Skip to main content
Top

2019 | OriginalPaper | Chapter

Frequency Island and Nonlinear Vibrating Systems

Authors : Ching Nok To, Hormoz Marzbani, Đại Võ Quốc, Milan Simic, M. Fard, Reza N. Jazar

Published in: Intelligent Interactive Multimedia Systems and Services

Publisher: Springer International Publishing

Activate our intelligent search to find suitable subject content or patents.

search-config
loading …

Abstract

Piecewise linear vibration isolator system is one of the development to introduce dual rate stiffness and damping. There are several vibrating behavior if the system is designed properly. Analytical treatment of the system determines some difficulties such as jump. This investigation indicates that such strong nonlinear systems have a new phenomenon called Frequency Island in their frequency response plot. Frequency Island is a possible isolated frequency response that the vibrating system may jump into the island and stays there until the excitation frequency moves out of the range of the island.
In this student existence, appearance, growing and disappearing of frequency island will be studied and examined. Frequency Island corresponds to large amplitude vibration for certain range of system parameters and considered as a dangerous phenomena in real system. As a result, understanding its appearance will help designers and engineers to design the system to avoid Frequency Island.

Dont have a licence yet? Then find out more about our products and how to get one now:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

  • über 102.000 Bücher
  • über 537 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Maschinenbau + Werkstoffe
  • Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 390 Zeitschriften

aus folgenden Fachgebieten:

  • Automobil + Motoren
  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Elektrotechnik + Elektronik
  • Energie + Nachhaltigkeit
  • Maschinenbau + Werkstoffe




 

Jetzt Wissensvorsprung sichern!

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

  • über 67.000 Bücher
  • über 340 Zeitschriften

aus folgenden Fachgebieten:

  • Bauwesen + Immobilien
  • Business IT + Informatik
  • Finance + Banking
  • Management + Führung
  • Marketing + Vertrieb
  • Versicherung + Risiko




Jetzt Wissensvorsprung sichern!

