Theoretical and experimental investigations on an X-shaped vibration isolator with active controlled variable stiffness

doi:10.1007/s10483-024-3135-6

Abstract

Abstract:

A novel X-shaped variable stiffness vibration isolator (X-VSVI) is proposed. The Runge-Kutta method, harmonic balance method, and wavelet transform spectra are introduced to evaluate the performance of the X-VSVI under various excitations. The layer number, the installation angle of the X-shaped structure, the stiffness, and the active control parameters are systematically analyzed. In addition, a prototype of the X-VSVI is manufactured, and vibration tests are carried out. The results show that the proposed X-VSVI has a superior adaptability to that of a traditional X-shaped mechanism, and shows excellent vibration isolation performance in response to different amplitudes and forms of excitations. Moreover, the vibration isolation efficiency of the device can be improved by appropriate adjustment of parameters.

Key words: bionic vibration isolation, X-shaped structure, variable stiffness structure, nonlinear dynamics, prototype experiment

2010 MSC Number:

Zeyu CHAI, J. T. HAN, Xuyuan SONG, Jian ZANG, Yewei ZHANG, Zhen ZHANG. Theoretical and experimental investigations on an X-shaped vibration isolator with active controlled variable stiffness. Applied Mathematics and Mechanics (English Edition), 2024, 45(8): 1371-1386.

