Spatial Decay in the Response of Damped Periodic Structures. Part II.
Final rept. 1 Sep 69-31 Mar 70,
ILLINOIS UNIV AT URBANA DEPT OF AERONAUTICAL AND ASTRONAUTICAL ENGINEERING
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The spatial variation in the steady state response of an infinitely long beam resting on uniformly spaced elastic supports is investigated analytically. The supports are assumed to provide elastic rotational and translational constraints for the beam. Three sources of damping are considered the structural damping of the beam material, the structural damping of the elastic supports, and the damping from the tuned dampers attached to individual spans. By use of the Floquet theory it is shown that the response may be characterized by two complex propagation constants which are simply related to the eigenvalues of the transfer matrix for a basic periodic unit between two consecutive supports. Each propagation constant corresponds to one type of flexure wave which decays exponentially from one support to the next farther away from the excitation, and the total response is the superposition of two such waves. The spatial decay is low when the structure is excited at a frequency within or near one of the distinct bands of natural frequencies. For the numerical examples reported herein where computation covers the first six natural frequency bands, one type of flexure wave is predominant in the first, second and the third frequency bands, and the other type of flexure wave is predominant in the fourth, fifth, and sixth frequency bands. Author