Appendix
Available only for authorised users
Literature
go back to reference Aagaah, M.R., Mahmoudian, N., Jazar, R.N., Mahinfalah, M.: Frequency response of vibration isolators with saturation spring element. In: 20th ASME Biennial Conference on Mechanical Vibration and Noise, Long Beach, CA, 24–28 September 2005 (2005) Aagaah, M.R., Mahmoudian, N., Jazar, R.N., Mahinfalah, M.: Frequency response of vibration isolators with saturation spring element. In: 20th ASME Biennial Conference on Mechanical Vibration and Noise, Long Beach, CA, 24–28 September 2005 (2005)
go back to reference Alam, F., Jazar, R.N., Faheem, A., Smith, L.V.: A study of vehicle ride performance using a quarter car model and half car model. In: ASME International Mechanical Engineering Congress and Exposition, Vancouver, British Columbia, Canada, 12–18 November 2010 (2010) Alam, F., Jazar, R.N., Faheem, A., Smith, L.V.: A study of vehicle ride performance using a quarter car model and half car model. In: ASME International Mechanical Engineering Congress and Exposition, Vancouver, British Columbia, Canada, 12–18 November 2010 (2010)
go back to reference Alkhatib, R., Jazar, R.N., Golnaraghi, M.F.: Optimal design of passive linear mounts with genetic algorithm method. J. Sound Vibr. 275(3–5), 665–691 (2004)CrossRef Alkhatib, R., Jazar, R.N., Golnaraghi, M.F.: Optimal design of passive linear mounts with genetic algorithm method. J. Sound Vibr. 275(3–5), 665–691 (2004)CrossRef
go back to reference Christopherson, J., Jazar, R.N.: Development of a new design hydraulic engine mount. In: ASME International Mechanical Engineering Congress and Exposition, Orlando, Florida, 5–11 November 2005 (2005a) Christopherson, J., Jazar, R.N.: Development of a new design hydraulic engine mount. In: ASME International Mechanical Engineering Congress and Exposition, Orlando, Florida, 5–11 November 2005 (2005a)
go back to reference Christopherson, J., Jazar, R.N.: Dynamic behavior comparison of passive hydraulic engine mounts, Part 1: mathematical analysis. J. Sound Vibr. 290, 1040–1070 (2006a)CrossRef Christopherson, J., Jazar, R.N.: Dynamic behavior comparison of passive hydraulic engine mounts, Part 1: mathematical analysis. J. Sound Vibr. 290, 1040–1070 (2006a)CrossRef
go back to reference Christopherson, J., Jazar, R.N.: Dynamic behavior comparison of passive hydraulic engine mounts, Part 2: finite element analysis. J. Sound Vibr. 290, 1071–1090 (2006b)CrossRef Christopherson, J., Jazar, R.N.: Dynamic behavior comparison of passive hydraulic engine mounts, Part 2: finite element analysis. J. Sound Vibr. 290, 1071–1090 (2006b)CrossRef
go back to reference Christopherson, J., Jazar, R.N.: Optimization of classical hydraulic engine mounts based on RMS method. J. Shock Vibr. 12(2), 119–147 (2005b)CrossRef Christopherson, J., Jazar, R.N.: Optimization of classical hydraulic engine mounts based on RMS method. J. Shock Vibr. 12(2), 119–147 (2005b)CrossRef
go back to reference Christopherson, J., Gustin, J., Jazar, R.N., Mahinfalah, M.: RMS optimization of a standard hydraulic engine mount. In: The 2004 ASME International Mechanical Engineering Congress and Exposition, Anaheim, CA, 14–19 November 2004 (2004) Christopherson, J., Gustin, J., Jazar, R.N., Mahinfalah, M.: RMS optimization of a standard hydraulic engine mount. In: The 2004 ASME International Mechanical Engineering Congress and Exposition, Anaheim, CA, 14–19 November 2004 (2004)
