[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

Smart Passive Vibration Isolation: Requirements and Unsolved Problems

Journal of Applied Nonlinear Dynamics 1(4) (2012) 341--386 | DOI:10.5890/JAND.2012.09.002

H. Marzbani; R.N. Jazar$^{1}$; A. Khazaei

$^{1}$ School of Aerospace, Mechanical, and Manufacturing Engineering, RMIT University, Melbourne, Australia

$^{2}$ Southern Polytechnic State University, Marietta, GA

Download Full Text PDF

 

Abstract

Vibration isolators are needed to control the relative displacement, acceleration, or most importantly the transmitted force to the base or to the isolated device. As a general rule, a good vibration isolator should be as soft as possible to reduce the transmitted force, and it should be hard to limit the relative displacement. Soft suspension provides large relative displacement in resonance zone. To limit the relative displacement while having a soft suspension, a limiting displacement design is needed. There are two practical designs, Hydraulic Engine Mount (HEM) and Piecewise Linear Suspension (PLS) which are being used in industry since 80s. Hydraulic engine mounts were invented to passively produce a low damping at low amplitude and a high damping at high amplitude. Similarly, piecewise linear suspension were introduced to provide a soft suspension at low amplitude and a hard suspension at high amplitude. Having dual behavior puts both HEM and PLS in the domain of nonlinear system which in turn brings many new phenomena never appeared in linear analysis. This article will review the necessity of having a dual behavior suspension and the design of the two practical designs. However, both of these designs have some challenging and unsolved problems. Introducing the problems opens avenue for supervisors, researchers, and students to direct their research practice and hopefully solve them.

