Abstract
In this paper, possible scenarios within the experimental dynamic response of a vibro-impact single-degree-of-freedom system, symmetrically constrained by deformable and dissipative bumpers, were identified and described. The different scenarios were obtained varying selected parameters, namely peak table acceleration \(\hbox {A}\), amplitude of the total gap between mass and bumpers \(\hbox {G}\) and bumper’s stiffness \(\hbox {B}\). Subsequently, using a Simplified Nonlinear Model results in good agreement with the experimental outcomes were obtained, although the model includes only the nonlinearities due to clearance existence and impact occurrence. Further numerical analysis highlighted other scenarios that can be obtained for values of the parameters not considered in the experimental laboratory campaign. Finally, to attempt a generalization of the results, suitable dimensionless parameters were introduced.
Similar content being viewed by others
References
Ibrahim, R.A.: Vibro-Impact Dynamics: Modeling, Mapping and Applications. Lecture Notes in Applied and Computational Mechanics, vol. 43. Springer, Heidelberg (2009)
Liu, Y., Wiercigroch, M., Pavlovskaia, E., Peng, Z.K.: Forward and backward motion control of a vibro-impact capsule system. Int. J. Nonlinear Mech. 70, 30–46 (2015)
Liu, Y., Pavlovskaia, E., Wiercigroch, M.: Experimental verification of the vibro-impact capsule model. Nonlinear Dyn. 83(1–2), 1029–1041 (2016)
Yan, Y., Liu, Y., Liao, M.: A comparative study of the vibro-impact capsule systems with one-sided and two-sided constraints. Nonlinear Dyn. 89(2), 1063–1087 (2017)
Gu, X.D., Deng, Z.C.H.: Dynamical analysis of vibro-impact capsule system with Hertzian contact model and random perturbation excitations. Nonlinear Dyn. 92(4), 1781–1789 (2018)
Yan, Y., Liu, Y., Manfredi, L., Prasad, S.: Modelling of a vibro-impact self-propelled capsule in the small intestine. Nonlinear Dyn. 96(1), 123–144 (2019)
Divenyi, S., Savi, M.A., Wiercigroch, M., Pavlovskaia, E.: Drill-string vibration analysis using non-smooth dynamics approach. Nonlinear Dyn. 70(2), 1017–1035 (2012)
Liu, X., Vlajic, N., Long, X., Meng, G., Balachandran, B.: Nonlinear motions of a flexible rotor with a drill bit: stick-slip and delay effects. Nonlinear Dyn. 72(1–2), 61–77 (2013)
Liu, X., Vlajic, N., Long, X., Meng, G., Balachandran, B.: Coupled axial-torsional dynamics in rotary drilling with state-dependent delay: stability and control. Nonlinear Dyn. 78(3), 1891–1906 (2014)
Liu, Y., Páez Chávez, J., De Sa, R., Walker, S.: Numerical and experimental studies of stick-slip oscillations in drill-strings. Nonlinear Dyn. 90(4), 2959–2978 (2017)
Vaziri, V., Kapitaniak, M., Wiercigroch, M.: Suppression of drill-string stick-slip vibration by sliding mode control: numerical and experimental studies. Eur. J. Appl. Math. 29(5), 805–825 (2018)
de Moraes, L.P.P., Savi, M.A.: Drill-string vibration analysis considering an axial-torsional-lateral nonsmooth model. J. Sound Vib. 438, 220–237 (2019)
Malhotra, P.: Dynamics of seismic impacts in base-isolated buildings. Earthq. Eng. Struct. Dyn. 26(8), 797–813 (1997)
Komodromos, P., Polycarpou, P.C., Papaloizou, L., Phocas, M.C.: Response of seismically isolated buildings considering poundings. Earthq. Eng. Struct. Dyn. 36(12), 1605–1622 (2007)
Polycarpou, P.C., Komodromos, P.: On poundings of a seismically isolated building with adjacent structures during strong earthquakes. Earthq. Eng. Struct. Dyn. 39(8), 933–940 (2010)
Polycarpou, P.C., Komodromos, P.: Earthquake-induced poundings of a seismically isolated building with adjacent structures. Eng. Struct. 32(7), 1937–1951 (2010)
Masroor, A., Mosqueda, G.: Experimental simulation of base-isolated buildings pounding against moat wall and effects on superstructure response. Earthq. Eng. Struct. Dyn. 41(14), 2093–2109 (2012)
Masroor, A., Mosqueda, G.: Impact model for simulation of base isolated buildings impacting flexible moat walls. Earthq. Eng. Struct. Dyn. 42, 357–376 (2013)
Mavronicola, E.A., Polycarpou, P.C., Komodromos, P.: Effect of planar impact modeling on the pounding response of base-isolated buildings. Front. Built Environ 2(11), 1–16 (2016)