go back to reference Christopherson, J., Jazar, R.N., Mahinfalah, M.: Chaotic behavior of hydraulic engine mount. In: ASME International Mechanical Engineering Congress and Exposition, Chicago, Illinois, 5–10 November 2006 (2006c) Christopherson, J., Jazar, R.N., Mahinfalah, M.: Chaotic behavior of hydraulic engine mount. In: ASME International Mechanical Engineering Congress and Exposition, Chicago, Illinois, 5–10 November 2006 (2006c)
go back to reference Christopherson, J., Jazar, R.N., Mahinfalah, M.: Dynamic analysis and nonlinear characteristics of suspended decoupler hydraulic engine mounts. In: CSME Forum 2006, Symposium on Intelligent Vehicles and Transportation Systems, Calgary, Alberta, Canada, 21–23 May 2006 (2006d) Christopherson, J., Jazar, R.N., Mahinfalah, M.: Dynamic analysis and nonlinear characteristics of suspended decoupler hydraulic engine mounts. In: CSME Forum 2006, Symposium on Intelligent Vehicles and Transportation Systems, Calgary, Alberta, Canada, 21–23 May 2006 (2006d)
go back to reference Christopherson, J., Mahinfalah, M., Jazar, R.N.: Frequency response of a base excited system with hydraulic mount. In: ASME-IMECE Symposium on Dynamic Response of Advanced Materials and Structures, Washington D.C., 15–21 November 2003 (2003) Christopherson, J., Mahinfalah, M., Jazar, R.N.: Frequency response of a base excited system with hydraulic mount. In: ASME-IMECE Symposium on Dynamic Response of Advanced Materials and Structures, Washington D.C., 15–21 November 2003 (2003)
go back to reference Christopherson, J., Mahinfalah, M., Jazar, R.N.: Suspended decoupler: a new design of hydraulic engine mount. Adv. Acoust. Vibr. 2012, 11 (2012). Article ID 826497 Christopherson, J., Mahinfalah, M., Jazar, R.N.: Suspended decoupler: a new design of hydraulic engine mount. Adv. Acoust. Vibr. 2012, 11 (2012). Article ID 826497
go back to reference Den Hartog, J.P., Heiles, R.M.: Forced vibration in nonlinear systems with various combinations of linear springs. Trans. ASME J. Appl. Mech. 58, 127–130 (1936) Den Hartog, J.P., Heiles, R.M.: Forced vibration in nonlinear systems with various combinations of linear springs. Trans. ASME J. Appl. Mech. 58, 127–130 (1936)
go back to reference Den Hartog, J.P., Mikina, S.J.: Forced vibrations with nonlinear spring constraints. Trans. ASME 54, 157 (1932). Paper APM-54-15 Den Hartog, J.P., Mikina, S.J.: Forced vibrations with nonlinear spring constraints. Trans. ASME 54, 157 (1932). Paper APM-54-15
go back to reference Deshpande, S., Mehta, S., Jazar, R.N.: Jump avoidance conditions for piecewise linear vibration isolator. In: 20th ASME Biennial Conference on Mechanical Vibration and Noise, Long Beach, CA, 24–28 September 2005 (2005a) Deshpande, S., Mehta, S., Jazar, R.N.: Jump avoidance conditions for piecewise linear vibration isolator. In: 20th ASME Biennial Conference on Mechanical Vibration and Noise, Long Beach, CA, 24–28 September 2005 (2005a)
go back to reference Deshpande, S., Mehta, S., Jazar, R.N.: Optimization of secondary suspension of piecewise linear vibration isolation systems. Int. J. Mech. Sci. 48(4), 341–377 (2006)CrossRef Deshpande, S., Mehta, S., Jazar, R.N.: Optimization of secondary suspension of piecewise linear vibration isolation systems. Int. J. Mech. Sci. 48(4), 341–377 (2006)CrossRef
go back to reference Deshpande, S., Mehta, S., Jazar, R.N.: Sensitivity of jump avoidance condition of piecewise linear vibration isolator to dynamical parameters. In: ASME International Mechanical Engineering Congress and Exposition, Orlando, Florida, USA, 5–11 November 2005b (2005b) Deshpande, S., Mehta, S., Jazar, R.N.: Sensitivity of jump avoidance condition of piecewise linear vibration isolator to dynamical parameters. In: ASME International Mechanical Engineering Congress and Exposition, Orlando, Florida, USA, 5–11 November 2005b (2005b)
