On the electrical equivalent circuits of gravitational-wave antennas

The electrical equivalent circuit of a Weber gravitational-wave antenna with piezoelectric transducers is derived for the various longitudinal normal modes by using the Lagrangian formalism. The analysis is applied to the antenna without piezoelectric ceramics, as well as with one or more ceramics operated in both passive and active mode. Particular attention is given to the dissipation problem in order to obtain an expression of the overall merit factor directly related to the physics of the actual dissipation processes. As an example the results are applied to a cylindrical bar with two ceramics: one for calibrating the antenna, the other as sensor of the motion. The values of the physical parameters and of the pertinent parameters of the equivalent circuit for the small antenna (20 kg) and those (predicted) for the intermediate antenna (390 kg) of the Rome group are given in the appendix. (author)