Abstract
In this paper, the impact damper is used to illustrate that the vibration of all modes of viscoelastic beams can be effectively suppressed. Hertz contact theory is used to model the collision process as a form of stiffness and damping. In addition, viscous damping added between the main mass and the small mass is also studied to increase the consumption of vibration energy of the cantilever beam. Because the collision is discontinuous, the equations with collision and without are established. The Runge-Kutta algorithm is used to solve the differential equation. Taking the first- and second-order mode vibration of the cantilever beam as an example, numerical results show that the multiple-order mode displacement response of the cantilever beam is reduced by the impact damper. Moreover, the mass of the vibrator and the collision gap is very sensitive to the vibration suppression effect of the cantilever beam.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Li, C., Zhuang, T., Zhou, S.T., et al.: Passive vibration control of a semi-submersible floating offshore wind turbine. Appl. Sci-Basel. 7, 509 (2017)
Ahmadabadi, Z.N., Khade, S.E.: Nonlinear vibration control of a cantilever beam by a nonlinear energy sink. Mech. Mach. Theory. 50, 134–149 (2014)
Tian, L., Rong, K.J., Zhang, P., Liu, Y.P.: Vibration control of a power transmission tower with pounding tuned mass damper under multi-component seismic excitations. Appl. Sci-Basel. 7, 447 (2017)
Roffel, A.J., Narasimhan, S., Asce, M., Haskett, T.: Performance of pendulum tuned mass dampers in reducing the responses of flexible structures. J. Struct. Eng. 139, 04013019 (2013)
Yao, B., Chen, Q., Xiang, H.Y., Gao, X.: Experimental and theoretical investigation on dynamic properties of tuned particle damper. Int. J. Mech. Sci. 80, 122–130 (2014)
Cheng, C.C., Wang, J.Y.: Free vibration analysis of a resilient impact damper. Int. J. Mech. Sci. 45(4), 589–604 (2003)
Park, J., Wang, S., Crocker, M.: Mass loaded resonance of a single unit impact damper caused by impacts and the resulting kinetic energy influx. J. Sound Vib. 323, 877–895 (2009)
Peterka, F.: Bifurcations and transition phenomena in an impact oscillator. Chaos, Solitons Fractals. 7, 1635–1647 (1996)
Gharib, M., ASCE, A.M., Karkoub, M.: Experimental investigation of linear particle chain impact dampers in free-vibration suppression. J. Struct. Eng. 143(2), 04016160 (2016)
Li, T., Qiu, D., Seguy, S., Berlioz, A.: Activation characteristic of a vibro-impact energy sink and its application to chatter control in turning. J. Sound Vib. 405, 1–18 (2017)
Wouw, V.D., Bosch, V.D., Kraker, D.A., Campen, D.H.: Experimental and numerical analysis of nonlinear phenomena in a stochastically excited beam system with impact. Chaos, Solitons Fractals. 9, 1409–1428 (1998)
Cheng, J.L., Xu, H.: Inner mass impact damper for attenuating structure vibration. Int. J. Solids Struct. 43, 5355–5369 (2000)
Afsharfard, A., Farshidianfar, A.: Design of nonlinear impact dampers based on acoustic and damping behavior. Int. J. Mech. Sci. 65, 125–133 (2012)
Afsharfard, A., Farshidianfar, A.: An efficient method to solve the strongly coupled nonlinear differential equations of impact dampers. Arch. Appl. Mech. 82, 977–984 (2012)
Du, Y.C., Wang, S.L.: Modeling the fine particle impact damper. Int. J. Mech. Sci. 52, 1015–1022 (2010)
Jam, J.E., Fard, A.A.: Application of single unit impact dampers to reduce undesired vibration of the 3R robot arms. Int. J. Aerosp. Sci. 2(2), 49–54 (2013)
Lu, Z., Lu, X.L., Lu, W.S., Masri, S.F.: Experimental studies of the effects of buffered particle dampers attached to a multi-degree-of-freedom system under dynamic loads. J. Sound Vib. 331(9), 2007–2022 (2012)
Misra, A., Cheung, J.: Particle motion and energy distribution in tumbling ball mills. Powder Technol. 105, 222–227 (1999)
Jankowski, R.: Analytical expression between the impact damping ratio and the coefficient of restitution in the non-linear viscoelastic model of structural pounding. Earthq. Eng. Struct. Dyn. 35(4), 517–524 (2016)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Geng, XF., Ding, H., Chen, LQ. (2021). Vibration Analysis of a Viscoelastic Beam Equipped with a Resilient Impact Damper. In: Oberst, S., Halkon, B., Ji, J., Brown, T. (eds) Vibration Engineering for a Sustainable Future. Springer, Cham. https://doi.org/10.1007/978-3-030-47618-2_27
Download citation
DOI: https://doi.org/10.1007/978-3-030-47618-2_27
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-47617-5
Online ISBN: 978-3-030-47618-2
eBook Packages: EngineeringEngineering (R0)