TABLE OF CONTENTS This chapter addresses the problem of how to find a system's response when the input excitation is not a simple sinusoid. If you think about it, it seems pretty obvious that almost no real system will have a purely sinusoidal input. Many, many of the inputs will be periodic; i.e., the input will be made up of an endlessly repeating waveform. But the chances that the waveform is a pure sine wave are pretty low. For instance, the repeated firings inside the cylinder of an internal combustion engine will produce a periodic, but not sinusoidal, loading on the piston. Thus we're motivated to figure out how we can determine a system's steady state response for these cases.
Furthermore, the input to our system might not even be periodic. Oftentimes the loading will be very transient in nature. An earthquake is a good example of a transient loading. The ground will shake for a few seconds and then stop. Our problem then consists of determining a structure's response to a loading that exists only for a finite amount of time. If the earthquake lasts for a long time, then we might actually view the problem in a steady state way. But if the earthquake is of short duration, then a transient viewpoint is more appropriate. A similar problem will occur when an airplane encounters a momentary updraft. The updraft will load the wings for only a short time, and the wings will then bend (and the airplane will displace),...