References

  1. [1]  Jazar, R.N.(2012), Advanced Vibrations: A Modern Approach, Springer Verlag, Berlin.
  2. [2]  Den Hartog, J.P. and Heiles, R.M. (1936), Forced vibration in nonlinear systems with various combinations of linear springs, Trans. ASME, Journal of Applied Mechanics, 58, 127-130.
  3. [3]  Nelson, F.C. (1994), Vibration isolation: a review, i. sinusoidal and random excitations, Shock and Vibration, 1(5), 485-493.
  4. [4]  Snowdon, J.C. (1968), Vibration and Shock in Damped Mechanical Systems, Wiley, New York.
  5. [5]  Snowdon, J.C. (1979), Vibration isolation: Use and characterization, The Journal of the Acoustical Society of America, 66, 1245-1274.
  6. [6]  Rivin, E.I., (1979), Principles and criteria of vibration isolation of machinery, Transaction of the ASME, Journal of Mechanical Design, 101, 682-692.
  7. [7]  Jazar, R.N. and Golnaraghi, M.F. (2001), Steady State Vibrations of a Piecewise Linear System, Proceedings of Design Engineering Technical Conferences, 18th ASME Biennial Conference on Mechanical Vibration and Noise, Pittsburgh, PA, Sept.9-12.
  8. [8]  Jazar, R.N., and Golnaraghi, M.F. (2002), Nonlinear modeling, experimental verification, and theoretical analysis of a hydraulic engine mount, Journal of Vibration and Control, 8, 87-116.
  9. [9]  Jazar, R.N., and Golnaraghi M.F. ( 2002), Engine mounts for automotive applications: a survey, The Shock and Vibration Digest, 34(5), 363-379.
  10. [10]  Jazar, R.N., Houim, R., Narimani, A. and Golnaraghi, M. F. ( 2006), Frequency Response and Jump Avoidance in a Nonlinear Passive Engine Mount, Journal of Vibration and Control, 12, 1205-1237.
  11. [11]  Jazar, R.N., Golnaraghi, M.F., Narimani, A. and Swanson, D.A. (2003), Practical Frequency and Time Optimal Design of Passive Linear Vibration Isolation Mounts, Vehicle System Dynamics, 39, 437-466.
  12. [12]  Alkhatib, R., Jazar, R.N., and Golnaraghi, M.F. (2004), Optimal design of passive linear suspension using genetic algorithm, Journal of Sound and Vibration, 275, 665-691.
  13. [13]  Natsiavas, S. and Gonzalez, H. (1992), Vibration of harmonically excited oscillators with asymmetric constraints, Journal of Applied Mechanics, 59, S284-S290.
  14. [14]  Narimani, A., Golnaraghi, M.E. and Jazar, R.N. (2004a), Frequency response of a piecewise linear vibration isolator, Journal of Vibration and Control,10, 1775-1794.
  15. [15]  Deshpande, S., Mehta, S., and Jazar, G.N. (2006), Optimization of secondary suspension of piecewise linear vibration isolation systems, International Journal of Mechanical Sciences, 48, 341-377.
  16. [16]  Christopherson, J. and Jazar, R.N.(2005). Optimization of classical hydraulic engine mounts based on RMS method, Shock and Vibration, 12, 119-147.
  17. [17]  Nayfeh A.H. and Mook, D.T. (1995), Nonlinear Oscillations, Wiley-Interscience Publications, New York.
  18. [18]  Narimani, A., Golnaraghi, M.F. and Jazar, R.N. (2004b), Sensitivity analysis of the frequency response of a piecewise linear system in a frequency island, Journal of Vibration and Control, 10, 175-198.
  19. [19]  Golnaraghi, M.F. and Jazar, R.N. (2001), Development and analysis of a simplified nonlinear model of a hydraulic engine mount, Journal of Vibration and Control, 7, 495-526.
  20. [20]  Lord, H.C. (1930), Vibration dampening mounting, US Patent 1,778,503, October 14, 1930.
  21. [21]  Brenner H. and Hamaekers A. (1979), Rubber elastic engine mounts or supports with hydraulic damping, especially for engine suspensions in motor vehicles, US Patent 4,161,304, July 17, 1979.
  22. [22]  Van Den Boom, J., Salwesky G., Godel F.U. and Leitner, W.(1980), Vibration absorbing elastomeric mount with hydraulic damping, US Patent 4,199,128, April 22, 1980.
  23. [23]  Brenner, H. and Hamaekers, A. (1980), Rubber elastic engine mounts or supports with hydraulic damping, US Patent 4,215,842, August 5, 1980.
  24. [24]  Ticks, G.H. (1981), Haydraulically damped rubber motor mounting, US Patent 4,277,056, July 7, 1981.
  25. [25]  Gold, T.P. and Muzechuk, R.A.(1986), Hydraulic-ElastomericMount, US Patent 4,588,173,May 13, 1986.
