Realization of a special class of admittances with one damper and one inerter

In this paper, we investigate the realization problem of a special class of positive-real admittances in a form similar to biquadratic functions but with an extra pole at s = 0, which is common in vehicle suspension designs. The number of inerters and dampers is restricted to one in each case and number of the springs is arbitrary. To solve the problem, we first convert a previous result by Chen & Smith, 2009 to a more direct form. A necessary and sufficient condition for realizability is then derived and explicit circuit arrangements are provided to cover the realizability conditions.