go back to reference Esmailzadeh, E., Jazar, R.N., Mehri, B.: Vibration of road vehicles with nonlinear suspension. Int. J. Eng. 10(4), 209–218 (1997) Esmailzadeh, E., Jazar, R.N., Mehri, B.: Vibration of road vehicles with nonlinear suspension. Int. J. Eng. 10(4), 209–218 (1997)
go back to reference Esmailzadeh, E., Mehri, B., Jazar, R.N.: Periodic solution of a second order autonomous, nonlinear system. J. Nonlinear Dyn. 10(4), 307–316 (1996)MathSciNetCrossRef Esmailzadeh, E., Mehri, B., Jazar, R.N.: Periodic solution of a second order autonomous, nonlinear system. J. Nonlinear Dyn. 10(4), 307–316 (1996)MathSciNetCrossRef
go back to reference Golnaraghi, M.F., Jazar, R.N.: Development and analysis of a simplified nonlinear model of a hydraulic engine mount. J. Vibr. Control 7(4), 495–526 (2001)CrossRef Golnaraghi, M.F., Jazar, R.N.: Development and analysis of a simplified nonlinear model of a hydraulic engine mount. J. Vibr. Control 7(4), 495–526 (2001)CrossRef
go back to reference Golnaraghi, M.F., Jazar, R.N.: Development and analysis of a simplified nonlinear model of a hydraulic engine mount. In: Eight Conference of Nonlinear Vibrations, Stability, and Dynamics of Structures, University of Virginia, Blacksburg, 23–27 July 2000 (2000) Golnaraghi, M.F., Jazar, R.N.: Development and analysis of a simplified nonlinear model of a hydraulic engine mount. In: Eight Conference of Nonlinear Vibrations, Stability, and Dynamics of Structures, University of Virginia, Blacksburg, 23–27 July 2000 (2000)
go back to reference Jazar, R.N.: Advanced Dynamics: Rigid Body, Multibody, and Aerospace Applications. Wiley, New York (2011)CrossRef Jazar, R.N.: Advanced Dynamics: Rigid Body, Multibody, and Aerospace Applications. Wiley, New York (2011)CrossRef
go back to reference Jazar, R.N.: Advanced Vibrations: A Modern Approach, 3rd edn. Springer, New York (2013)CrossRef Jazar, R.N.: Advanced Vibrations: A Modern Approach, 3rd edn. Springer, New York (2013)CrossRef
go back to reference Jazar, R.N., Golnaraghi, M.F.: Steady state vibrations of a piecewise linear system. In: 18th ASME Biennial Conference on Mechanical Vibration and Noise, Pittsburgh, Pennsylvania, USA, 9–12 September 2001 (2001) Jazar, R.N., Golnaraghi, M.F.: Steady state vibrations of a piecewise linear system. In: 18th ASME Biennial Conference on Mechanical Vibration and Noise, Pittsburgh, Pennsylvania, USA, 9–12 September 2001 (2001)
go back to reference Jazar, R.N., Golnaraghi, M.F.: Engine mounts for automotive applications: a survey. Shock Vibr. Digest 34(5), 363–379 (2002a) Jazar, R.N., Golnaraghi, M.F.: Engine mounts for automotive applications: a survey. Shock Vibr. Digest 34(5), 363–379 (2002a)
go back to reference Jazar, R.N., Golnaraghi, M.F.: Nonlinear modeling, experimental verification, and theoretical analysis of a hydraulic engine mount. J. Vibr. Control 8(1), 87–116 (2002b)MATH Jazar, R.N., Golnaraghi, M.F.: Nonlinear modeling, experimental verification, and theoretical analysis of a hydraulic engine mount. J. Vibr. Control 8(1), 87–116 (2002b)MATH
go back to reference Jazar, R.N.: Frequency island in nonlinear vibration isolator. In: 3rd Canadian Conference on Nonlinear Solid Mechanics, Toronto, Ontario, Canada, 25–29 June 2008 (2008) Jazar, R.N.: Frequency island in nonlinear vibration isolator. In: 3rd Canadian Conference on Nonlinear Solid Mechanics, Toronto, Ontario, Canada, 25–29 June 2008 (2008)
