Abstract
We investigate dynamic characteristics of vibratory compaction system with asymmetrical hysteresis. An asymmetrical model derived from Bouc-Wen differential equation is employed to describe hysteretic behavior of vibration engineering. A practical polynomial expression for hysteretic restoring force is deduced to be substituted into standard equation of the system, assuming that the non-linearity of the restoring force is weak. An asymptotic method, which combines Krylov-Bogolyubov-Mitropolsky (KBM) method with harmonic balance (HB) method, is applied to analyze steady-state responses of the asymmetrical hysteretic system subjected to harmonic excitation. Dynamic responses, such as the restoring force time histories and frequency responses of the system for the first order approximate, are obtained. Furthermore, numerical solution obtained using Runge-Kutta method as well as results of experiments (asphalt compaction on the Beijing-Fuzhou highway) are compared with the asymptotic solution. These results investigated that asymmetrical hysteretic model and the methods applied in this paper are quite appropriate for engineering applications.
Similar content being viewed by others
References
Riedler M, Leitner H, Prillhofer B, Winter G, Eichlseder W (2007) Lifetime simulation of thermo-mechanically loaded components. Meccanica 42:47–59
Sorokin SV, Terentiev AV, Karihaloo BL (1999) Nonlinear dynamics and stability of a two D.O.F. elastic/elasto-plastic model system. Meccanica 34:311–336
Ayoub A (2007) Seismic analysis of wood building structures. Eng Struct 29:213–223
Viallet E, Bolsee G, Ladouceur B, Goubin T, Rigaudeau J (2003) Validation of PWR core seismic models with shaking table tests on interacting scale 1 fuel assemblies. In: Transactions of 17th international conference on structural mechanics in reactor technology (SMiRT 17), Prague, Czech Republic, 17–22 August 2003, pp 1–8
Hong SR, Choi SB, Choi YT, Wereley NM (2005) A hydro-mechanical model for hysteretic damping force prediction of ER damper: experimental verification. J Sound Vib 285:1180–1188
Caughey TK (1960) Sinusoidal excitation of a system with bilinear hysteresis. J Appl Mech (Trans ASME) 27:640–643
Iwan WD, Furuike DM (1973) The transient and steady-state response of a hereditary system. Int J Non-Linear Mech 8:395–406
Zhang YF, Iwan WD (2003) Some observations on two piecewise-linear dynamic systems with induced hysteretic damping. Int J Non-Linear Mech 38:753–765
Aoki S, Watanabe T (2004) Practical response analysis of a mass-spring impact system with hysteresis damping. Nucl Eng Des 234:1–9
Capecchi D, Vestroni F (1986) Steady-state dynamic analysis of hysteretic systems. J Eng Mech 111:1515–1531
Jin JD, Zhang YF, Wei W (2006) Steady-state response of a binon-linear hysteretic system. Int J Non-Linear Mech 41:926–935
Bouc R (1967) Forced vibrations of a mechanical system with hysteresis. In: Proceedings of the 4th conference on non-linear oscillation, Prague, Czechoslovakia, 5–9 September 1967, p 315
Wen YK (1976) Method for random vibration of hysteretic systems. J Eng Mech 102:249–263
Chang SI (2004) Bifurcation analysis of a non-linear hysteretic oscillator under harmonic excitation. J Sound Vib 276:215–225
Awrejcewicz J, Dzyubak LP (2005) Influence of hysteretic dissipation on chaotic responses. J Sound Vib 284:513–519
Wong CW, Ni YQ, Lau SL (1994) Steady-state oscillation of hysteretic differential model, I: response analysis. J Eng Mech 120:2271–2297
Wong CW, Ni YQ, Ko JM (1994) Steady-state oscillation of hysteretic differential model, II: performance analysis. J Eng Mech 120:2299–2325
Noori M, Dimentberg M, Hou Z, Christodoulidou R, Alexandrou A (1995) First-passage study and stationary response analysis of a BWB hysteresis model using quasi-conservative stochastic averaging method. Probab Eng Mech 10:161–170
Grabe J (1993) Continuous inverse calculation of soil stiffness from the dynamic behavior of a driving vibratory roller. Arch Appl Mech 63:472–478
Mooney MA, Gorman PB, Gonzalez JN (2005) Vibration-based health monitoring of earth structures. Struct Health Monit 4:137–152
Yoo TS, Selig ET (1979) Dynamics of vibratory-roller compaction. J Geotech Geoenviron Eng 105:1211–1231
Pietzsch D, Poppy W (1992) Simulation of soil compaction with vibratory rollers. J Terramech 29:585–597
Okuizumi N, Kimura K (2004) Multiple time scale analysis of hysteretic systems subjected to harmonic excitation. J Sound Vib 272:675–701
Worden K, Tomlinson GR (2001) Nonlinearity in structural dynamics: detection, identification. Institute of Physics Publishing, Bristol
Han QK, Wen BC (1998) Analysis of a forced vibration system with asymmetrical hysteresis. J Vib Eng 11:291–297
Li HG, Meng G (2007) Nonlinear dynamics of a SDOF oscillator with Bouc-Wen hysteresis. Chaos Solitons Fractals 34:337–343
Liu CS, Huang ZM (2004) The steady state responses of s.d.o.f. viscous elasto-plastic oscillator under sinusoidal loadings. J Sound Vib 273:149–173
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Shen, PH., Lin, SW. Mathematic modeling and characteristic analysis for dynamic system with asymmetrical hysteresis in vibratory compaction. Meccanica 43, 505–515 (2008). https://doi.org/10.1007/s11012-008-9114-x
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11012-008-9114-x