Steady Periodic Vibrations

1.

In a Nut Shell: Displacement, x(t), of an undamped mechanical system (figure below) subjected to a forcing function, f(t), undergoes steady periodic vibrations. The steady state response, (also called the steady periodic solution and is also the particular solution),xp(t), is governed by the forcing function since there is no damping to diminish the response. The differential equation of motion is: m x’’ + k x = f(t) ----------------------------------- (1) where m = mass of the system x’’ = d^2x/dt^2 k = spring constant x(t) = displacement of the mass f(t) = forcing function

2.

Representation of Forcing Function, f(t) Fourier Series provide a way to represent more complicated (more realistic) forcing functions, f(t), with direct applications to vibration problems. Suppose f(t) is represented as follows: ∞ f(t) = ∑ bn sin (nπt/L) ----------------------------------- (2) n = 1 where bn are the Fourier coefficients (to be determined) Click here to continue with discussion of steady periodic vibrations.

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