TrendMD

Figures/Tables 22

Fig. 1

Fig. 2

Fig. 3

Fig. 4

Fig. 5

Fig. 6

Fig. 7

Fig. 8

Table 1

Table 2

Fig. 9

Fig. 10

Fig. 11

Fig. 12

Fig. 13

Fig. 14

Fig. 15

Fig. 16

Fig. 17

Fig. 18

Fig. 19

Fig. 20

References 44

1	FEI, H., SONG, E. Z., MA, X. Z., and JIANG, D. W. Research on whole-spacecraft vibration isolation based on predictive control. Procedia Engineering, 16, 467- 476 (2011)
2	ZHANG, Y. W., FANG, B., and CHEN, Y. Vibration isolation performance evaluation of the discrete whole-spacecraft vibration isolation platform for flexible spacecraft. Meccanica, 47, 1185- 1195 (2012)
3	LIU, L. K., and ZHENG, G. T. Parameter analysis of PAF for whole-spacecraft vibration isolation. Aerospace Science and Technology, 11, 464- 472 (2007)
4	SMITH, S. D., SMITH, J. A., and BOWDEN, D. R. Transmission characteristics of suspension seats in multi-axis vibration environments. International Journal of Industrial Ergonomics, 38, 434- 446 (2008)
5	XU, K. F., ZHANG, Y. W., ZHU, Y. P., ZANG, J., and CHEN, L. Q. Dynamics analysis of active variable stiffness vibration isolator for whole-spacecraft systems based on nonlinear output frequency response functions. Acta Mechanica Solida Sinica, 33 (6), 731- 743 (2020)
6	LI, L., WANG, L., YUAN, L., ZHENG, R., WU, Y. P., SUI, J., and ZHONG, J. Micro-vibration suppression methods and key technologies for high-precision space optical instruments. Acta Astronautica, 180, 417- 428 (2021)
7	CHEN, S. Y., YANG, Z. H., YING, M. X., ZHENG, Y. W., LIU, Y. J., and PAN, Z. W. Parallel load-bearing and damping system design and test for satellite vibration suppression. Applied Sciences, 10, 1548 (2020)
8	TANG, J., CAO, D. Q., REN, F., and LI, H. B. Design and experimental study of a VCM-based whole-spacecraft vibration isolation system. Journal of Aerospace Engineering, 31 (5), 04018045 (2018)
9	ZHANG, F., XU, M. L., SHAO, S. B., and XIE, S. L. A new high-static-low-dynamic stiffness vibration isolator based on magnetic negative stiffness mechanism employing variable reluctance stress. Journal of Sound and Vibration, 476, 115322 (2020)
10	WU, J. L., ZENG, L. Z., HAN, B., ZHOU, Y. F., LUO, X., LI, X. Q., and CHEN, X. W. Analysis and design of a novel arrayed magnetic spring with high negative stiffness for low-frequency vibration isolation. International Journal of Mechanical Sciences, 216, 106980 (2022)
11	LU, Z. Q., BRENNAN, M. J., YANG, T. J., LI, X. H., and LIU, Z. G. An investigation of a two-stage nonlinear vibration isolation system. Journal of Sound and Vibration, 332 (6), 1456- 1464 (2013)
12	LU, Z. Q., CHEN, L. Q., BRENNAN, M. J., LI, J. M., and DING, H. The characteristics of vibration isolation system with damping and stiffness geometrically nonlinear. Journal of Physics: Conference Series, 744 (1), 012115 (2016)
13	LU, Z. Q., BRENNAN, M. J., DING, H., and CHEN, L. Q. High-static-low-dynamic-stiffness vibration isolation enhanced by damping nonlinearity. Science China Technological Sciences, 62 (7), 1103- 1110 (2019)
14	GATTU, G. Statics and dynamics of a nonlinear oscillator with quasi-zero stiffness behaviour for large deflections. Communications in Nonlinear Science and Numerical Simulation, 83, 105143 (2020)
15	ZHAO, F., JI, J. C., LUO, Q. T., CAO, S. Q., CHEN, L. M., and DU, W. L. An improved quasi-zero stiffness isolator with two pairs of oblique springs to increase isolation frequency band. Nonlinear Dynamics, 104 (1), 349- 365 (2021)
16	YANG, K., TONG, W. H., LIN, L. Q., YURCHENKO, D., and WANG, J. L. Active vibration isolation performance of the bistable nonlinear electromagnetic actuator with the elastic boundary. Journal of Sound and Vibration, 52, 116588 (2022)
17	WANG, A. X., WANG, S. Q., XIA, H. W., MA, G. C., ZHANG, L., and LIU, W. Adaptive neural control of microgravity active vibration isolation system subject to output constraint and unexpected disturbance. Acta Astronautica, 213, 168- 176 (2023)
18	QIAN, Y. C., XIE, Y., JIA, J. J., and ZHANG, L. Development of active microvibration isolation system for precision space payload. Applied Sciences, 12 (9), 4548 (2022)
19	XIE, X., HE, P. T., WU, D., and ZHANG, Z. Y. Ultra-low frequency active vibration isolation in high precision equipment with electromagnetic suspension: analysis and experiment. Precision Engineering, 84, 91- 101 (2023)
20	BIAN, J., and JING, X. J. Nonlinear passive damping of the X-shaped structure. Procedia Engineering, 199, 1701- 1706 (2017)
21	JING, X. J. The X-structure/mechanism approach to beneficial nonlinear design in engineering. Applied Mathematics and Mechanics (English Edition), 43 (7), 979- 1000 (2022) doi: 10.1007/s10483-022-2862-6
