Theoretical Investigation on the Dynamic Characteristics of One Degree of Freedom Vibration System Equipped with Inerter of Variable Inertance
In this paper, a theoretical investigation on the dynamic characteristics of one degree of freedom vibration system equipped with inerter of variable inertance, is presented. Differential equation of movement was solved under proper initial conditions in the case of free undamped/damped vibration, considered in the absence/presence of the inerter in the mechanical system. Influence of inertance on the amplitude of vibration, phase angle, natural frequency, damping ratio, and logarithmic decrement was clarified. It was mainly found that the inerter decreases the natural frequency of the undamped system and also of the damped system if the damping ratio is below 0.707. On the other hand, the inerter increases the natural frequency of the damped system if the damping ratio exceeds 0.707. Results obtained in this work are useful for the adequate design of inerters.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1128919Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 632
 M.C. Smith, “Synthesis of Mechanical Networks: The Inerter”, IEEE Transactions on Automatic Control, 47(10), pp. 1648–1662, 2002.
 I.F. Lazar, S.A. Neild, and D.J. Wagg, “Design and Performance Analysis of Inerter-Based Vibration Control Systems”, Proc. of IMAC XXXII Conference and Exposition on Structural Dynamics, pp. 1–7, 2014.
 M.C. Smith, and F.C. Wang, “Performance Benefits in Passive Vehicle Suspensions Employing Inerters”, Vehicle System Dynamics, 42(4), pp. 235–257, 2004.
 Y. Shen, L. Chen, X. Yang, D. Shi, and J. Yang, “Improved Design of Dynamic Vibration Absorber by Using the Inerter and its Application in Vehicle Suspension”, Journal of Sound and Vibration, 369(1), pp. 148–158, 2016.
 J. Yang, “Force Transmissibility and Vibration Power Flow Behaviour of Inerter-Based Vibration Isolators”, Journal of Physics: Conference Series 744(012234), pp. 1–8, 2016.
 M.Z.Q. Chen, Y. Hu, L. Huang, and G. Chen, “Influence of Inerter on Natural Frequencies of Vibration Systems”, Journal of Sound and Vibration, 333(7), pp. 1874–1887, 2014.
 J. Yang, Y.P. Xiong, and J.T. Xing, “Dynamics and Power Flow Behaviour of a Nonlinear Vibration Isolation System with a Negative Stiffness Mechanism”, Journal of Sound and Vibration, 332(1), pp. 167–183, 2013.
 M. Zilletti, “Feedback Control Unit with an Inerter Proof-Mass Electrodynamic Actuator”, Journal of Sound and Vibration, 369(1), pp. 16–28, 2016.
 Y. Hu, M.Z.Q. Chen, and Z. Shu, “Passive Vehicle Suspensions Employing Inerters with Multiple Performance Requirements”, Journal of Sound and Vibration, 333(8), pp. 2212–2225, 2014.
 J.Z. Jiang, A.Z. Matamoros-Sanchez, R.M. Goodall, and M.C. Smith, “Passive Suspensions Incorporating Inerters for Railway Vehicles”, Vehicle System Dynamics, 50 Supplement, pp. 263–276, 2012.
 F.C. Wang, M.K. Liao, B.H. Liao, H.J. Sue, and H.A. Chan, “The Performance Improvements of Train Suspension Systems with Mechanical Networks Employing Inerters”, Vehicle System Dynamics, 47(7), pp. 805–830, 2009.
 F.C. Wang, M.F. Hong, and C.W. Chen, “Building Suspensions with Inerters”, PI Mechanical Engineering C, 224 (8), pp. 1605–1616, 2010.
 F.C. Wang, C.W. Chen, M.K. Liao, and M.F. Hong, “Performance Analyses of Building Suspension Control with Inerters”, Proc. of 46th IEEE Conference on Decision and Control, 4434186, pp. 3786–3791, 2007.
 K. Ikago, K. Saito, and N. Inoue, “Seismic Control of Single-Degree-of- Freedom Structure using Tuned Viscous Mass Damper”, Earthquake Engineering and Structural Dynamics, 41(3), pp. 453–474, 2012.
 I.F. Lazar, S.A. Neild, and D.J. Wagg, “Using an Inerter-Based Device for Structural Vibration Suppression”, Earthquake Engineering and Structural Dynamics, 43(8), pp. 1129–1147, 2014.
 I.F. Lazar, S.A. Neild, and D.J. Wagg, “Performance Analysis of Cables with Attached Tuned-Inerter- Dampers”, Proc. of 33rd IMAC Dynamics of Civil Structures, 2, pp. 433–441, 2015.
 J.P. Den Hartog, Mechanical Vibrations. London: McGraw-Hill, 1940.
 D.J. Inman, and R.J. Singh, Engineering Vibration. New York: Prentice Hall, 2001.
 H. Benaroya, and M.L. Nagurka, Mechanical Vibration: Analysis, Uncertainties, and Control. London: CRC Press, 3rd ed., 2010.