Oscillations in Systems with Non-Linear Reactance

Abstract

A theoretical study is presented of the properties of a condenser, one plate of which is free to vibrate, when it is included in a circuit containing a generator, the frequency of which is higher than the resonant frequency of the plate and unrelated thereto. It is shown that the plate may be maintained in oscillation at a frequency at or near its mechanical resonance, at the expense of the energy supplied by the generator, provided certain conditions are satisfied. The most favorable condition is one in which the plate is resonant at the frequency of its vibration and the electric circuit is resonant at that of the generator, and at the difference between the generator and plate frequencies, and is anti-resonant at their sum. Under these conditions the generator voltage must exceed a threshold value determined by the impedances and frequencies. This threshold voltage increases as the conditions become less favorable. Expressions are given for the values of the oscillations as functions of the voltage when the threshold is exceeded. When the sum frequency is absent, the energies dissipated at the plate and difference frequencies are in the ratio of the two frequencies. The oscillations described represent a special case of a class of similar oscillations, all of which depend on the presence of a non-linear reactance. Another special case is a molecular model capable of reproducing the main features of the Raman effect.