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.