Applied Mathematics and Mechanics (English Edition) ›› 2024, Vol. 45 ›› Issue (1): 85-110.doi: https://doi.org/10.1007/s10483-024-3070-7
• Articles • Previous Articles Next Articles
Yong WANG1,2, Peili WANG1, Haodong MENG3, Liqun CHEN4,*(
)
Email Alert
RSSReceived:2023-05-25
Online:2024-01-01
Published:2023-12-26
Contact:
Liqun CHEN
E-mail:lqchen@shu.edu.cn
Supported by:2010 MSC Number:
Yong WANG, Peili WANG, Haodong MENG, Liqun CHEN. Dynamic performance and parameter optimization of a half-vehicle system coupled with an inerter-based X-structure nonlinear energy sink. Applied Mathematics and Mechanics (English Edition), 2024, 45(1): 85-110.
Fig. 1
Schematic diagram of the half-vehicle system coupled with IX-NES (color online)"
Table 1
Structural parameters of the half-vehicle system coupled with the IX-NES"
 |
Fig. 2
Geometric deformation of the X-structure (color online)"
Fig. 3
Comparison between the exact expression and Taylor series expansion of the nonlinear stiffness terms f1(zs, φ, zbf) and f2(zs, φ, zbr) (α = 45°, L = 0.15 m, kbf = kbr = 1 800 N·m–1, and φ = 0.01 rad) (color online)"
Fig. 4
Comparison between the analytical and numerical results of the dynamic response for the half-vehicle system coupled with the IX-NES under road harmonic excitation (A = 0.05 m, v = 20 m·s–1, L = 0.15 m, α = 45°, kbf = kbr = 1 800 N·m–1, cbf = cbr = 1 200 N·s·m–1, and bf = br = 100 kg) (color online)"
Fig. 5
Schematic diagram of the half-vehicle system coupled with X-NES (color online)"
Fig. 6
Comparison of the dynamic performance indices for three half-vehicle systems with different vehicle speeds under road harmonic excitation (A = 0.05 m, L = 0.15 m, α = 45°, kbf = kbr = 1 800 N·m–1, cbf = cbr = 1 200 N·s·m–1, and bf = br = 100 kg) (color online)"
Fig. 7
Dynamic performance indices of the half-vehicle system coupled with the IX-NES for different rod lengths under road harmonic excitation (A = 0.05 m, v = 20 m·s–1, α = 45°, kbf = kbr =1 800 N·m–1, cbf = cbr = 1 200 N·s·m–1, and bf = br = 100 kg) (color online)"
Fig. 8
Dynamic performance indices of the half-vehicle system coupled with the IX-NES for different initial angles under road harmonic excitation (A = 0.05 m, v = 20 m·s–1, L = 0.15 m, kbf = kbr =1 800 N·m–1, cbf = cbr = 1 200 N·s·m–1, and bf = br = 100 kg) (color online)"
Fig. 9
Dynamic performance indices of the half-vehicle system coupled with the IX-NES for different stiffness coefficients under road harmonic excitation (A = 0.05 m, v = 20 m·s–1, L = 0.15 m, α = 45°, cbf = cbr = 1 200 N·s·m–1, and bf = br = 100 kg) (color online)"
Fig. 10
Dynamic performance indices of the half-vehicle system coupled with the IX-NES for different damping coefficients under road harmonic excitation (A = 0.05 m, v = 20 m·s–1, L = 0.15 m, α = 45°, kbf = kbr =1 800 N·m–1, and bf = br = 100 kg) (color online)"
Fig. 11
Dynamic performance indices of the half-vehicle system coupled with the IX-NES for different inertances under road harmonic excitation (A = 0.05 m, v = 20 m·s–1, L = 0.15 m, α = 45°, kbf = kbr =1 800 N·m–1, and cbf = cbr = 1 200 N·s·m–1) (color online)"
Fig. 12
Comparison of the dynamic performance indices for three half-vehicle systems under road random excitation (v = 20 m·s–1, L = 0.15 m, α = 45°, kbf = kbr =1 800 N·m–1, cbf = cbr = 1 200 N·s·m–1, bf = br = 100 kg, and maf = mar = 100 kg) (color online)"
Table 2
