Processing, 22(7), 1582-1594(2008)
[48] BAYMA, R. S., ZHU, Y. P., and LANG, Z. Q. The analysis of nonlinear systems in the frequency domain using nonlinear output frequency response functions. Automatica, 94, 452-457(2018)
[49] YANG, K., ZHANG, Y. W., DING, H., and CHEN, L. Q. The transmissibility of nonlinear energy sink based on nonlinear output frequency-response functions. Communications in Nonlinear Science and Numerical Simulation, 44, 184-192(2017)
[50] PENG, Z. K., LANG, Z. Q., BILLINGS, S. A., and TOMLISON, G. R. Comparisons between harmonic balance and nonlinear output frequency response function in nonlinear system analysis. Journal of Sound and Vibration, 311(1), 56-73(2008)
[51] CARBONI, B. and LACARBONARA, W. Nonlinear vibration absorber with pinched hysteresis:theory and experiments. Journal of Engineering Mechanics, 142(5), 04016023(2016)
[52] LANG, Z. Q. and BILLINGS, S. A. Output frequency characteristics of nonlinear system. International Journal of Control, 64(6), 1049-1067(1996)
[53] PENG, Z. K., LANG, Z. Q., and BILLINGS, S. A. Resonances and resonant frequencies for a class of nonlinear systems. Journal of Sound and Vibration, 300(3-5), 993-1014(2007)
[54] BILLINGS, S. A. and JONES, J. C. Mapping non-linear integro-differential equations into the frequency domain. International Journal of Control, 52(4), 863-879(1990)
[55] FANG, Z. W., ZHANG, Y. W., LI, X., DING, H., and CHEN, L. Q. Integration of a nonlinear energy sink and a giant magnetostrictive energy harvester. Journal of Sound and Vibration, 391, 35-49(2017)
[56] FANG, Z. W., ZHANG, Y. W., LI, X., DING, H., and CHEN, L. Q. Complexification-averaging analysis on a giant magnetostrictive harvester integrated with a nonlinear energy sink. Journal of Vibration and Acoustics, 140(2), 021009(2017)
[57] CARBONI, B. and LACARBONARA, W. Nonlinear vibration absorber with pinched hysteresis:theory and experiments. Journal of Engineering Mechanics, 142(5), 04016023(2016)
[58] TSIATAS, G. C. and CHARALAMPAKIS, A. E. A new hysteretic nonlinear energy sink (HNES). Communications in Nonlinear Science and Numerical Simulation, 60, 1-11(2018)

Options

Outlines

模态框（Modal）标题

Abstract

Cite this article

References