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.<\/p>\r\n","references":"[1]\tM.C. Smith, \u201cSynthesis of Mechanical Networks: The Inerter\u201d, IEEE Transactions on Automatic Control, 47(10), pp. 1648\u20131662, 2002.\r\n[2]\tJ. Yang, \u201cForce Transmissibility and Vibration Power Flow Behaviour of Inerter-Based Vibration Isolators\u201d, Journal of Physics: Conference Series 744(012234), pp. 1\u20138, 2016.\r\n[3]\tM.Z.Q. Chen, Y. Hu, L. Huang, and G. Chen, \u201cInfluence of Inerter on Natural Frequencies of Vibration Systems\u201d, Journal of Sound and Vibration, 333(7), pp. 1874\u20131887, 2014.\r\n[4]\tJ. Yang, Y.P. Xiong, and J.T. Xing, \u201cDynamics and Power Flow Behaviour of a Nonlinear Vibration Isolation System with a Negative Stiffness Mechanism\u201d, Journal of Sound and Vibration, 332(1), pp. 167\u2013183, 2013.\r\n[5]\tB. Suciu, and Y. Tsuji, \u201cTheoretical Investigation on the Dynamic Characteristics of One Degree of Freedom Vibration System Equipped with Inerter of Variable Inertance\u201d, International Journal of Mechanical, Aerospace, Industrial, Mechatronic and Manufacturing Engineering, 11(3), pp. 414\u2013422, 2017.\r\n[6]\tF. A. Firestone, \u201cA New Analogy between Mechanical and Electrical System Elements\u201d, The Journal of the Acoustical Society of America, 3, pp. 249\u2013267, 1933.\r\n[7]\tS. Darlington, \u201cA History of Network Synthesis and Filter Theory for Circuits Composed of Resistors, Inductors, and Capacitors\u201d, IEEE Transactions on Circuits and Systems, 31, pp. 3\u201313, 1984.\r\n[8]\tI. J. Busch-Vishniac, Electromechanical Sensors and Actuators. Berlin: Springer Science & Business Media, 1999.\r\n[9]\tC.W. de Silva, Vibration: Fundamentals and Practice, London: CRC Press, 2nd ed., 2006.\r\n[10]\tJ.P. Den Hartog, Mechanical Vibrations. London: McGraw-Hill, 1940.\r\n[11]\tD.J. Inman, and R.J. Singh, Engineering Vibration. New York: Prentice Hall, 2001.\r\n[12]\tH. Benaroya, and M.L. Nagurka, Mechanical Vibration: Analysis, Uncertainties, and Control. London: CRC Press, 3rd ed., 2010.","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 135, 2018"}