RMS values of the dynamic performance indices for three half-vehicle systems under road random excitation (v = 20 m·s–1, L = 0.15 m, α = 45°, kbf = kbr =1 800 N·m–1, cbf = cbr = 1 200 N·s·m–1, and bf = br = 100 kg)"
 |
Fig. 13
The RMS values of the dynamic performance indices of the half-vehicle system coupled with the IX-NES for different rod lengths under road random excitation (v = 20 m·s–1, α = 45°, kbf = kbr =1 800 N·m–1, cbf = cbr = 1 200 N·s·m–1, and bf = br = 100 kg) (color online)"
Fig. 14
The RMS values of the dynamic performance indices of the half-vehicle system coupled with the IX-NES for different initial angles under road random excitation (v = 20 m·s–1, L = 0.15 m, kbf = kbr =1 800 N·m–1, cbf = cbr = 1 200 N·s·m–1, and bf = br = 100 kg) (color online)"
Fig. 15
The RMS values of the dynamic performance indices of the half-vehicle system coupled with the IX-NES for different stiffness coefficients under road random excitation (v = 20 m·s–1, L = 0.15 m, α = 45°, cbf = cbr = 1 200 N·s·m–1, and bf = br = 100 kg) (color online)"
Fig. 16
The RMS values of the dynamic performance indices of the half-vehicle system coupled with the IX-NES for different damping coefficients under road random excitation (v = 20 m·s–1, L = 0.15 m, α = 45°, kbf = kbr =1 800 N·m–1, and bf = br = 100 kg) (color online)"
Fig. 17
The RMS values of the dynamic performance indices of the half-vehicle system coupled with the IX-NES for different inertances under road random excitation (v = 20 m·s–1, L = 0.15 m, α = 45°, kbf = kbr =1 800 N·m–1, and cbf = cbr = 1 200 N·s·m–1) (color online)"
Table 3
The optimized structural parameters of the IX-NES"
 |
Fig. 18
Comparison of vehicle body vertical and pitching accelerations for three different half-vehicle systems under road random excitation (color online)"
Table 4
The RMS values of the dynamic performance indices for three different half-vehicle systems"
 |
| 1 | RAJAMANI, R. Vehicle Dynamics and Control, Springer, New York (2012) |
| 2 | ZHOU, H. C., JIANG, Z., WANG, G. L., and ZHANG, S. P. Aerodynamic characteristics of isolated loaded tires with different tread patterns: experiment and simulation. Chinese Journal of Mechanical Engineering, 34, 1- 16 (2021) |
| 3 | DING, R. K., WANG, R. C., MENG, X. P., and CHEN, L. Energy consumption sensitivity analysis and energy-reduction control of hybrid electromagnetic active suspension. Mechanical Systems and Signal Processing, 134, 106301 (2019) |
| 4 | DU, H., and ZHANG, N. Constrained H∞ control of active suspension for a half-car model with a time delay in control. Proceedings of the Institution of Mechanical Engineers, Part D: Journal of Automobile Engineering, 222, 665- 684 (2008) |
| 5 | WANG, Y., LI, S. M., CHENG, C., and SU, Y. Q. Adaptive control of a vehicle-seat-human coupled model using quasi-zero-stiffness vibration isolator as seat suspension. Journal of Mechanical Science and Technology, 32, 2973- 2985 (2018) |
| 6 | MO, C., and SUNWOO, M. A semiactive vibration absorber (SAVA) for automotive suspensions. International Journal of Vehicle Design, 29 (1-2), 83- 95 (2001) |
| 7 | MCKILLIP, D., SWAYZE, J., and MATHEY, J. Experimental method development for steering wheel system optimization with integral dynamic tuned absorber. SAE Technical Paper, 2275 (2005) |
| 8 | AUBERT, A. C., and HOWLE, A. Design issues in the use of elastomers in automotive tuned mass dampers. SAE Technical Paper, 2198 (2007) |
