Free vibration analysis of nonlinear resilient impact dampers
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O R I G I N A L PA P E R
Free vibration analysis of nonlinear resilient impact dampers Aref Afsharfard · Anooshiravan Farshidianfar
Received: 5 August 2012 / Accepted: 10 January 2013 © Springer Science+Business Media Dordrecht 2013
Abstract In the present study, free vibration of a vibratory system equipped with an impact damper, which incorporates the Hertzian contact theory, is investigated. A nonlinear model of an impact damper is constructed using spring, mass, and viscous damper. To increase accuracy of the solution, deformation of the impact damper during the collision with and the main mass is considered. The governing coupled nonlinear differential equations of a cantilever beam equipped with the impact damper are solved using the parameter expanding perturbation method. Contact durations, which are obtained using the presented method, are compared with previous results. Gap sizes of the impact dampers are classified to two main parts. The effects of selecting the gap sizes regarding to the discussed classification are investigated on the application of the impact dampers. Based on types of collision between colliding masses, the so-called “effectiveness” is defined. Finally, it is shown variation of the damping inclination with the gap size is similar to variation of the effectiveness. Keywords Resilient impact damper · Hertzian contact theory · Perturbation method · Damping inclination · Effectiveness A. Afsharfard () · A. Farshidianfar Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran e-mail: [email protected]
1 Introduction For many years, researchers have extensively investigated mechanical systems whose elements collide with each other during operation because impacts occur very often in many modern technical devices [1–5]. An impact damper is a small loose mass within a main mass. There are many advantages in using impact dampers over traditional passive devices: They are inexpensive, simple in design, robust and effective in harsh environments with a wide range of frequencies [6]. Applications of the impact dampers to reduce undesired vibrations of turbine blades, machine tools have been investigated [7–10]. It is shown the impact dampers would operate more efficiently than classical dynamic vibration dampers [11]. Bapat and Sankar showed that the coefficient of restitution has a great effect on the performance of impact dampers [12]. They demonstrated that in the case of single unit impact dampers, optimized parameters at resonance are not necessarily optimal at other frequencies. Popplewell and Liao introduced an accurate approximation to determine the optimum clearance of a rigid damper [8]. Ema and Marui investigated the characteristics of an impact damper in free damped vibration [13]. They indicated that the damping capability of the vibratory system could be significantly improved using a proper impact damper. Cheng and Xu obtained a relation between coefficient of restitution and impact damping ratio [14]. They showed that the optimal initial d
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