TABLE OF CONTENTS So far, the way we've viewed 2 DOF systems has been reasonably similar to the way we've dealt with SDOFs. We've seen that 2 DOF systems support eigenvector responses, but we haven't particularly exploited this fact. Now we'll do so.
One obvious characteristic of the general 2 DOF systems we've seen so far is that the system equations are coupled. It's impossible to solve for the response of x 1 without at the same time solving for x 2 (where x 1 and x 2 are the two coordinates of our system). We even have names for the particular types of coupling we might run into. For instance, the following equation is said to be mass coupled, or inertially coupled:
because the two equations are coupled through the [ M] matrix. In a like manner, (4.7.2) is stiffness coupled or spring coupled because the coupling comes through the [ K] matrix.
A fully uncoupled set of equations would look like
For this case, we see that the equation governing the response of x 1 has nothing to do with x 2's behavior. Thus we can solve either equation independently of the other; they're uncoupled.
It's clear that uncoupled equations are nice to have, since it's always easier to solve two independent equations than it is to solve a simultaneous set of equations. The question is, Can we somehow transform our particular equations...