go back to reference Jazar, R.N., Houim, R., Narimani, A., Golnaraghi, F.: Nonlinear passive engine mount, frequency response and jump avoidance. J. Vibr. Control 12(11), 1205–1237 (2006a) Jazar, R.N., Houim, R., Narimani, A., Golnaraghi, F.: Nonlinear passive engine mount, frequency response and jump avoidance. J. Vibr. Control 12(11), 1205–1237 (2006a)
go back to reference Jazar, R.N., Mahinfalah, M., Aagaah, M.R., Nazari, G.: Comparison of exact and approximate frequency response of a piecewise linear vibration isolator, DETC2005-84522. In: 20th ASME Biennial Conference on Mechanical Vibration and Noise, Long Beach, CA, 24–28 September 2005 (2005) Jazar, R.N., Mahinfalah, M., Aagaah, M.R., Nazari, G.: Comparison of exact and approximate frequency response of a piecewise linear vibration isolator, DETC2005-84522. In: 20th ASME Biennial Conference on Mechanical Vibration and Noise, Long Beach, CA, 24–28 September 2005 (2005)
go back to reference Jazar, R.N., Mahinfalah, M., Alimi, M.A., Khazaei, A.: Periodic behavior of a nonlinear third order vibrating system. In: International Congress and Exposition, ASME-IMECE 2002, New Orleans, Louisiana, 17–22 November 2002 (2002a) Jazar, R.N., Mahinfalah, M., Alimi, M.A., Khazaei, A.: Periodic behavior of a nonlinear third order vibrating system. In: International Congress and Exposition, ASME-IMECE 2002, New Orleans, Louisiana, 17–22 November 2002 (2002a)
go back to reference Jazar, R.N., Mahinfalah, M., Deshpande, S.: Design of a piecewise linear vibration isolator for jump avoidance. IMechE Part K J. Multi-Body Dyn. 221(K3), 441–450 (2007) Jazar, R.N., Mahinfalah, M., Deshpande, S.: Design of a piecewise linear vibration isolator for jump avoidance. IMechE Part K J. Multi-Body Dyn. 221(K3), 441–450 (2007)
go back to reference Jazar, R.N., Mahinfalah, M., Christopherson, J.: Suspended decoupler design of hydraulic engine mount. In: ASME International Mechanical Engineering Congress and Exposition (IMECE 2011), Denver, Colorado, 11–17 November 2011 (2011) Jazar, R.N., Mahinfalah, M., Christopherson, J.: Suspended decoupler design of hydraulic engine mount. In: ASME International Mechanical Engineering Congress and Exposition (IMECE 2011), Denver, Colorado, 11–17 November 2011 (2011)
go back to reference Jazar, R.N., Mahinfalah, M., Narimani, A., Golnaraghi, M.F.: Smart passive suspension design consideration for one DOF systems. In: CSME Forum 2006, Symposium on Intelligent Vehicles and Transportation Systems, Calgary, Alberta, Canada, 21–23 May 2006 (2006b) Jazar, R.N., Mahinfalah, M., Narimani, A., Golnaraghi, M.F.: Smart passive suspension design consideration for one DOF systems. In: CSME Forum 2006, Symposium on Intelligent Vehicles and Transportation Systems, Calgary, Alberta, Canada, 21–23 May 2006 (2006b)
go back to reference Jazar, R.N., Narimani, A., Golnaraghi, M.F., Swanson, D.A.: Practical frequency and time optimal design of passive linear vibration isolation mounts. J. Veh. Syst. Dyn. 39(6), 437–466 (2003)CrossRef Jazar, R.N., Narimani, A., Golnaraghi, M.F., Swanson, D.A.: Practical frequency and time optimal design of passive linear vibration isolation mounts. J. Veh. Syst. Dyn. 39(6), 437–466 (2003)CrossRef
go back to reference Jazar, R.N., Narimani, A., Golnaraghi, M.F.: Sensitivity analysis of frequency response of a piecewise linear system in frequency island. In: Ninth Conference of Nonlinear Vibrations, Stability, and Dynamics of Structures, Blacksburg, Virginia, 28 July–1 August 2002 (2002b) Jazar, R.N., Narimani, A., Golnaraghi, M.F.: Sensitivity analysis of frequency response of a piecewise linear system in frequency island. In: Ninth Conference of Nonlinear Vibrations, Stability, and Dynamics of Structures, Blacksburg, Virginia, 28 July–1 August 2002 (2002b)