Reggio, A., De Angelis, M.: Optimal design of an equipment isolation system with nonlinear hysteretic behavior. Earthq. Eng. Struct. Dyn. 42, 1907–1930 (2013)
Reggio, A., De Angelis, M.: Combined primary-secondary system approach to the design of an equipment isolation system with high-damping rubber bearings. J. Sound Vib. 333, 2386–2403 (2014)
Sarebanha, A., Mosqueda, G., Kim, M.K., Kim, J.H.: Seismic response of base isolated nuclear power plants considering impact to moat walls. Nucl. Eng. Des. 328, 58–72 (2018)
Jankowski, R., Wilde, K., Fujino, Y.: Reduction of pounding effects in elevated bridges during earthquakes. Earthq. Eng. Struct. Dyn. 29(2), 195–212 (2000)
Guo, A.X., Li, Z.J., Li, H., Ou, J.P.: Experimental and analytical study on pounding reduction of base isolated highway bridges using MR dampers. Earthq. Eng. Struct. Dyn. 38(11), 1307–1333 (2009)
Hao, H., Bi, K.M., Chouw, N., Ren, W.X.: State-of-the-art review on seismic induced pounding response of bridge structures. J. Earthq. Tsunami 7(3), 1350019-1–1350019-19 (2013)
Anagnostopoulos, S.A.: Pounding of building in series during earthquake. Earthq. Eng. Struct. Dyn. 16, 443–456 (1988)
Polycarpou, P.C., Komodromos, P.: Numerical investigation of potential mitigation measures for poundings of seismically isolated buildings. Earthq. Struct. 2(1), 1–24 (2011)
Polycarpou, P.C., Komodromos, P., Polycarpou, A.C.: A nonlinear impact model for simulating the use of rubber shock absorbers for mitigating the effects of structural pounding during earthquakes. Earthq. Eng. Struct. Dyn. 42(1), 81–100 (2013)
Renzi, E., De Angelis, M.: Optimal semi-active control and non-linear dynamic response of variable stiffness structures. J. Vib. Control 11(10), 1253–1289 (2005)
Arena, A., Lacarbonara, W., Casalotti, A.: Payload oscillations control in harbor cranes via semi-active vibration absorbers: modeling, simulations and experimental results. Proc. Eng. 199, 501–509 (2017)
Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge, UK (1985)
Goldsmith, W.: Impact—The Theory and Physical Behaviour of Colliding Solids. Edward Arnold Ltd., London (1960)
Rigaud, E., Perret-Liaudet, J.: Experiments and numerical results on non-linear vibrations of an impacting Hertzian contact. Part 1: harmonic excitation. J. Sound Vib. 265, 289–307 (2003)
Muthukumar, S., DesRoches, R.: A Hertz contact model with non-linear damping for pounding simulation. Earthq. Eng. Struct. Dyn. 35, 811–828 (2006)
Machado, M., Moreira, P., Flores, P., Lankarani, H.M.: Compliant contact force models in multibody dynamics: evolution of the Hertz contact theory. Mech. Mach. Theory 53, 99–121 (2012)
Skrinjar, L., Slavič, J., Boltežar, M.: A review of continuous contact-force models in multibody dynamics. Int. J. Mech. Sci. 145, 171–187 (2018)
Flores, P., Machado, M., Silva, M., Martins, J.: On the continuous contact force models for soft materials in multibody dynamics. Multibody Syst. Dyn. 25, 357–375 (2011)
Flores, P., Lankarani, H.M.: Contact Force Models for Multibody Dynamics. Springer, Berlin (2016)
Hertz, H.: Ueber die Berührung fester elastischer Körper. Journal für die reine und angewandte Mathematik 91, 156–171 (1881)
Půst, L., Peterka, F.: Impact oscillator with Hertz’s model of contact. Meccanica 38, 99–114 (2003)
Dubowsky, S., Freudenstein, F.: Dynamic analysis of mechanical systems with clearances - part 1: formation of dynamic model. J. Eng. Ind. 93(1), 305–309 (1971)
Khulief, Y.A., Shabana, A.A.: A continuous force model for the impact analysis of flexible multibody systems. Mech. Mach. Theory 22(3), 213–224 (1987)
Hunt, K., Crossley, E.: Coefficient of restitution interpreted as damping in vibroimpact. J. Appl. Mech. 42(2), 440–445 (1975)
Wagg, D.J., Bishp, S.R.: Chatter, sticking and chaotic impacting motion in a two-degree of freedom impact oscillator. Int. J. Bifurcat. Chaos 11(1), 57–71 (2001)
Wagg, D.J., Bishp, S.R.: Dynamics of a two degree of freedom vibro-impact system with multiple motion limiting constraints. Int. J. Bifurcat. Chaos 14(1), 119–140 (2004)
Luo, G.W., Lv, X.H., Shi, Y.Q.: Vibro-impact dynamics of a two-degree-of freedom periodically-forced system with a clearance: diversity and parameter matching of periodic-impact motions. Int. J. Nonlinear Mech. 65, 173–195 (2014)