  26. [26]  Quast, J.R. (1987) , Hydraulic damping rubber engine mount, US Patent 4,645,189, February 24, 1987.
  27. [27]  Andra, R. and Hofman, M. (1987). Elastic Engine Mount with Hydraulic Damping, US Patent 4,650,168, March 17, 1987.
  28. [28]  Hollerweger, H., Aden, B., Kuipers, G. and Van Den Boom, J. (1987), Hydraulic engine mount, US Patent 4,671,227, June 9, 1987.
  29. [29]  Carlson, E.D., Smith, J.E. and Muzechuk, R.A. (1988), Variable hydraulic elastomeric mount assembly, US Patent 4,756,513, July 12, 1988.
  30. [30]  Christopherson, J. and Jazar, R.N.(2006), Dynamic behavior comparison of passive hydraulic engine mounts. Part 1: mathematical analysis, Journal of Sound and Vibration, 290, 1040-1070.
  31. [31]  Bernuchon, M. (1984), A New Generation of Engine Mounts, SAE Paper # 840259.
  32. [32]  Corcoran, P.E. and Ticks, G.H. (1984), Hydraulic engine mount characteristics, SAE Paper # 840407.
  33. [33]  Flower, W.C. (1985), Understanding hydraulic mounts for improved vehicle noise, vibration and ride qualities, SAE Paper # 850975.
  34. [34]  Ushijima, T. and Dan, T. (1986), Nonlinear B.B.A. for predicting vibration of vehicle with hydraulic engine mounts, SAE Paper # 860550.
  35. [35]  Ushijima, T., Takano, K., and Kojima, H. (1988), High performance hydraulic mount for improving vehicle noise and vibration, SAE Paper # 880073.
  36. [36]  Colgate, J.E., Chang, C.T., Chiou, Y.C., Liu, W.K., and Keer, L. M. (1995), Modelling of a hydraulic engine mount focusing on response to sinusoidal and composite excitations, Journal of Sound and Vibration, 184, 503-528.
  37. [37]  Margolis, D. and Wilson, R. (1997), Modeling, simulation and physical understanding of hydromounts, Master's thesis, University of California.
  38. [38]  Ishihama, M., Satoh, S., Seto, K., and Nagamatsu, A. (1994), Vehicle vibration reduction by transfer function phase control on hydraulic engine mounts, JSME International Journal Series C, 37(3), 536-541.
  39. [39]  Muller, M., Weltin, O., Freudenberg, C., Law, D., Roberts, M., and Siebler, T. (1994), Engine mounts and NVH, Automotive Engineering , July.
  40. [40]  Muller, M., Eckel, H., Leibach, M. and Bors, W. (1996), Reduction of noise and vibration in vehicles by approximate engine mount systems and active absorbers, SAE Paper.
  41. [41]  Royston, T.J. and Singh, R. (1995), Periodic response of non-linear engine mounting systems, SAE Technical Paper Series 951297.
  42. [42]  Royston, T.J. and Singh, R. (1996a), Optimization of passive and active non-linear vibration mounting systems based on vibratory power transmission, Journal of Sound and Vibration, 194, 295-316.
  43. [43]  Royston, T.J. and Singh, R. (1996b), Periodic response of mechanical systems with local non-linearities using an enhanced galerkin technique, Journal of Sound and Vibration, 194, 243-263.
  44. [44]  Royston, T.J. and Singh R., Vibratory power flow through a non-linear path into a multi-resonant receiver, Journal of Acoustical Society of America, 101(4), 2059-2069, 1997.
  45. [45]  Royston, T.J. and Singh, R. (1997), Study of non-linear hydraulic enginemounts focusing on decoupler modeling and design, SAE Transaction Journal of Passenger Cars, 6, 106(2), 2759-2769. # 960185.
  46. [46]  Little, E. and Kashani, R. (1995), Adaptive-passive and active hydraulic engine mounts, ASME Advanced Automotive Technologies, DSC-Vol.56/DE-Vol.86, 135-140.
  47. [47]  Seto, K., Sawatari, K., Nagamatsu, A., Ishihama, M. and Doi, K. (1991), Optimum design method for hydraulic engine mounts, SAE Paper # 911055.
  48. [48]  Gau, S.J. and Cotton, J.D. (1995), Experimental study and modeling of hydraulic mount and engine system, SAE Paper # 951348.
  49. [49]  Kim, G. (1992), Study of passive and adaptive hydraulic mounts, PhD thesis, Ohio State University.
  50. [50]  Singh, R., Kim, G. and Ravindra, P.V. (1992), Linear analysis of automotive hydro-mechanical mount with emphasis on decoupler characteristics, Journal of Sound and Vibration, 158, 219-243.
  51. [51]  Kim, G. and Singh, R. (1992), Resonance, isolation and shock control characteristics of automotive nonlinear hydraulic engine mounts, Transportation Systems, proceedings of ASME/WAM DSC, 44, 165- 180.
