Question

How do you determine whether or not to consider transient solutions in the investigation of a vibration problem?

Answer 1

A system subjected to periodic excitation has two components of motion :-

a) Transient state

b) Steady state

In most of the cases the transient part is not important as it dies out soon, and the steady part is the one that persists.

The response of a system is purely transient where the excitation is of aperiodic nature like a shock pulse or a transient excitation. After the duration of the excitation, the system undergoes vibrations with its natural frequency with an amplitude depending upon the type and duration of the excitation. It is in such cases transient vibration are importance. Laplace transform is used for the analysis of transient solutions.

Some practical examples of shock excited transient vibrations are rock explosions, gunfires, punching operations etc.

In these cases as response are purely transient so there will be need to determine the transient solutions.