Analysis for Inerter-Based Vibration System

  • Michael Z. Q. ChenEmail author
  • Yinlong Hu


This chapter investigates the influence of inerter on the natural frequencies of vibration systems. First of all, the natural frequencies of a single-degree-of-freedom (SDOF) system and a two-degree-of-freedom (TDOF) system are derived algebraically and the fact that inerter can reduce the natural frequencies of these systems is demonstrated. Then, to further investigate the influence of inerter in a general vibration system, a multi-degree-of-freedom system (MDOF) is considered. Sensitivity analysis is performed on the natural frequencies and mode shapes to demonstrate that the natural frequencies of the MDOF system can always be reduced by increasing the inertance of any inerter. The condition for a general MDOF system of which the natural frequencies can be reduced by an inerter is also derived. Finally, the influence of inerter position on the natural frequencies is investigated and the efficiency of inerter in reducing the largest natural frequencies is verified by simulating a six-degree-of-freedom system, where a reduction of more than \(47\%\) is obtained by employing only five inerters.


Natural frequency Single-degree-of-freedom system Two-degree-of-freedom system Multi-degree-of-freedom system Sensitivity analysis 


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© Springer Nature Singapore Pte Ltd. and Science Press, Beijing 2019

Authors and Affiliations

  1. 1.School of AutomationNanjing University of Science and TechnologyNanjingChina
  2. 2.College of Energy and Electrical EngineeringHohai UniversityNanjingChina

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