Wave-number frequency response of beams to an array of point drives

An analytical model using Timoshenko beam theory is formulated for the free response of a thick free–free beam and the forced response of the same beam to an array of point drives. To validate this model, comparisons are made between predictions and measurements of the free response of the beam and of the forced response of the beam using one, two, and three point drives. Measured and predicted results of the magnitude and phase of the beam admittance and the wave-number-frequency response of the beam are compared. Excellent agreement between theory and experiment is noted, especially when the measured forcing functions were input to the model. The analytical model is then used to investigate the wave-number response of the beam to an array of point drives. The forced wave-number response is achieved by an array of point drives that are amplitude weighted to form a standing wave pattern. Analytical model calculations of the wave-number-frequency response of the beam show that the unwanted free wave-number response of the beam at resonance frequencies can be reduced by: (1) applying Hanning shading to the point drives, and (2) increasing the damping in the beam so that admittance measurements of the beam can be made at nonresonance frequencies and forced wave numbers.