Vibration reduction of beams under successive traveling loads by means of linear and nonlinear dynamic absorbers Farhad S. Samani a,b,n , Francesco Pellicano b a Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran b Department of Mechanical and Civil Engineering, University of Modena and Reggio Emilia, V. Vignolese, 905, 41125 Modena, Italy article info Article history: Received 15 June 2010 Received in revised form 5 January 2012 Accepted 5 January 2012 Handling Editor: H. Ouyang abstract The goal of the present work is to assess the performances of dynamic vibration absorbers (DVA) in suppressing the vibrations of a simply supported beam subjected to an infinite sequence of regularly spaced concentrated moving loads. In particular, several types of DVA are considered: linear, cubic, higher odd-order monomials and piecewise linear stiffness; linear, cubic and linear-quadratic viscous damping. The purpose is to clarify if nonlinear DVAs show improvements with respect to the classical linear devices. The dynamic scenario is deeply investigated in a wide range of operating conditions, spanning the parameter space of the DVA (damping, stiffness). Nonlinear stiffness can lead to complex dynamics such as quasi-periodic, chaotic and sub-harmonic responses; moreover, acting on the stiffness nonlinearity no improvement is found with respect to the linear DVA. A nonlinear non-symmetric dissipation in the DVA leads to a great reduction of the beam response, the reduction is larger with respect to the linear DVA. & 2012 Elsevier Ltd. All rights reserved. 1. Introduction The problem of repetitive moving loads is classified here as a beam subjected to an infinite series of traveling loads with constant velocity, which repeat at regular time intervals. Such problems are relevant in the transportation industry as well as in the consumer electronics industry; e.g. in a video cassette recorder, a system of 2–4 heads repetitively cross the magnetic tape as a signal is read from, or written on to, the video tape [1]. The critical speed for repetitive loading differs from the critical speed for a single load, which corresponds to the apparent critical speed. Bolotin [2] studied a beam subjected to an infinite sequence of loads with uniform space intervals d and constant speed v; in his study, the ratio d/v (time interval) was identified as a key parameter. For the same problem, Fry ´ ba [3] concluded that the response of the forced steady-state vibration will attain its maximum when the time intervals between two successive moving loads are equal to some periods of the beam in free vibration or to an integer multiple thereof [4]. Yang et al. [5] investigated the resonance and cancellation phenomena in train induced vibration on bridges; in particular, the cancellation consists of a special combination of load speed and distance for which the structural response is zero (an anti-resonance). Timoshenko [6] determined the response of a finite length Euler–Bernoulli beam, due to a Contents lists available at SciVerse ScienceDirect journal homepage: www.elsevier.com/locate/jsvi Journal of Sound and Vibration 0022-460X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. doi:10.1016/j.jsv.2012.01.002 n Corresponding author at: Department of Mechanical Engineering, Shahid Bahonar University of Kerman, Kerman, Iran. Tel.: þ98 3412111763; fax: þ98 3412120964. E-mail addresses: farhad.samani@uk.ac.ir, farhad.samani@yahoo.com (F.S. Samani), francesco.pellicano@unimore.it (F. Pellicano). Journal of Sound and Vibration 331 (2012) 2272–2290