  52. [52]  Kim, G. and Singh, R. (1993), Nonlinear analysis of automotive hydraulic engine mount, Journal of Dynamic Systems, Measurement, and Control, 115, 482-487.
  53. [53]  Kim, G. and Singh, R. (1995), A study of passive and adaptive hydraulic engine mount systems with emphasis on non-linear characteristics, Journal of Sound and Vibration, 179, 427-453.
  54. [54]  Brach, R.M.(1997), Automotive powerplant isolation strategies, SAE Paper # 971942.
  55. [55]  Lee, K.H., Choi, Y.T., and Hong, S.P. (1995), Performance analysis of hydraulic engine mount by using bond graph method, SAE Paper # 951347
  56. [56]  Jeong, T. and Singh, R. (2001), Inclusion of measured frequency- and amplitude-dependent mount properties in vehicle or machinery models, Journal of Sound and Vibration, 245, 385-415.
  57. [57]  Geisberger, A.A. (2000), Hydraulic engine mount modeling, parameter identification and experimental validation, Masters Thesis, University of Waterloo.
  58. [58]  Tiwari, M., Adiguna, H. and Singh, R. (2003), Experimental characterization of a nonlinear hydraulic engine mount, Noise Control Engineering Journal, 51, 36-49.
  59. [59]  Shangguan, W.-B. and Lu, Z.H. (2004), Experimental study and simulation of a hydraulic engine mount with fully coupled fluid-structure interaction finite element analysis model, Computers & amp; Structures, 82, 1751-1771.
  60. [60]  Mohareri, O. and Arzanpour, S. (2011), Energy harvesting from vibration of a hydraulic engine mount using a turbine, paper presented to Mechatronics (ICM),IEEE International Conference.
  61. [61]  Mansour, H., Arzanpour, S., Golnaraghi, M.F. (2011), Active decoupler hydraulic engine mount design with application to variable displacement engine, Journal of vibration Control, 17, :1498-1508.
  62. [62]  Christopherson, J., Manifalah, M., Jazar R.N. (2012), Suspended decoupler: A new design of hydraulic engine mount, Journal of advance in Acoustics and Vibration.
  63. [63]  He, S. and Singh, R.(2005), Estimation of amplitude and frequency dependent parameters of hydraulic engine mount given limited dynamic stiffness measurements, Noise Control Engineering Journal, 53(6), 271-285.
  64. [64]  Lee J.H. and Kim K.J. (2005), An efficient technique for design of hydraulic engine mount via design variable embedded damping modeling, Journal of Vibration and Acoustics, 127(1), 93-99.
  65. [65]  He, S. and Singh, R. (2007a), Approximate step response of a nonlinear hydraulic mount using a simplified linear model, Journal of Sound and Vibration, 299, 656-663.
  66. [66]  He, S. and Singh, R. (2007b), Discontinuous compliance nonlinearities in the hydraulic engine mount, Journal of Sound and Vibration, 307, 545-563.
  67. [67]  Choi, S.-B.S. and Song, H.-J.H. (2002) Vibration Control of a Passenger Vehicle Utilizing a Semi-Active ER Engine Mount, Vehicle System Dynamics, 37, 193-216.
  68. [68]  Yoon, J.Y. and Singh, R. (2010), Estimation of dynamic force transmitted by hydraulic mount using motion and/or pressure measurements and quasi-linear models, Noise Control Engineering Journal, 58(4), 403-419.
  69. [69]  Yoon, J.-Y. and Singh, R. (2010), Indirect measurement of dynamic force transmitted by a nonlinear hydraulic mount under sinusoidal excitation with focus on super-harmonics, Journal of Sound and Vibration, 329, 5249-5272.
  70. [70]  Adiguna, H., Tiwari, M., Singh, R., Tseng, H.E. and Hrovat, D. (2003), Transient response of a hydraulic engine mount, Journal of Sound and Vibration, 268, 217-248.
  71. [71]  Nakai, M., Murata, S. and Hagio, S. (2002), Analysis of piecewise linear systems with boundaries in displacement and time, Journal of Vibration and Acoustics, 124, 527-536.
  72. [72]  Vahdati, N. and Heidari, S. (2010), A novel semi-active fluid mount using a multi-layer piezoelectric beam,Journal of Vibration and Control, 16(4), 2215-2234.
  73. [73]  Davis, L.C. (1999), Model of magnetorheological elastomers , Journal of Applied Physics, 85, 3348-3351.
  74. [74]  Duclos, T.G. (1987), An externally tunable hydraulic mount which uses electro-rheological fluid, SAE Paper # 870963.