Luo, G.W., Zhu, X.F., Shi, Y.Q.: Dynamics of a two-degree-of freedom periodically-forced system with a rigid stop: Diversity and evolution of periodic-impact motions. J. Sound Vib. 334, 338–362 (2015)
Luo, T., Wang, Z.: Periodically forced system with symmetric motion limiting constraints: dynamic characteristics and equivalent electronic circuit realization. Int. J. Nonlinear Mech. 81, 283–302 (2016)
Hao, Z., Cao, Q., Wiercigroch, M.: Two-sided damping constraint control strategy for high-performance vibration isolation and end-stop impact protection. Nonlinear Dyn. 86, 2129–2144 (2016). https://doi.org/10.1007/s11071-016-2685-5
Wang, J., Shen, Y., Yang, S.: Dynamical analysis of a single degree-of-freedom impact oscillator with impulse excitation. Adv. Mech. Eng. 9(7), 1–10 (2017). https://doi.org/10.1177/1687814017716619
Gritli, H., Belghith, S.: Diversity in the nonlinear dynamic behavior of a one-degree-of-freedom impact mechanical oscillator under OGY-base d state-feedback control law: Order, chaos and exhibition of the border-collision bifurcation. Mech. Mach. Theory 124, 1–41 (2018)
de S Rebouças, G.F., Santos, I.F., Thomsen, J.J.: Unilateral vibro-impact systems—experimental observations against theoretical predictions based on the coefficient of restitution. J. Sound Vib. 440, 346–371 (2019)
Andreaus, U., De Angelis, M.: Nonlinear dynamic response of a base-excited SDOF oscillator with double-side unilateral constraints. Nonlinear Dyn. 84, 1447–1467 (2016)
Andreaus, U., Baragatti, P., De Angelis, M., Perno, S.: A preliminary experimental study about two-sided impacting SDOF oscillator under harmonic excitation. J. Comput. Nonlin. Dyn. 12, 061010 (2017)
Andreaus, U., Baragatti, P., De Angelis, M., Perno, S.: Shaking table tests and numerical investigation of two-sided damping constraint for end-stop impact protection. Nonlinear Dyn. 90, 2387–2421 (2017)
Andreaus, U., De Angelis, M.: Experimental and numerical dynamic response of a SDOF vibro-impact system with double gaps and bumpers under harmonic excitation. Int. J. Dyn. Control 7(4), 1278–1292 (2019)
Andreaus, U., De Angelis, M.: Influence of the characteristics of isolation and mitigation devices on the response of SDOF vibro-impact systems with two-sided bumpers and gaps via shaking table tests. Struct. Control Health. Monit. e2517 (2020). https://doi.org/10.1002/stc.2517
Stefani, G., De Angelis, M., Andreaus, U.: Experimental dynamic response of a SDOF oscillator constrained by two symmetrically arranged deformable and dissipative bumpers under harmonic base excitation. In: Lacarbonara, W., Balachandran, B., Ma, J., Tenreiro Machado, J. Stepan, G. (eds.) Nonlinear Dynamics and Control, pp. 119–127. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-34747-5_12
Stefani, G., De Angelis, M., Andreaus, U.: Experimental and numerical investigation of base isolated SDOF system impact against bumpers under harmonic base excitation. In: Papadrakakis, M., Fragiadakis, M. (eds) Proceedings of the 7th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2019), vol. 2, pp. 3333–3343 (2019). https://doi.org/10.7712/120119.7150.19207
Stefani, G., De Angelis, M., Andreaus, U.: Experimental and numerical response analysis of a unilaterally constrained SDOF system under harmonic base excitation. In: Carcaterra A., Paolone A., Graziani G. (eds) Proceedings of XXIV AIMETA Conference 2019. Lecture Notes in Mechanical Engineering, pp. 1488–1497. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-41057-5_120
Naeim, F., Kelly, J.M.: Design of Seismic Isolated Structures: From Theory to Practice. Wiley, Chichester (1999)
Acknowledgements
The funding was provided by Sapienza Università di Roma (Grant Nos. RM116154C359801B and RP116154F1DB0EAF).
Author information
Authors and Affiliations
Corresponding author
Ethics declarations
Conflict of interest
The authors declare that they have no conflict of interest.
Additional information
Publisher's Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Stefani, G., De Angelis, M. & Andreaus, U. Scenarios in the experimental response of a vibro-impact single-degree-of-freedom system and numerical simulations. Nonlinear Dyn 103, 3465–3488 (2021). https://doi.org/10.1007/s11071-020-05791-4
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11071-020-05791-4