The quenching of nonlinear oscillations by dither

The suppression of unwanted vibrations in a system by the injection of a high- frequency dither is a well-known engineering technique. Very little has been published about the theory of this method and what has been published has often been lacking in mathematical rigour. This work is an attempt to correct this situation. Chapter I discusses the background of the problem. Chapter II uses small parameter theory to examine the mechanism of quenching in certain special cases. In Chapter III an interesting aspect of quenching is discussed in some depth for a special 2-dimensional problem. Chapter IV discusses sufficient conditions for quenching to occur in general systems.