Design of optimum vibration absorbers for a bus vehicle to suppress unwanted vibrations against harmonic and random road excitations

Document Type : Article


Department of Mechanical Engineering, Sharif University of Technology, Tehran, P.O. Box 11155-9567, Iran


Unwanted vibrations of the vehicles are regarded as harmful threats to the human health from various biomechanical and psychophysical aspects. Road roughness has been considered as the main cause of unwanted vibrations in bus vehicles. Vertical seat vibrations have been found via simulation of a ten degree of freedom (10-DOF) model of an intercity bus vehicle under harmonic and random excitations caused by road roughness. To suppress undesirable vibrations, mass-spring-damper passive absorbers are proposed in a thirteen degrees of freedom (13-DOFs) model of the bus. By optimizing the characteristics of the embedded passive absorbers under each seat, and implementation of the designed absorbers, it is observed that the vertical displacement amplitudes in the frequency response of the seats are reduced especially near the bus resonance frequencies. In addition, the vertical displacement and acceleration amplitudes are decreased in the random excitation of the road roughness. According to the results, optimized mass-spring-damper absorbers are suggested as a practical solution to suppress the unwanted vibration effects in the bus vehicle.


1. Abakumov, A.M., Antropov, V.E., and Randi, D.G.
\Electrotechnical vibration isolation system with a
magnetorheological damper", In 2017 International
Conference on Industrial Engineering, Applications
and Manufacturing (ICIEAM), pp. 1{4. IEEE (2017).
2. Gan, Z., Hillis, A.J., and Darling, J. \Adaptive control
of an active seat for occupant vibration reduction",
Journal of Sound and Vibration, 349, pp. 39{55
3. Taskin, Y., Hacioglu, Y., Ortes, F., et al. \Experimental
investigation of biodynamic human body models
subjected to whole-body vibration during a vehicle
ride", International Journal of Occupational Safety
and Ergonomics, 25(4), pp. 1{5 (2018).
4. International Organization of Standardization, ISO
7096, Earth-Moving Machinery: Laboratory Evaluation
of Operator Seat Vibration, Geneva (2000).
5. International Organization for Standardization, ISO
2631-1 \Mechanical vibration and shock-evaluation of
human exposure to whole body vibration - Part 1:
General requirements" (1997).
6. Ciloglu, H., Alziadeh, M., Mohany, A., et al. \Assessment
of the whole body vibration exposure and the
dynamic seat comfort in passenger aircraft", International
Journal of Industrial Ergonomics, 45, pp. 116{
23 (2015).
7. Alperovitch-Najenson, D., Santo, Y., Masharawi, Y.,
et al. \Low back pain among professional bus drivers:
ergonomic and occupational-psychosocial risk factors",
IMAJ, 12, pp. 26{31 (2010).
8. Bovenzi, M., Schust, M., Menzel, G., et al. \Relationships
of low back outcomes to internal spinal load:
a prospective cohort study of professional drivers",
International Archives of Occupational and Environmental
Health, 88(4), pp. 487{99 (2015).
9. Gruber, G.J. and Ziperman, H.H., Relationship Between
Whole-Body Vibration and Morbidity Patterns
Among Motor Coach Operators, National Institute
of Occupational Safety and Health, Cincinnati, Ohio
10. Bovenzi, M. \Low back pain disorders and exposure to
whole-body vibration in the workplace", Seminars in
Perinatology, 20(1), pp. 38{53 (1996).
11. Magnusson, M.L., Pope, M.H., Wilder, D.G., et al.
\Are occupational drivers at an increased risk for
developing musculoskeletal disorders", Spine, 21(6),
pp. 710{717 (1996).
12. Kim, J.H., Dennerlein, J.T., and Johnson, P.W. \The
e ect of a multi-axis suspension on whole body vibration
exposures and physical stress in the neck and
low back in agricultural tractor applications", Applied
Ergonomics, 68, pp. 80{89 (2018).
13. Pope, M.H. and Novotny, J.E. \Spinal biomechanics",
J. Biomech. Eng., 115, pp. 569{574 (1993).
14. Pope, M.H., Andersson, G.B.J., Frymoyer, J.W., et al.,
Occupational Low Back Pain: Assessment, Treatment,
and Prevention, Mosby Yearbook, St. Louis, pp. 95{
113 (1991).
15. Webster, B.S. and Snook, S.H. \The cost of 1989
workers' compensation low back pain claims", Spine,
19, pp. 1111{1116 (1994).
16. Johanning, E. \Back disorder intervention strategies
for mass transit operators exposed to whole-body
vibration-comparison of two transit system approaches
and practices", Journal of Sound and Vibration,
215(4), pp. 629{634 (1998).
17. Teschke, K., Nicol, A., Davies, Ju, H., et al. \Whole
body vibration and back disorders among motor vehicle
drivers and heavy equipment operators: a review
of the scienti c evidence", Report to: Workers Compensation
Board of British Columbia, Vancouver, BC
18. Dreischarf, M., Shirazi-Adl, A., Arjmand, N., et al.
\Estimation of loads on human lumbar spine: a review
of in vivo and computational model studies", Journal
of Biomechanics, 49(6), pp. 833{845 (2016).
19. Fritz, M. \Description of the relation between the
forces acting in the lumbar spine and whole-body
vibrations by means of transfer functions", Clinical
Biomechanics, 15, pp. 234{240 (2000).
