Theoretical Study on the Forced Vibration of One Degree of Freedom System, Equipped with Inerter, under Load-Type or Displacement-Type Excitation
Authors: Barenten Suciu
In this paper, a theoretical study on the forced vibration of one degree of freedom system equipped with inerter, working under load-type or displacement-type excitation, is presented. Differential equations of movement are solved under cosinusoidal excitation, and explicit relations for the magnitude, resonant magnitude, phase angle, resonant frequency, and critical frequency are obtained. Influence of the inertance and damping on these dynamic characteristics is clarified. From the obtained results, one concludes that the inerter increases the magnitude of vibration and the phase angle of the damped mechanical system. Moreover, the magnitude ratio and difference of phase angles are not depending on the actual type of excitation. Consequently, such kind of similitude allows for the comparison of various theoretical and experimental results, which can be broadly found in the literature.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1315959Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 380
 M.C. Smith, “Synthesis of Mechanical Networks: The Inerter”, IEEE Transactions on Automatic Control, 47(10), pp. 1648–1662, 2002.
 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.
 B. Suciu, and Y. Tsuji, “Theoretical Investigation on the Dynamic Characteristics of One Degree of Freedom Vibration System Equipped with Inerter of Variable Inertance”, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 11(3), pp. 414–422, 2017.
 F. A. Firestone, “A New Analogy between Mechanical and Electrical System Elements”, The Journal of the Acoustical Society of America, 3, pp. 249–267, 1933.
 S. Darlington, “A History of Network Synthesis and Filter Theory for Circuits Composed of Resistors, Inductors, and Capacitors”, IEEE Transactions on Circuits and Systems, 31, pp. 3–13, 1984.
 I. J. Busch-Vishniac, Electromechanical Sensors and Actuators. Berlin: Springer Science & Business Media, 1999.
 C.W. de Silva, Vibration: Fundamentals and Practice, London: CRC Press, 2nd ed., 2006.
 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.