Abstract
The resonant frequency of a reciprocating point load on an elastic beam is considered. Employing the elementary beam theory and applying the Fourier expansion technique, the exact solution is obtained in the form of double series. We have found that the resonant frequency of the reciprocating load is given by ωn,m* = ωn*/m, where ωn* is the natural frequency of thenth mode of the beam vibration andmis an integer ranging from 1 to infinity. Checking the vibration mode, we have concluded that there is an infinite number of resonant frequencies for a single mode of vibration. This multi-resonance for a single mode may prove to be quite interesting to engineers.
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