This study is concerned with modelling and analyses of a vibro-impact system consisting of a crank-slider mechanism and one oscillator attached to it, where the system is exposed to a non-ideal excitation. The impact occurs during the motion of the oscillator when it fits a base, and the excitation of the driving source is affected by this behaviour. The aim is to determine the interaction between a driving torque and the motion of the oscillator. To achieve this aim in a methodologically sound manner, both vibrating and vibro-impact systems with an ideal and non-ideal excitation are analysed. Analytical and numerical solutions are obtained for the vibrating system with the ideal excitation. Numerical analyses of the vibrating system with the non-ideal excitation is then conducted, where the characteristic curves for this system are found analytically. Numerical simulations are also carried out for other two systems and the results obtained are shown in terms of frequency–response diagrams, time-displacement diagrams and basins of attraction. The results found for different systems are compared mutually, and the differences between them are pointed out. Impact solutions for different regions of the excitation frequency are shown. For the vibro-impact system with the non-ideal excitation, the average value of its frequency is used.
This is a preview of subscription content, access via your institution.
Buy single article
Instant access to the full article PDF.
Tax calculation will be finalised during checkout.
Babitsky VI (1998) Theory of vibro- impact systems and applications. Springer, Berlin
Karayannis I, Vakakis AF, Georgiades F (2008) Vibro-impact attachments as shock absorbers. Proc Inst Mech Eng Part C J Mech Eng Sci 222:1899–1908
Rong H, Wang X, Xu W, Fang T (2010) Resonant response of a non-linear vibro-impact system to combined deterministic harmonic and random excitations. Int J Non-Linear Mech 45(5):474–481
Liu Y, Wiercigroch M, Pavlovskaia E, Yu H (2013) Modelling of a vibro-impact capsule system. Int J Mech Sci 66:2–11
Tosic P (2018) Forced oscillations of vibro-impact system (In Serbian). Master thesis, University of Novi Sad, Serbia
Marzbanrad J, Shahsavar M, Beyranvand B (2017) Analysis of force and energy density transferred to barrier in a single degree of freedom vibro-impact system. J Cent South Univ 24(6):1351–1359
Raouf AI (2009) Vibro-impact dynamics—modeling, mapping and applications. Springer, Berlin
Batako AD, Babitsky VI, Halliwell NA (2004) Modelling of vibro-impact penetration of self-exciting percussive-rotary drill bit. J Sound Vib 271:209–225
Yuri VM, Reshetnikova SN (2006) Dynamical interaction of an elastic system and a vibro-impact absorber. Math Probl Eng 2006:1–15
Kononenko VO (1969) Vibrating systems with a limited power supply. Iliffe, London
Zukovic M, Cveticanin L, Maretic R (2012) Dynamics of the cutting mechanism with flexible support and non-ideal forcing. Mech Mach Theory 58:1–12
Cveticanin L, Zukovic M, Balthazar JM (2018) Dynamics of mechanical systems with non-ideal excitation. Mathematical Engineering. Springer, Berlin
Balthazar JM, Mook DT, Weber HI, Fenili A, Belato D, Felix JLP (2003) An overview on non-ideal vibrations. Meccanica 38:613–621
Cveticanin L, Zukovic M (2015) Motion of a motor-structure non-ideal system. Eur J Mech A Solids 53:229–240
Cveticanin L, Zukovic M (2013) Non-ideal mechanical system with an oscillator with rational nonlinearity. J Vib Control 21(11):2149–2164
Karthikeyan M, Bisoi A, Samantaray AK, Bhattacharyya R (2015) Sommerfeld effect characterization in rotors with non-ideal drive from ideal drive response and power balance. Mech Mach Theory 91:269–288
Kovacic I, Zukovic M (2016) Coupled purely nonlinear oscillators: normal modes and exact solutions for free and forced responses. Nonlinear Dyn 87(1):713–726
Samantaray AK, Dasgupta SS, Bhattacharyya RR (2010) Sommerfeld effect in rotationally symmetric planar dynamics systems. Int J Eng Sci 48(1):21–36
Warminski J, Balthazar JM (2003) Vibrations of a parametrically and self-excited system with ideal and non-ideal energy sources. J Braz Soc Mech Sci Eng 25(4):413–420
Zukovic M, Cveticanin L (2009) Chaos in non-ideal mechanical system with clearance. J Vib Control 15(8):1229–1246
Lampart M, Zapomel J (2013) Dynamics of the electromechanical system with impact element. J Sound Vib 332:701–713
Lampart M, Zapomel J (2014) Dynamic properties of the electromechanical system damped by an impact element with soft stops. Int J Appl Mech 06(02):1450016
Moraes FH, Pontes BR Jr, Silveira M, Balthazar JM (2013) Influence of ideal and non-ideal excitation sources on the dynamics of a nonlinear vibro-impact system. J Theor Appl Mech 51:763–774
Souza SLT, Caldas IL, Viana RL, Balthazar JM (2008) Control and chaos for vibro-impact and non-ideal oscillators. J Theor Appl Mech 46:641–664
Moraes FH, Pontes BR Jr, Silveira M, Balthazar JM (2005) Impact dampers for controlling chaos in systems with limited power supply. J Sound Vib 279:955–967
Dormand JR, Prince PJ (1980) A family of embedded Runge–Kutta formulae. J. Comp. Appl. Math. 6:19–26
Shampine LF, Reichelt MW (1997) The MATLAB ODE suite. SIAM J Sci Comput 18:1–22
The first and the third author acknowledge support of the Ministry of Education and Science of the Republic of Serbia.
Conflict of interest
:The Authors declare that there is no conflict of interest.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
About this article
Cite this article
Zukovic, M., Hajradinovic, D. & Kovacic, I. On the dynamics of vibro-impact systems with ideal and non-ideal excitation. Meccanica 56, 439–460 (2021). https://doi.org/10.1007/s11012-020-01280-5
- Vibro-impact systems
- Frequency–response diagram
- Impact solutions
- Non-ideal excitation
- Limited power supply