go back to reference Jazar, R.N.: Vehicle Dynamics: Theory and Application, 3rd edn. Springer, New York (2018) Jazar, R.N.: Vehicle Dynamics: Theory and Application, 3rd edn. Springer, New York (2018)
go back to reference Marzbani, H., Fard, M., Jazar, R.N.: Chaotic behavior of hydraulic engine mount. In: 20th International Conference on Knowledge Based and Intelligent Information and Engineering Systems, KES 2016, New York, United Kingdom, 5–7 September 2016 (2016) Marzbani, H., Fard, M., Jazar, R.N.: Chaotic behavior of hydraulic engine mount. In: 20th International Conference on Knowledge Based and Intelligent Information and Engineering Systems, KES 2016, New York, United Kingdom, 5–7 September 2016 (2016)
go back to reference Marzbani, H., Jazar, R.N., Fard, M.: Comparison between hydraulic engine mounts and piecewise linear vibration isolators, science and motor vehicles 2013. In: JUMV International Automotive Conference 2013 Belgrade, Serbia, 23–24 April 2013 (2013a) Marzbani, H., Jazar, R.N., Fard, M.: Comparison between hydraulic engine mounts and piecewise linear vibration isolators, science and motor vehicles 2013. In: JUMV International Automotive Conference 2013 Belgrade, Serbia, 23–24 April 2013 (2013a)
go back to reference Marzbani, H., Jazar, R.N., Fard, M.: Hydraulic engine mounts: a survey. J. Vibr. Control 19(16), 1439–1463 (2013b)CrossRef Marzbani, H., Jazar, R.N., Fard, M.: Hydraulic engine mounts: a survey. J. Vibr. Control 19(16), 1439–1463 (2013b)CrossRef
go back to reference Marzbani, H., Jazar, R.N., Khazaei, A.: Smart passive vibration isolation: requirements and unsolved problems. J. Appl. Nonlinear Dyn. 1(4), 341–386 (2012)CrossRef Marzbani, H., Jazar, R.N., Khazaei, A.: Smart passive vibration isolation: requirements and unsolved problems. J. Appl. Nonlinear Dyn. 1(4), 341–386 (2012)CrossRef
go back to reference Narimani, A., Golnaraghi, M.F., Jazar, R.N.: Frequency response of a piecewise linear system. J. Vibr. Control 10(12), 1775–1894 (2004a) Narimani, A., Golnaraghi, M.F., Jazar, R.N.: Frequency response of a piecewise linear system. J. Vibr. Control 10(12), 1775–1894 (2004a)
go back to reference Narimani, A., Jazar, R.N., Golnaraghi, M.F.: Sensitivity analysis of frequency response of a piecewise linear system in frequency island. J. Vibr. Control 10(2), 175–198 (2004b) Narimani, A., Jazar, R.N., Golnaraghi, M.F.: Sensitivity analysis of frequency response of a piecewise linear system in frequency island. J. Vibr. Control 10(2), 175–198 (2004b)
go back to reference Narimani, A., Golnaraghi, M.F., Jazar, R.N.: Optimizing piecewise linear isolator for steady state vibration. In: ASME-IMECE Symposium on Dynamic Response of Advanced Materials and Structures, Washington D.C., 15–21 November 2003 (2003) Narimani, A., Golnaraghi, M.F., Jazar, R.N.: Optimizing piecewise linear isolator for steady state vibration. In: ASME-IMECE Symposium on Dynamic Response of Advanced Materials and Structures, Washington D.C., 15–21 November 2003 (2003)
go back to reference Narimani, A., Jazar, R.N., Golnaraghi, M.F.: Vibration analysis of a piecewise linear system. In: USNCTAM14 Fourteenth U.S. National Congress of Theoretical and Applied Mechanics, Blacksburg, Virginia, 23–28 June 2002 (2002) Narimani, A., Jazar, R.N., Golnaraghi, M.F.: Vibration analysis of a piecewise linear system. In: USNCTAM14 Fourteenth U.S. National Congress of Theoretical and Applied Mechanics, Blacksburg, Virginia, 23–28 June 2002 (2002)
