TABLE OF CONTENTS In Section 4.4 we determined what frequencies of excitation will cause the response at the driven mass to equal zero for a 2 DOF system. The problem was stated differently, of course. We said that our original SDOF system had severe vibrations, and we determined how to reduce the vibrations to zero by the addition of a second mass-spring assembly. The end result, however, is the same as if we'd started with a 2 DOF system and asked what frequency of forcing, applied to the first mass, would result in that mass being stationary. You'll recall that in the process of solving the problem we noticed that, as far as the system response was concerned, a stationary mass was the same as a rigidly fixed mass. Thus the correct frequency of excitation turned out to be the natural frequency of the remaining mass and springs.
The same thing can be seen in MDOF systems. In an MDOF system, we have n masses. Our question will become, What frequency of force excitation, applied to a particular mass, will cause a particular mass in the system to have no motion? Consider the serial chain of mass and springs shown in Figure 4.21a. A sinusoidal force is applied to m 1, and we want to determine the frequencies of excitation at which m 1 will be stationary. Then we'll ask whether m 2 can also be stationary. After we've examined the different masses,...