| 9 | WANG, R. R., JING, H., YAN, F. J., KARIMI, H. R., and CHEN, N. Optimization and finite-frequency H∞ control of active suspensions in in-wheel motor driven electric ground vehicles. Journal of the Franklin Institute, 352 (2), 468- 484 (2015) |
| 10 | LIU, M. C., GU, F. H., and ZHANG, Y. Z. Ride comfort optimization of in-wheel-motor electric vehicles with in-wheel vibration absorbers. Energies, 10 (10), en10101647 (2017) |
| 11 | DING, H., and CHEN, L. Q. Designs, analysis, and applications of nonlinear energy sinks. Nonlinear Dynamics, 100, 3061- 3107 (2020) |
| 12 | VAKAKIS, A. F., GENDELMAN, O. V., BERGMAN, L. A., MOJAHED, A., and GZAL, M. Nonlinear targeted energy transfer: state of the art and new perspectives. Nonlinear Dynamics, 108, 711- 741 (2022) |
| 13 |
WEI, Y. M., WEI, S., ZHANG, Q. L., DONG, X. J., PENG, Z. K., and ZHANG, W. M. Targeted energy transfer of a parallel nonlinear energy sink. Applied Mathematics and Mechanics (English Edition), 40 (5), 621- 630 (2019)
doi: 10.1007/s10483-019-2477-6 |
| 14 |
DING, H., and SHAO, Y. F. NES cell. Applied Mathematics and Mechanics (English Edition), 43 (12), 1793- 1804 (2022)
doi: 10.1007/s10483-022-2934-6 |
| 15 | CHEN, Y. Y., QIAN, Z. C., CHEN, K., TAN, P., and TESFAMARIAM, S. Seismic performance of a nonlinear energy sink with negative stiffness and sliding friction. Structural Control and Health Monitoring, 26 (11), e2437 (2019) |
| 16 | LI, X., MOJAHED, A., CHEN, L. Q., BERGMAN, L. A., and VAKAKIS, A. F. Shock response mitigation of a large-scale structure by modal energy redistribution facilitated by a strongly nonlinear absorber. Acta Mechanica Sinica, 38, 121464 (2022) |
| 17 |
GUO, H. L., CHEN, Y. S., and YANG, T. Z. Limit cycle oscillation suppression of 2-DOF airfoil using nonlinear energy sink. Applied Mathematics and Mechanics (English Edition), 34 (10), 1277- 1290 (2013)
doi: 10.1007/s10483-013-1744-8 |
| 18 | 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) |
| 19 | LIU, Y., MOJAHED, A., BERGMAN, L. A., and VAKAKIS, A. F. A new way to introduce geometrically nonlinear stiffness and damping with an application to vibration suppression. Nonlinear Dynamics, 96, 1819- 1845 (2019) |
| 20 |
XUE, J., ZHANG, Y., DING, H., and CHEN, L. Q. Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation. Applied Mathematics and Mechanics (English Edition), 41, 1- 14 (2020)
doi: 10.1007/s10483-020-2560-6 |
| 21 |
CHEN, J. E., LI, J. L., YAO, M. H., LIU, J., ZHANG, J. H., and SUN, M. Nonreciprocity of energy transfer in a nonlinear asymmetric oscillator system with various vibration states. Applied Mathematics and Mechanics (English Edition), 44 (5), 727- 744 (2023)
doi: 10.1007/s10483-023-2987-9 |
| 22 | LIU, Y., and WANG, Y. Vibration suppression of a linear oscillator by a chain of nonlinear vibration absorbers with geometrically nonlinear damping. Communications in Nonlinear Science and Numerical Simulation, 118, 107016 (2023) |
| 23 | SMITH, M. C. Synthesis of mechanical networks: the inerter. IEEE Transactions on Automatic Control, 47 (10), 1648- 1662 (2002) |
| 24 | WANG, Y., DING, H., and CHEN, L. Q. Averaging analysis on a semi-active inerter-based suspension system with relative-acceleration-relative-velocity control. Journal of Vibration and Control, 26 (13-14), 1199- 1215 (2020) |
| 25 | ZHANG, X. L., GENG, C., NIE, J. M., and GAO, Q. The missing mem-inerter and extended mem-dashpot found. Nonlinear Dynamics, 101, 835- 856 (2020) |
