Novel inerter-based absorbers for suppressing beams vibration under successive moving loads
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Novel inerter‑based absorbers for suppressing beams vibration under successive moving loads Razie Ebrahimnejad1 · Farhad S. Samani1,2 Received: 9 April 2020 / Accepted: 22 September 2020 © Springer Nature Switzerland AG 2020
Abstract Inerter-based vibration absorbers are new generations of tuned mass dampers. The property of the inerter is that the relative acceleration between its two terminals is proportional to produced force. This paper proposes the use of inerterbased vibration absorbers for suppressing the beam vibration under successive moving loads. The vibrational system possesses continuous beam model accompanying by inerter-based vibration absorbers. The effectiveness of this new type of vibration absorber compared with the ordinary linear vibration absorber. The partial differential governing equation converts to a system of ordinary differential equations using the Bubnov–Galerkin method. The optimal parameters of the inerter-based vibration absorbers are presented. The results show that this novel vibration absorber can reduce vibration 37% more than the optimized classical linear vibration absorbers. Some results give quasi-beating response for the beam possesses inerter-based vibration absorbers. Keywords Inerter-based vibration absorbers · Tuned mass dampers · Successive moving loads
1 Introduction For long bridges and other structures under high speed, moving loads, the vibration is an important issue. Many researchers worked on beams vibration under moving loads, Refs. [1–3]. Applying dynamic vibration absorbers (DVAs) is a method to reduce unwanted vibrations, Refs. [4–7]. The effectiveness of nonlinear DVAs applied to beams excited by successive moving loads was analyzed in [8, 9]. These papers showed that nonlinear dynamic dampers are more effective to reduce the maximum amplitude of vibrations; while linear DVAs are more effective in eliminating vibration sooner for the cases of transient excitation. A new type of passive DVAs is the inerter-based vibration absorber (IBVA), which introduced first by Smith [10] in 2002. The inerter in IBVA has the property that the force
generated by IBVA is proportional to the relative acceleration between two joints. The proportionality of inerter constant is called inertance which measures in kilograms. In 2005 the inerter was profitably used as a part of suspension in Formula One racing cars [11]. Chen et al. [12] investigated the effect of using an inerter as a part of vibration absorber on the natural frequencies of one, two and more degree of freedom systems. They showed that the natural frequencies of system can be decreased by increasing the inertance of inerter. The advantages of using an inerter to reduce vibration of multi-storey buildings under earthquake vibrations excitation in comparison to TMD vibration absorbers have been studied by Lazar et al. [13]. In their subsequent study [14] they compared the application of inerter-based vibration absorbers with viscose vibration absorber to reduce vibrations of cables and they showed that the
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