Engineering Structures 30 (2008) 282–286 www.elsevier.com/locate/engstruct Short communication Optimal design of a damped dynamic vibration absorber for vibration control of structure excited by ground motion W.O. Wong ∗ , Y.L. Cheung Department of Mechanical Engineering, The Hong Kong Polytechnic University, Hong Kong Received 15 June 2006; received in revised form 12 October 2006; accepted 12 March 2007 Available online 17 April 2007 Abstract Optimum parameters of a dynamic vibration absorber of non-traditional form have been derived for suppressing vibration of a single degree- of-freedom system due to ground motion. The reduction of transmission of motion from the support to the mass of the structure is compared for the cases of using the traditional and the proposed dynamic absorbers. Under the optimum tuning condition of the absorbers, it is proved analytically that the proposed absorber provides a larger suppression of resonant vibration amplitude of the primary system excited by ground motion than the traditional absorber. c  2007 Elsevier Ltd. All rights reserved. Keywords: Vibration absorber; Tuned mass damper; Damping 1. Introduction Dynamic vibration absorbers can be used for passive control of narrowband vibration. As described in the classical textbooks on dynamic vibration absorber [1–3], an undamped dynamic vibration absorber is an auxiliary mass–spring system which, when correctly tuned and attached to a vibrating body subject to a harmonic excitation, eliminates steady-state motion of the point to which it is attached. The traditional damped vibration absorber has a damper added between the absorber mass m and the primary mass M as shown in Fig. 1(a) to limit the vibration amplitude when the lower resonance is experienced during system start-up and stopping. However, it is not possible to eliminate steady-state vibrations of the original mass after damping is added in the auxiliary mass–spring system. Optimization of the frequency and damping parameters of the traditional damped vibration absorber for minimization of the resonant vibration amplitudes based on the fixed-points theory is well documented in the textbook of Den Hartog [1]. Recent advances of absorber designs involve addition of active controlled elements [4–6], adaptive elements that can be used to change the tuned condition of the absorber [7,8], ∗ Corresponding author. Tel.: +852 2766 6667; fax: +852 2365 4703. E-mail address: mmwowong@polyu.edu.hk (W.O. Wong). and passive device with non-traditional elements for broad- band vibration control [9–11]. These advanced absorbers are useful in applications requiring the change of tuning parameters as the main system changes in time. On the other hand, the traditional dynamic vibration absorber may provide a cheaper and convenient solution for vibration suppression and isolation of vibrating systems with harmonic excitation. In this paper, the optimum tuning frequency and damping of a damped dynamic vibration absorber of non-traditional form as shown in Fig. 1(b) have been derived for suppressing vibration of a single-degree- of-freedom system due to ground motion. The derivation of the formulae for the optimum tuning frequency and damping of the absorber was based on the fixed-points theory of Den Hartog [1]. It is proved that the proposed absorber provides a larger suppression of resonant vibration amplitude of the primary system excited by ground motion than the traditional absorber. 2. The traditional damped dynamic vibration absorber A schematic diagram of a traditional damped dynamic vibration absorber attached to an undamped mass–spring system is shown in Fig. 1(a). This vibration model is called model A in the following discussion. The amplitude ratio 0141-0296/$ - see front matter c  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.engstruct.2007.03.007