ON SOME GENERAL PROPERTIES OF COMBINED DYNAMICAL SYSTEMS.
There are several well-known results due to Rayleigh left bracket 1 right bracket on the effects of mass and stiffness addition to a dynamical system. In this paper these results are reconsidered and generalized using the methods previously employed by the author dynamics of combined systems composed of several component systems left bracket 3 right bracket . Specifically it is shown that, if two component systems are connected at a point, each combined system frequency is increased from its component value or, in the exceptional case, is unchanged. This may appear, at first, to contradict Rayleigh's results on mass addition. However, it does not since the mass added may be viewed as a rigid body with one or more zero natural frequencies.