22	FENG, X., JING, X. J., and GUO, Y. Q. Vibration isolation with passive linkage mechanisms. Nonlinear Dynamics, 106 (3), 1891- 1927 (2021)
23	YAN, G., QI, W. H., SHI, J. W., YAN, H., ZOU, H. X., ZHAO, L. C., WU, Z. Y., FANG, X. Y., LI, X. Y., and ZHANG, W. M. Bionic paw-inspired structure for vibration isolation with novel nonlinear compensation mechanism. Journal of Sound and Vibration, 525, 116799 (2022)
24	ZENG, R., WEN, G. L., ZHOU, J. X., and ZHAO, G. Limb-inspired bionic quasi-zero stiffness vibration isolator. Acta Mechanica Sinica, 37 (7), 1152- 1167 (2021)
25	YAN, G., ZOU, H. X., WANG, S., ZHAO, L. C., WU, Z. Y., and ZHANG, W. M. Bio-inspired toe-like structure for low-frequency vibration isolation. Mechanical Systems and Signal Processing, 162, 108010 (2022)
26	JIN, G. X., WANG, Z. H., and YANG, T. Z. Cascaded quasi-zero stiffness nonlinear low-frequency vibration isolator inspired by human spine. Applied Mathematics and Mechanics (English Edition), 43 (6), 813- 824 (2022) doi: 10.1007/s10483-022-2852-5
27	WU, Z. J., JING, X. J., BIAN, J., LI, F. M., and ALLEN, R. Vibration isolation by exploring bio-inspired structural nonlinearity. Bioinspiration and Biomimetics, 10 (5), 056015 (2015)
28	BIAN, J., and JING, X. J. Analysis and design of a novel and compact X-structured vibration isolation mount (X-mount) with wider quasi-zero-stiffness range. Nonlinear Dynamics, 101 (4), 2195- 2222 (2020)
29	ZHOU, S. H., LIU, Y. L., JIANG, Z. Y., and REN, Z. H. Nonlinear dynamic behavior of a bio-inspired embedded X-shaped vibration isolation system. Nonlinear Dynamics, 110 (1), 153- 175 (2022)
30	SONG, Y., ZHANG, C., LI, Z. L., LI, Y., LIAN, J. Y., SHI, Q. L., and YAN, B. Study on dynamic characteristics of bio-inspired vibration isolation platform. Journal of Vibration and Control, 28, 1470- 1485 (2022)
31	CHAI, Y. Y., JING, X. J., and CHAO, X. International journal of mechanical sciences X-shaped mechanism based enhanced tunable QZS property for passive vibration isolation. International Journal of Mechanical Sciences, 218, 107077 (2022)
32	JING, X. J., ZHANG, L. L., FENG, X., SUN, B., and LI, Q. K. A novel bio-inspired anti-vibration structure for operating hand-held jackhammers. Mechanical Systems and Signal Processing, 118, 317- 339 (2019)
33	DAI, H. H., JING, X. J., WANG, Y., YUE, X. K., and YUAN, J. P. Post-capture vibration suppression of spacecraft via a bio-inspired isolation system. Mechanical Systems and Signal Processing, 105, 214- 240 (2018)
34	JING, X. J., ZHANG, L. L., JIANG, G. Q., FENG, X., GUO, Y. Q., and XU, Z. D. Critical factors in designing a class of x-shaped structures for vibration isolation. Engineering Structures, 199, 109659 (2019)
35	HAN, C., LIU, X. G., WU, M. Y., and LIANG, W. L. A new approach to achieve variable negative stiffness by using an electromagnetic asymmetric tooth structure. Shock and Vibration, 2018, 7476387 (2018)
36	HU, Z., WANG, X., YAO, H. X., WANG, G. Y., and ZHENG, G. T. Theoretical analysis and experimental identification of a vibration isolator with widely-variable stiffness. Journal of Vibration and Acoustics, 140 (5), 051014 (2018)
37	LI, R. P., DU, C. B., GUO, F., YU, G. J., and LIN, X. G. Performance of variable negative stiffness MRE vibration isolation system. Advances in Materials Science and Engineering, 2015, 837657 (2015)
38	CHEN, R. Z., LI, X. P., YANG, Z. M., XU, J. C., and YANG, H. X. A variable positive-negative stiffness joint with low frequency vibration isolation performance. Measurement: Journal of the International Measurement Confederation, 185, 110046 (2021)
39	WU, T. H., and LAN, C. C. A wide-range variable stiffness mechanism for semi-active vibration systems. Journal of Sound and Vibration, 363, 18- 32 (2016)
40	ZHAO, J. L., SUN, Y., DING, J. H., SUN, Y., WANG, M., YUAN, S. J., PU, H. Y., LUO, J., XIE, Z. J., QIN, Y., WEI, J., XIE, S. R., and PENG, Y. Shock isolation capability of an electromagnetic variable stiffness isolator with bidirectional stiffness regulation. IEEE/ASME Transactions on Mechatronics, 26 (4), 2038- 2047 (2021)
41	CHURCHILL, C. B., SHAHAN, D. W., SMITH, S. P., KEEFE, A. C., and MCKNIGHT, G. P. Materials engineering: dynamically variable negative stiffness structures. Science Advances, 2 (2), e1500778 (2016)
42	ZHANG, Y. W., LI, Z., XU, K. F., and ZANG, J. A lattice sandwich structure with the active variable stiffness device under aerodynamical condition. Aerospace Science and Technology, 116, 106849 (2021)
43	ZHANG, Z., LU, Z. Q., DING, H., and CHEN, L. Q. An inertial nonlinear energy sink. Journal of Sound and Vibration, 450, 199- 213 (2019)
44	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)

