Parametric and Direct Resonances in a Base-Excited Beam Carrying a Top Mass
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In this chapter, nonlinear resonances in a coupled shaker-beam-top mass system are investigated both numerically and experimentally. The imperfect, vertical beam carries the top mass and is axially excited by the shaker at its base. The weight of the top mass is below the beam’s static buckling load. A semi-analytical model is derived for the coupled system. In this model, Taylor-series approximations are used for the inextensibility constraint and the curvature of the beam. The steady-state behavior of the model is studied using numerical tools. In the model with a single beam mode, parametric and direct resonances are found, which affect the dynamic stability of the structure. The model with two beam modes not only shows an additional second harmonic resonance, but also reveals some extra small resonances in the low-frequency range, some of which can be identified as combination resonances. The experimental steady-state response is obtained by performing a (stepped) frequency sweep-up and sweep-down with respect to the harmonic input voltage of the amplifier-shaker combination. A good correspondence between the numerical and experimental steady-state responses is obtained.
KeywordsPeriod Doubling Bifurcation Beam Mode Subharmonic Resonance Generalize DOFs Slender Beam
This research is supported by the Dutch Technology Foundation STW, applied science division of NWO and the technology programme of the Ministry of Economic Affairs (STW project EWO.5792).
- Anderson et al(1996)Anderson, Nayfeh, and Balachandran.
- Doedel et al(1998)Doedel, Paffenroth, Champneys, Fairgrieve, Kuznetsov, Oldeman, Sandstede, and Wang.Doedel, E., Paffenroth, R., Champneys, A., Fairgrieve, T., Kuznetsov, Y., Oldeman, B., Sandstede, B., Wang, X.: AUTO97: Continuation and bifurcation software for ordinary differential equations (with HOMCONT). Technical Report, Concordia University (1998)Google Scholar
- Mallon(2008).Mallon, N.: Dynamic stability of thin-walled structures: a semi-analytical and experimental approach. PhD thesis, Eindhoven University of Technology (2008)Google Scholar
- Mallon et al(2006)Mallon, Fey, and Nijmeijer.Mallon, N., Fey, R., Nijmeijer, H.: Dynamic stability of a base-excited thin beam with top mass. In: Proc. of the 2006 ASME IMECE, Nov. 5-10, Paper 13148, Chicago, USA, pp 1–10 (2006)Google Scholar
- Mettler(1962).Mettler, E.: Dynamic buckling. In: Handbook of engineering mechanics (Flügge, W., ed.). McGraw-Hill, London (1962)Google Scholar
- Nayfeh and Pai(2004).
- Noijen et al(2007)Noijen, Mallon, Fey, Nijmeijer, and Zhang.
- Ribeiro and Carneiro(2004).
- Son et al(2008)Son, Uchiyama, Lacarbonara, and Yabuno.
- TueDACS(2008).TueDACS: TUeDACS Advanced Quadrature Interface (2008)Google Scholar
- Verbeek et al(1995)Verbeek, de Kraker, and van Campen.
- Yabuno et al(1998)Yabuno, Ide, and Aoshima.
- Yabuno et al(2003)Yabuno, Okhuma, and Lacarbonara.Yabuno, H., Okhuma, M., Lacarbonara, W.: An experimental investigation of the parametric resonance in a buckled beam. In: Proceedings of the ASME DETC’03, Chicago, USA, pp 2565–2574 (2003)Google Scholar
- Zavodney and Nayfeh(1989).