20. Krause, N., Rugulies, R., Ragland, D.R., et al. \Physical
workload, ergonomic problems, and incidence of
low back injury: a 7.5-year prospective study of San
Francisco transit operators", American Journal of
Industrial Medicine, 46(6), pp. 570{585 (2004).
21. Tiemessen, I.J.H., Hulshof, C.T.J., and Frings-Dresen,
M.H.W. \Low back pain in drivers exposed to whole
body vibration: analysis of a dose response pattern",
Occupational and Environmental Medicine, 65, pp.
667{675 (2008).
22. National Research Council, Musculoskeletal Disorders
and the Workplace, National Academy Press, Washington,
DC (2001).
23. Dong, R., Krajnak, K., Wirth, O., et al., Introduction:
Conference on Human Vibration, Morgantown, WV:
DHHS/CDC/NIOSH, 1 (2006).
24. Wang, M., Yu, J., Liu, N., et al. \Low back pain among
taxi drivers: a cross-sectional study", Occupational
Medicine, 67(4), pp. 290{295 (2017).
25. Viswamurthy, S.R. and Ganguli, R. \Performance sensitivity
of helicopter global and local optimal harmonic
vibration controller", Computers & Mathematics with
Applications, 56(10), pp. 2468{2480 (2008).
26. Maciejewski, I., Meyer, L., and Krzyzynski, T.
\Modelling and multi-criteria optimization of passive
seat suspension vibro-isolating properties", Journal of
Sound and Vibration, 324(3{5), pp. 520{538 (2009).
254 A. Rezazadeh and H. Moradi/Scientia Iranica, Transactions B: Mechanical Engineering 28 (2021) 241{254
27. Verros, G., Natsiavas, S., and Papadimitriou, C.
\Design optimization of quarter-car models with passive
and semi-active suspensions under random road
excitation", Journal of Vibration and Control, 11, pp.
581{606 (2005).
28. Segla, S. and Trisovic, N. \Optimization of semi-active
seat suspension", American Journal of Mechanical
Engineering, 1(7), pp. 221{225 (2013).
29. Gan, Z., Hillis, A.J., and Darling, J. \Adaptive control
of an active seat for occupant vibration reduction",
Journal of Sound and Vibration, 349, pp. 39{55
30. Eason, R.P., Sun, C., Dick, A.J., and Nagarajaiah, S.
\Attenuation of linear oscillator using a nonlinear and
semi-active tuned mass damper in series", Journal of
Sound and Vibration, 332, pp. 154{166 (2013).
31. Choi, S.B., Nam, M.H., and Lee, B.K. \Vibration
control of a MR seat damper for commercial vehicles",
Journal of Intelligent Material Systems and Structures,
11, pp. 936{944 (2000).
32. Chen, Y., Wickramasinghe, V., and Zimcik, D.G.
\Development of adaptive helicopter seat for aircrew
vibration reduction", Journal of Intelligent Material
Systems and Structures, 22(5), pp. 22{489 (2011).
33. Stein, G.J. \A driver's seat with active suspension
of electro-pneumatic type", Journal of Vibration and
Acoustics, 119(2), pp. 230{235 (1997).
34. Maciejewski, I., Glowinski, S., and Krzyzynski, T.
\Active control of a seat suspension with the system
adaptation to varying load mass", Mechatronics,
24(8), pp. 1242{1253 (2014).
35. Lathkar, M.S., Shendge, P.D., and Phadke, S.B.
\Active control of uncertain seat suspension system
based on a state and disturbance observer", IEEE
Transactions on Systems, Man, and Cybernetics: Systems,
50(3), pp. 840{850 (2017).
36. Hrovat, D. \Optimal active suspensions for 3d vehicle
models", Proceedings of the American Control Conference,
Arizona, USA, 2, pp. 1534{1541 (1991).
37. Stein, G.J. \Results of investigation of an electropneumatic
active vibration control system", Proc. Inst.
Mech. Eng. Part D: J. Autom Eng., 209, pp. 227{234
38. Sun, W., Li, J., Zhao, Y., and Gao, H. \Vibration
control for active seat suspension systems via dynamic
output feedback with limited frequency characteristic",
Mechatronics, 21(1), pp. 250{260 (2011).
39. Orecny, M., Segl'a, S., Hunady, R., et al. \Application
of a magneto-rheological damper and a dynamic
absorber for a suspension of a working machine seat",
Procedia Engineering, 96, pp. 338{344 (2014).
40. Bouazara, M., Richard, M.J., and Rakheja, S. \Safety
and comfort analysis of a 3-D vehicle model with
optimal non-linear active seat suspension", Journal of
Terramechanics, 43(2), pp. 97{118 (2006).
41. Sekulic, D., Dedovic, V., Rusov, S., et al. \Analysis of
vibration e ects on the comfort of intercity bus users
by oscillatory model with ten degrees of freedom",
Applied Mathematical Modelling, 37(18{19), pp. 8629{
8644 (2013).
42. \Catalogue of technical data and selling prices, IKARBUS
Belgrade", Factory for the Production of Buses
and Special-Purpose Vehicles (2004).
43. Johannesson, P., Podgorski, K., and Rychlik, I.
\Laplace distribution models for road topography and
roughness", International Journal of Vehicle Performance,
3(3), pp. 224{258 (2017).
44. Kim, J.H., Abdel-Malek, K., Yang, J., and Marler,
R.T. \Prediction and analysis of human motion dynamics
performing various tasks", International Journal
of Human Factors Modelling and Simulation, 1(1),
pp. 69{94 (2006).
45. Rezazadeh, A. and Berniker, M. \Force eld generalization
and the internal representation of motor
learning", PloS One, 14(11) (2019).
46. Fard, M.A., Tadashi, I., and Hikaru, I. \Dynamics
of the head-neck complex in response to the trunk
horizontal vibration: Modeling and identi cation", J.
Biomech. Eng., 125(4), pp. 533{539 (2003).