go back to reference Natsiavas, S., Gonzalez, H.: Vibration of Harmonically Excited Oscillators with Asymmetric Constraints. Trans. ASME J. Appl. Mech. 59, S284–S290 (1992)CrossRef Natsiavas, S., Gonzalez, H.: Vibration of Harmonically Excited Oscillators with Asymmetric Constraints. Trans. ASME J. Appl. Mech. 59, S284–S290 (1992)CrossRef
go back to reference Natsiavas, S.: Dynamic of piecewise linear oscillators with Van der Pol type damping. Int. J. Non-Linear Mech. 26(¾), 349–366 (1991)CrossRef Natsiavas, S.: Dynamic of piecewise linear oscillators with Van der Pol type damping. Int. J. Non-Linear Mech. 26(¾), 349–366 (1991)CrossRef
go back to reference Nayfeh, A.H., Mook, D.: Nonlinear Oscillations. Wiley, New York (1979)MATH Nayfeh, A.H., Mook, D.: Nonlinear Oscillations. Wiley, New York (1979)MATH
go back to reference Pogorilyi, O., Trivailo, M., Jazar, R.N.: Challenges in exact response of piecewise linear vibration isolator. In: Dai, L., Jazar, R.N. (eds.) Nonlinear Approaches in Engineering Applications, vol. 3. Springer, New York (2015a) Pogorilyi, O., Trivailo, M., Jazar, R.N.: Challenges in exact response of piecewise linear vibration isolator. In: Dai, L., Jazar, R.N. (eds.) Nonlinear Approaches in Engineering Applications, vol. 3. Springer, New York (2015a)
go back to reference Pogorilyi, O., Trivailo, M., Jazar, R.N.: On the piecewise linear exact solution. Nonlinear Eng. Model. Appl. 3(4), 189–196 (2014) Pogorilyi, O., Trivailo, M., Jazar, R.N.: On the piecewise linear exact solution. Nonlinear Eng. Model. Appl. 3(4), 189–196 (2014)
go back to reference Pogorilyi, O., Trivailo, M., Jazar, R.N.: Sensitivity analysis of piecewise linear vibration isolator with dual rate spring and damper. Nonlinear Eng. Model. Appl. 4(1), 1–13 (2015b)CrossRef Pogorilyi, O., Trivailo, M., Jazar, R.N.: Sensitivity analysis of piecewise linear vibration isolator with dual rate spring and damper. Nonlinear Eng. Model. Appl. 4(1), 1–13 (2015b)CrossRef
go back to reference Schulman, J.N.: Chaos in piecewise linear systems. Phys. Rev. A 28(1), 477–479 (1983)CrossRef Schulman, J.N.: Chaos in piecewise linear systems. Phys. Rev. A 28(1), 477–479 (1983)CrossRef
go back to reference Stahl, P., Jazar, R.N.: Frequency response analysis of piecewise nonlinear vibration isolator. In: 20th ASME Biennial Conference on Mechanical Vibration and Noise, Long Beach, CA, 24–28 September 2005 (2005a) Stahl, P., Jazar, R.N.: Frequency response analysis of piecewise nonlinear vibration isolator. In: 20th ASME Biennial Conference on Mechanical Vibration and Noise, Long Beach, CA, 24–28 September 2005 (2005a)
go back to reference Stahl, P., Jazar, R.N.: Stability analysis of a piecewise nonlinear vibration isolator. In: ASME International Mechanical Engineering Congress and Exposition, Orlando, Florida, 5–11 November 2005 (2005b) Stahl, P., Jazar, R.N.: Stability analysis of a piecewise nonlinear vibration isolator. In: ASME International Mechanical Engineering Congress and Exposition, Orlando, Florida, 5–11 November 2005 (2005b)
go back to reference Virgin, L.N.: Introduction to Experimental Nonlinear Dynamics. Cambridge University Press, New York (2000)MATH Virgin, L.N.: Introduction to Experimental Nonlinear Dynamics. Cambridge University Press, New York (2000)MATH
Metadata
Title
Frequency Island and Nonlinear Vibrating Systems
Authors
Ching Nok To
Hormoz Marzbani
Đại Võ Quốc
Milan Simic
M. Fard
Reza N. Jazar
Copyright Year
2019
DOI
https://doi.org/10.1007/978-3-319-92231-7_15

Premium Partner