  75. [75]  Turnip, A., Hong, K.S., and Park, S. (2009), Modeling of a hydraulic engine mount for active pneumatic engine vibration control using the extended Kalman filter, Journal of Mechanical Science and Technology, 23(1), 229-236.
  76. [76]  Mansour, H., Arzanpour, S. and Golnaraghi, F. (2012), Design of a solenoid valve based active engine mount, Journal of Vibration and Control, 18(8), 1221-1232.
  77. [77]  Tikani, R., Vahdati, N., Ziaei-Rad, S., and Esfahanian, M. (2011), A new hydraulic engine mount design without the peak frequency, Journal of Vibration and Control, 17, 1644-1656.
  78. [78]  Geisberger, A., Khajepour, A., and Golnaraghi, F. (2000), Non-linear modeling and experimental verification of a MDOF hydraulic engine mount, Control of Vibration and Noise-New Millennium, 2000 ASME International Congress and Exposition, Orlando, FL.
  79. [79]  Tang, Y.G., Zheng, H.Y., Gu, J.Y., and Jiang, D.N. (2003), Study on the vibration reduction of the double pistons hydraulic engine mount,
  80. [80]  Ahn, Y.K., Song, J.D. and Yang, B.S. ( 2003), Optimal design of engine mount using an artificial life algorithm, Journal of sound and vibration, 261(2), 309-328.
  81. [81]  Truong, T.Q., Ahn, Y.K., and Ahn, K.K. (2005), Optimal switching parameter control of semi-active engine mount, Gyeonggi-Do., Korea: ICCASS2005, Kintex, Gyeonggi-Do., Korea.
  82. [82]  Rasekhipour, Y. and Ohadi, A. ( 2011), Optimization of hydraulic engine mounts through simplified and full vehicle models, Lecture Notes in Engineering and Computer Science, 2192.
  83. [83]  Christopherson, J., Jazar, R.N., and Mahinfalah, M.( 2006), Chaotic behavior of hydraulic engine mount, ASME Conference Proceedings, 469-476.
  84. [84]  Babitsky, V.I. and Krupenin V.L. ( 2001), Vibration of Strongly Nonlinear Discontinuous Systems, Springer, New York.
  85. [85]  Chaterjee, S., Mallik, A.K. and Ghosh, A. (1996), Periodic response of piecewise non-linear oscillators under harmonic excitation, Journal of sound and vibration, 191(1), 129-144.
  86. [86]  Den Hartog, J.P. and Mikina, S.J. (1932), Forced vibrations with nonlinear spring constraints, Trans. ASME, 54, paper APM-54-15, pp. 157.
  87. [87]  Den Hartog, J.P. and Heiles, R.M. (1936), Forced vibration in nonlinear systems with various combinations of linear springs, Trans. ASME, Journal of Applied Mechanics, 58, 127-130.
  88. [88]  Gurtin, M.E. (1992), On the use of clearance in viscous dampers to limit high frequency force transmission, Trans ASME, Journal of Engineering for Industry, 50-52.
  89. [89]  Maezawa, S. (1961) A perfect fourier series solution for the steady forced vibration of a piecewise linear system, Proc. International Symp. on Nonlinear Oscillations, Kiev, vol. I, 327-341.
  90. [90]  Maezawa, S. (1962), Perfect fourier series solution for subharmonic vibration of a piecewise linear system; nonlinear vibration problems, Second Conf. on Nonlinear Vibrations, Warsaw, 156-164.
  91. [91]  Masri, S.F.(1978), Analytical and Experimental Studies of a Dynamic System with a Gap,Trans. of ASME, J. of Mechanical Design, 100, 480-486.
  92. [92]  Watanbe, T. (1978), Forced vibration of a continues system with nonlinear boundary cognitions, Trans. ASME, J. of Mechanical Design, 100, 487-491.
  93. [93]  Loud, W.S., (1968), Branching phenomena for periodic solutions of non-autonomous piecewise linear systems, Int. J. Non-Linear Mech., 3, 273-293.
  94. [94]  Iwan, W.D., (1973), A generalization of the concept of equivalent linearization, International Journal of Non-Linear Mechanics, 8, 279-287.
  95. [95]  Rosenberg, R.M. (1966), Steady state forced vibrations, International Journal of Non-Linear Mechanics, 1, 95-108.
  96. [96]  Masri, S.F. and Stott S.J. (1978), Random excitation of a nonlinear vibration neutralizer, Trans. ASME, Journal of Mechanical Design, 100, 681-689.
  97. [97]  Badarkhan, F. (1982), Lagrangian formulation and first integrals of piecewise linear dissipative systems, Journal of Sound and Vibration, 82(2), 227-234.
  98. [98]  Schulman, J. N., (1983), Chaos in piecewise linear systems, Physical Review A, 28(1), 477-479.
