### ASA 128th Meeting - Austin, Texas - 1994 Nov 28 .. Dec 02

## 5aSA11. Apparent anomalies in the forced vibration of a damped beam.

**Mauro Pierucci
**

**
Wensen Liu
**

**
**
*Group in Appl. Mech., College of Eng., San Diego State Univ., San Diego,
CA 92182-1311
*

*
*
An infinitely long Bernoulli beam with linear damping is acted upon by a
localized force given by (delta)(x)u(t)e[sup i(omega)t]. The results are then
obtained in wave-number space and the inversion is carried out by using an FFT
algorithm. Several interesting and not previously reported results will be
presented. The solution in the transform domain is composed of four terms: two
transient terms with wave numbers equal to k[radical (eta)[radical and k and
two steady-state terms; one propagates energy into the far field while the
other is a decaying localized disturbance. The disturbance created by this near
field sloshes energy back and forth near the location of the forcing function.
The apparent backward traveling wave which is present in the steady-state
condition is not due to the localized continuous reflection of energy from the
distributed damping but is due to the requirement that the beam vibration has
to have continuity of displacement and slope. The force responsible for the
continuity of the slope is the culprit for this apparent phenomena. If the
forcing function is cos (omega)t, the steady-state solution can be obtained
within 20 periods, while if the function sin (omega)t is used, then the
steady-state solution cannot be obtained until more than 10[sup 6] periods.