| 26 | WANG, Y., JIN, X. Y., ZHANG, Y. S., DING, H., and CHEN, L. Q. Dynamic performance and stability analysis of an active inerter-based suspension with time-delayed acceleration feedback control. Bulletin of the Polish Academy of Sciences-Technical Sciences, 70 (2), e140687 (2022) |
| 27 | JIANG, J. Z., MATAMOROS-SANCHEZ, A. Z., GOODALL, R. M., and SMITH, M. C. Passive suspensions incorporating inerters for railway vehicles. Vehicle System Dynamics, 50 (S1), 263- 276 (2012) |
| 28 | WANG, Y., LI, H. X., MENG, H. D., and WANG, Y. Dynamic characteristics of underframe semi-active inerter-based suspended device for high-speed train based on LQR control. Bulletin of the Polish Academy of Sciences-Technical Sciences, 70 (4), e141722 (2022) |
| 29 | YANG, J., JIANG, J. Z., and NEILD, S. A. Dynamic analysis and performance evaluation of nonlinear inerter-based vibration isolators. Nonlinear Dynamics, 99, 1823- 1839 (2020) |
| 30 | WANG, Y., LI, H. X., CHENG, C., DING, H., and CHEN, L. Q. Dynamic performance analysis of a mixed-connected inerter-based quasi-zero stiffness vibration isolator. Structural Control and Health Monitoring, 27 (7), e2604 (2020) |
| 31 | LU, Z. Q., GU, D. H., DING, H., LACARBONARA, W., and CHEN, L. Q. A ring vibration isolator enhanced by shape memory pseudoelasticity. Applied Mathematical Modelling, 100, 1- 15 (2021) |
| 32 | WANG, Y., LI, H. X., JIANG, W. A., DING, H., and CHEN, L. Q. A base excited mixed-connected inerter-based quasi-zero stiffness vibration isolator with mistuned load. Mechanics of Advanced Materials and Structures, 29 (25), 4224- 4242 (2022) |
| 33 | HU, Y., and CHEN, M. Z. Q. Performance evaluation for inerter-based dynamic vibration absorbers. International Journal of Mechanical Sciences, 99, 297- 307 (2015) |
| 34 | ZHANG, S. Y., JIANG, J. Z., and NEILD, S. A. Optimal configurations for a linear vibration suppression device in a multi-storey building. Structural Control and Health Monitoring, 24 (3), e1887 (2017) |
| 35 | 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) |
| 36 | JAVIDIALESAADI, A., and WIERSCHEM, N. E. An inerter-enhanced nonlinear energy sink. Mechanical Systems and Signal Processing, 129, 449- 454 (2019) |
| 37 | ZHANG, Z., LU, Z. Q., DING, H., and CHEN, L. Q. An inertial nonlinear energy sink. Journal of Sound and Vibration, 405, 34- 47 (2019) |
| 38 | CHEN, H. Y., MAO, X. Y., DING, H., and CHEN, L. Q. Elimination of multimode resonances of composite plate by inertial nonlinear energy sinks. Mechanical Systems and Signal Processing, 135, 106383 (2020) |
| 39 | ZHANG, Z., DING, H., ZHANG, Y. W., and CHEN, L. Q. Vibration suppression of an elastic beam with boundary inerter-enhanced nonlinear energy sinks. Acta Mechanica Sinica, 37, 387- 401 (2021) |
| 40 |
JING, X. J. The X-structure/mechanism approach to beneficial nonlinear design in engineering. Applied Mathematics and Mechanics (English Edition), 43, 979- 1000 (2022)
doi: 10.1007/s10483-022-2862-6 |
| 41 | YAN, G., ZOU, H. X., WANG, S., ZHAO, L. C., WU, Z. Y., and ZHANG, W. M. Bio-inspired vibration isolation: methodology and design. ASME Applied Mechanics Reviews, 73 (2), 020801 (2021) |
| 42 | YAN, G., ZOU, H. X., WANG, S., ZHAO, L. C., GAO, Q. H., TAN, T., and ZHANG, W. M. Large stroke quasi-zero stiffness vibration isolator using three-link mechanism. Journal of Sound and Vibration, 478, 115344 (2020) |
