Vibration Absorbers for Hysterically Damped Mass-Loaded Beams

A procedure for designing dynamic vibration absorbers for a general mass-loaded beam system of variable cross-sectional area, when it is subjected to an arbitrarily distributed simple harmonic force excitation, is presented. The procedure gives flexibility for choosing the number of absorbers depending upon the number of significant modes to be suppressed. The beam is assumed to be hysteretically damped and each absorber is a spring-mass-damper system. For each absorber, for a selected mass, the stiffness and damping coefficients are optimized so as to minimize the dynamic response corresponding to the resonance frequency at which they are tuned to operate. The interaction between the absorbers is also accounted for in the analysis. This general procedure for designing vibration absorbers is then applied to a space structure modeled as a mass-loaded free-free beam, to suppress the first two resonances when it is subjected to a concentrated simple harmonic force excitation. The frequency response is presented in a graphical form. Furthermore, it is also shown that optimizing the beam system first and then designing vibration absorbers for this beam system will result in a small dynamic response. Although the analysis is general enough to cover beams of nonuniform cross-section, the examples presented in this paper of the above simplified model of the space structure have been restricted to beams of uniform cross-section.