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Controllable dampers based on smart fluids contain internal passages through which the working fluid flows and wherein the controlled pressure drop occurs under the influence of magnetic or electric fields. In this paper, the dynamics of such dampers are analysed through a series of theoretical dynamic models of increasing detail and complexity. The models capture the medium- and high-frequency dynamics of the damping force output of the damper and include the lumped mass of the fluid contained in the internal flow passages, the piston and rod assembly mass, and the compressibility of the fluid and pressurized gas contained within the chambers of the damper. The models are derived in state-space form from which transfer functions and natural frequencies are obtained analytically and then calculated for each of the systems. The results are presented in the form of frequency responses (Bode plots). Finally, the effects of the key geometric parameters of the damper and of the relevant fluid properties on the damper force output dynamics are presented and discussed.

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The dynamic interaction between a Linear Induction Motor primary, modeled as a spring-mass-damper element, and its secondary-rail, modeled as a prestressed, continuously supported, infinitely long beam, is studied theoretically. The existence of two transition speeds is established. At the lower transition speed, the frequency and damping ratio of the coupled system response attain their minimum and maximum values, respectively. The system is unstable at speeds higher than the second transition speed. Using a rotating annular disk to simulate the secondary rail, measured values of the frequency and damping ratio confirm the validity of the mathematical model for speeds up to nearly the lower transition speed.