Lumped element vibrators

Abstract

The mechanical elements of lumped element vibrators are all independent of one another and their theory is more involved than that of vibrators with continuously distributed parameters. One very informative parameter is the locus of the admittance in the complex plane. Unless the vibrator is heavily damped, the driving point admittance is a spiral whose turns are transcribed in a clockwise sense as the frequency is increased. In contrast, some of the turns of the transfer admittance may be transcribed in an anticlockwise sense. Lumped element vibrators may also have “active modes,” although the whole vibrator is passive. This means that exciting the vibrator in a certain frequency range reduces its input resistance. An example of a vibrator with an active mode is a magnetic transducer. Circuit theory makes it possible to deal efficiently with lumped element vibrators. A few very simple rules help to greatly simplify the computations and to predict the dynamical behavior of such vibrators. The most important of these rules will be derived and the theory will be illustrated with the detailed analysis of two coupled dumbbell vibrators, which represent the simplest possible mechanical bandpass filter. Such a filter has a considerably more complex behavior than an electrical bandpass. Unless the receiver is located at the proper point, the coupled dumbbell vibrators may act like an all pass, or exhibit no or very deformed pass ranges. [This work was sponsored by the Office of Naval Research, Code 474.].