The response of internally damped cantilever beams to sinusoidal vibration is described theoretically. An expression for the magnitude of the force transmitted to the terminations of the beams is derived when both a primary and a secondary force are employed to excite the beams at arbitrary positions along their length. It is demonstrated that the transmitted force can be attenuated significantly through broad ranges of frequency when the primary and secondary forces are of equal magnitude and their location is chosen suitably. The effect of varying the relatively‐phase angle between the driving forces is considered. The influence of the secondary force upon the driving‐point impedance that is presented to the primary force at a separate location is also discussed. Consideration is given to the magnitude of the force transmitted across a beam when a single driving force excites the beam at its free end and the beam is mass‐loaded, in turn, at its free end, at its midpoint, and simultaneously at its free end and at its midpoint.

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