[1]	Runqing CAO, Zilong GUO, Wei CHEN, Huliang DAI, Lin WANG. Nonlinear dynamics of a circular curved cantilevered pipe conveying pulsating fluid based on the geometrically exact model [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(2): 261-276.
[2]	Shihua ZHOU, Dongsheng ZHANG, Bowen HOU, Zhaohui REN. Vibration isolation performance analysis of a bilateral supported bio-inspired anti-vibration control system [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 759-772.
[3]	Duquan ZUO, B. SAFAEI, S. SAHMANI, Guoling MA. Nonlinear free vibrations of porous composite microplates incorporating various microstructural-dependent strain gradient tensors [J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(6): 825-844.
[4]	Yaode YIN, Demin ZHAO, Jianlin LIU, Zengyao XU. Nonlinear dynamic analysis of dielectric elastomer membrane with electrostriction [J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(6): 793-812.
[5]	Lei LI, Hanbiao LIU, Jianxin HAN, Wenming ZHANG. Nonlinear modal coupling in a T-shaped piezoelectric resonator induced by stiffness hardening effect [J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(6): 777-792.
[6]	Lei XIA, Jiaojiao SUN, Zuguang YING, Ronghua HUAN, Weiqiu ZHU. Dynamics and response reshaping of nonlinear predator-prey system undergoing random abrupt disturbances [J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(8): 1123-1134.
[7]	Kun ZHOU, Qiao NI, Wei CHEN, Huliang DAI, Zerui PENG, Lin WANG. New insight into the stability and dynamics of fluid-conveying supported pipes with small geometric imperfections [J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(5): 703-720.
[8]	A. SARAFRAZ, S. SAHMANI, M. M. AGHDAM. Nonlinear primary resonance analysis of nanoshells including vibrational mode interactions based on the surface elasticity theory [J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(2): 233-260.
[9]	Yunyue CONG, Houjun KANG, Tieding GUO. Analysis of in-plane 1:1:1 internal resonance of a double cable-stayed shallow arch model with cables' external excitations [J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(7): 977-1000.
[10]	Houjun KANG, Tieding GUO, Weidong ZHU, Junyi SU, Bingyu ZHAO. Dynamical modeling and non-planar coupled behavior of inclined CFRP cables under simultaneous internal and external resonances [J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(5): 649-678.
[11]	Nan ZHANG, Bin CHENG, Hexi BAOYIN. A new physical model on the capillary phenomenon of granular particles [J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(1): 127-138.
[12]	Kuan LU, Yushu CHEN, Lei HOU. Bifurcation characteristics analysis of a class of nonlinear dynamical systems based on singularity theory [J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(9): 1233-1246.
[13]	Minghui FU, Kelang LU, Weihua LI, S. V. SHESHENIN. New way to construct high order Hamiltonian variational integrators [J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(8): 1041-1052.
[14]	Bensong YU, Dongping JIN, Hao WEN. Nonlinear dynamics of flexible tethered satellite system subject to space environment [J]. Applied Mathematics and Mechanics (English Edition), 2016, 37(4): 485-500.
[15]	Qiaoyun YAN, Hu DING, Liqun CHEN. Nonlinear dynamics of axially moving viscoelastic Timoshenko beam under parametric and external excitations [J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(8): 971-984.