| 43 | YAN, G., WU, Z. Y., WEI, X. S., WANG, S., ZOU, H. X., ZHAO, L. C., QI, W. H., and ZHANG, W. M. Nonlinear compensation method for quasi-zero stiffness vibration isolation. Journal of Sound and Vibration, 523, 16743 (2021) |
| 44 | WANG, X., MA, T. B., REN, H. L., and NING, J. G. A local pseudo arc-length method for hyperbolic conservation laws. Acta Mechanica Sinica, 30, 956- 965 (2014) |
| [1] | Honglin WAN, Xianghong LI, Yongjun SHEN. Study on vibration reduction of two-scale system coupled with dynamic vibration absorber [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(8): 1335-1352. |
| [2] | Hongyan CHEN, Youcheng ZENG, Hu DING, Siukai LAI, Liqun CHEN. Dynamics and vibration reduction performance of asymmetric tristable nonlinear energy sink [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(3): 389-406. |
| [3] | Jinxin DOU, Zhenping LI, Hongliang YAO, Muchuan DING, Guochong WEI. Torsional vibration suppression and electromechanical coupling characteristics of electric drive system considering misalignment [J]. Applied Mathematics and Mechanics (English Edition), 2024, 45(11): 1987-2010. |
| [4] | Yang JIN, Tianzhi YANG. Enhanced vibration suppression and energy harvesting in fluid-conveying pipes [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1487-1496. |
| [5] | Hu DING, J. C. JI. Vibration control of fluid-conveying pipes: a state-of-the-art review [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(9): 1423-1456. |
| [6] | Shengtao ZHANG, Jiaxi ZHOU, Hu DING, Kai WANG, Daolin XU. Fractional nonlinear energy sinks [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(5): 711-726. |
| [7] | Yuyang SONG, Liqun CHEN, Tianzhi YANG. Geometrically nonlinear inerter for vibration suppression [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(11): 1871-1886. |
| [8] | Weixing ZHANG, Wei ZHANG, Xiangying GUO. Vertical vibration control using nonlinear energy sink with inertial amplifier [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(10): 1721-1738. |
| [9] | A. MOSLEMI, M. R. HOMAEINEZHAD. Effects of viscoelasticity on the stability and bifurcations of nonlinear energy sinks [J]. Applied Mathematics and Mechanics (English Edition), 2023, 44(1): 141-158. |
| [10] | Hu DING, Yufei SHAO. NES cell [J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(12): 1793-1804. |
| [11] | Meng YANG, Xingjiu LUO, Xiaoqiang ZHANG, Hu DING, Liqun CHEN. Enhancing suspension vibration reduction by diagonal inerter [J]. Applied Mathematics and Mechanics (English Edition), 2022, 43(10): 1531-1542. |
| [12] | Jian'en CHEN, Wei ZHANG, Jun LIU, Wenhua HU. Vibration absorption of parallel-coupled nonlinear energy sink under shock and harmonic excitations [J]. Applied Mathematics and Mechanics (English Edition), 2021, 42(8): 1135-1154. |
| [13] | Jiren XUE, Yewei ZHANG, Hu DING, Liqun CHEN. Vibration reduction evaluation of a linear system with a nonlinear energy sink under a harmonic and random excitation [J]. Applied Mathematics and Mechanics (English Edition), 2020, 41(1): 1-14. |
| [14] | Yimin WEI, Sha WEI, Qianlong ZHANG, Xinjian DONG, Zhike PENG, Wenming ZHANG. Targeted energy transfer of a parallel nonlinear energy sink [J]. Applied Mathematics and Mechanics (English Edition), 2019, 40(5): 621-630. |
| [15] | 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 (English Edition), 2019, 40(12): 1791-1804. |
| Viewed | ||||||
|
Full text |
|
|||||
|
Abstract |
|
|||||