  99. [99]  Shaw, S.W. and Holmes, P.J. (1983), A periodically forced piecewise linear oscillator, Journal of Sound and Vibration, 90(1), 129-155.
  100. [100]  Nguyen, D.T., Noah, S.T. and Kettleborough, C.F. (1986), Impact behaviour of an oscillator with limiting stops, Part I: A parametric study, Journal of Sound and Vibration, 109, 293-307.
  101. [101]  Natsiavas, S. (1989), Periodic response and stability of oscillators with symmetric trilinear restoring force, Journal of Sound and Vibration, 134(2), 315-331.
  102. [102]  Natsiavas, S. (1992), Steady state oscillations and stability of non-linear dynamic vibration absorbers, Journal of Sound and Vibration, 156(2), 227-245.
  103. [103]  Natsiavas, S. and Tratkas, P. (1996) , On vibration isolation of mechanical systems with non-linear foundations, Journal of Sound and Vibration, 194(2), 173-185.
  104. [104]  Mahfouz, I.A. and Badarkhan, F. (1990), Chaotic behaviour of some piecewise-linear systems, part II: Systems with clearance, Journal of Sound and Vibration, 143( 2), 289-328.
  105. [105]  Dai, L. and Singh, M.C. (1994), On oscillatory motion of spring-mass systems subjected to piecewise constant forces, Journal of Sound and Vibration, 173(2), 217-231.
  106. [106]  Padmanabhan, C. and Singh, R. (1995), Dynamics of a piecewise non-linear system subject to dual harmonic excitation using parametric continuation, Journal of Sound and Vibration, 184(5), 767-799.
  107. [107]  Narayanan, S. and Sekar, P. (1995), Periodic and chaotic responses of an sdf system with piecewise linear stiffness subjected to combined harmonic and flow induced excitations, Journal of Sound and Vibration, 184(2), 281-298.
  108. [108]  Wang, Y. (1995), Dynamics of Unsymmetric Piecewise-Linear / Non-linear Systems using Finite Elements in Time, Journal of Sound and Vibration, 185(1), 155-170.
  109. [109]  Natsiavas, S. (1998), Stability of piecewise linear oscillators with viscous and dry friction damping, Journal of Sound and Vibration, 217(3), 507-522.
  110. [110]  Chircurel-Uziel E. (2001), Exact, single equation, closed-form solution of vibrating systems with piecewise linear springs, Journal of Sound and Vibration, 245(2), 285-301.
  111. [111]  Xu, L., Lu, M.W., and Cao, Q. (2003), Bifurcation and chaos of a harmonically excited oscillator with both stiffness and viscous damping piecewise linearities by incremental harmonic balance method, Journal of Sound and Vibration, 264, 873-882.
  112. [112]  Jiang, D., Pierre, C., and Shaw, S. (2004), Large-amplitude non-linear normal modes of piecewise linear systems, Journal of sound and vibration, 272(3), 869-891.
  113. [113]  Luo, A.C.J. (2004), The mapping dynamics of periodic motions for a three-piecewise linear system under a periodic excitation, Journal of Sound and Vibration, under print.
  114. [114]  Malatkar, P. and Nayfeh, A.H. (2002), Calculation of the Jump frequencies in the response of s.d.o.f. Non-linear systems, Journal of Sound and Vibration, 254(5), 1005-1011.
  115. [115]  Sevin, E. and Pilkey, W.D. (1968), Optimization of Shock Isolation Systems, SAE Technical Paper series, SAE paper # 680749.
  116. [116]  Nissen J.C. (1985), Optimization of a non-linear dynamic vibration absorber, Journal of Sound and Vibration, 99(1), 149-154.
  117. [117]  Chakasani, R.M. (1986), Ride performance potential of active suspension systems - part 1: simplified analysis based on a quarter car model, Symposium on Simulation and Control of Ground Vehicles and Transportation Systems- ASME Winter annual meeting, 187-203.
  118. [118]  Jordanov, I.N. and Cheshankov, B.I. (1987), Optimal design of Linear and Non-linear dynamic vibration absorbers, Journal of Sound and Vibration, 123(1), 157-170.
  119. [119]  Lin, Y. and Zhang, Y. (1989), Suspension optimization by a frequency domain equivalent optimal control algorithm, Journal of Sound and Vibration, 133(2), 239-249.
  120. [120]  Christopherson, J. and Jazar, R.N., (2006b), Dynamic behavior comparison of passive hydraulic engine mounts. Part 2: finite element analysis, Journal of Sound and Vibration, 290, 1071-1090.

Copyright © 2011-2024 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates