Abstract
The behavior of a nonlinear pendulum working as a tuned mass damper (TMD) for slender structures is analyzed in this paper. The influence of the inherent nonlinearity of the oscillations of the pendulum, together with the dry friction damping, in its vibration control behavior is modeled as a 2 DOF system with the usual linear elements together with nonlinear spring and damping elements between the equivalent mass of the structure and the mass of the TMD. Due to the frequency-energy dependence of the oscillations of the system, the frequency response functions (FRFs) are no longer invariant and the displacement response is dependent on the level of excitation, so the nonlinear normal modes (NNMs) are computed using numerical computations. The comparison of the results with the behavior of the underlying linear normal modes (LNMs) is shown and discussed and well as the influence of the nonlinear elastic, damping and force coefficients.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Williamson CHK, Govardhan R (2008) A brief review of recent results in vortex induced vibrations. J Wind Eng Ind Aerodyn 96(6–7):713–735
Frahm H (1909) Device for damping vibrations of bodies. U.S. Patent No. 989958, 30 Oct 1909
Ormondroyd J, Den Hartog JP (1928) The theory of the dynamic vibration absorber. Trans ASME, APM-50-7:9–22
Carvalhaes C, Suppes P (2008) Approximations for the period of the simple pendulum based on the arithmetic-geometric mean. Am J Phys 76(12):1150–1154
Nelson R, Olsson MG (1986) The pendulum – Rich physics from a simple system. Am J Phys 54(2):112–121
Jankowski R, Kujawa M, Szymczak C (2004) Reduction of steel chimney vibrations with a pendulum damper. Task Q 8(1):71–78
Brownjohn JMW, Carden EP, Goddard RC, Oudin G, Koo K (2009) Real-time performance tracking on a 183 m concrete chimney and tuned mass damper system. In: 3rd International Operational Modal Analysis Conference (IOMAC), Ancona (Italy)
Friswell MI, Mottershead JE (1995) Finite element model updating in structural dynamics. Kluwer Academic, Dorcdrecht
García-Diéguez M, Koo KY, Middleton CM, Brownjohn JMW, Goddard C (2010) Model updating for a 183 m of reinforced concrete chimney. In: 3rd International Operational Modal Analysis Conference (IOMAC), Ancona (Italy)
Harris CM (1988) Shock and vibration handbook. McGraw-Hill, New York
Clough RW, Penzien J (1993) Dynamics of structures. McGraw-Hill, New York. International edition
Shaw SW, Pierre C (1991) Non-linear normal modes and invariant manifolds. J Sound Vib 150:170–173
Rosenberg RM (1960) Normal modes of nonlinear dual-mode systems. J Appl Mech 27:263–268
Kerschen G, Peeters M, Golinval JC, Vakakis AF (2009) Nonlinear normal modes, part I: a useful frame work for the structural dynamicist. Mech Syst Signal Process 23:170–194
Peeters M, Viguié R, Sérandour G, Kerschen G, Golinval JC (2009) Nonlinear normal modes, part II: toward a practical computation using numerical continuation techniques. Mech Syst Signal Process 23:195–216
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 The Society for Experimental Mechanics, Inc.
About this paper
Cite this paper
López-Reyes, P.M., Lorenzana, A., Belver, A.V., Lavín, C.E. (2013). Response of a Pendulum TMD with Large Displacements. In: Kerschen, G., Adams, D., Carrella, A. (eds) Topics in Nonlinear Dynamics, Volume 1. Conference Proceedings of the Society for Experimental Mechanics Series, vol 35. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6570-6_22
Download citation
DOI: https://doi.org/10.1007/978-1-4614-6570-6_22
Published:
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4614-6569-0
Online ISBN: 978-1-4614-6570-6
eBook Packages: EngineeringEngineering (R0)