LOCALIZATION OF VIBRATION IN DISORDERED MULTISPAN BEAMS WITH DAMPING

The combined effects of disorder and structural damping on the dynamic s of a multi-span beam with slight randomness in the spacing between s upports are investigated. A wave transfer matrix approach is chosen to calculate the free and forced harmonic responses of this nearly perio dic structure. It is shown that both harmonic waves and normal modes o f vibration that extend throughout the ordered, undamped beam become s patially attenuated if either small damping or small disorder is prese nt in the system. The physical mechanism which causes the attenuation, however, is one of energy dissipation in the case of damping but one of energy confinement in the case of disorder. The corresponding rates of spatial exponential decay are approximated by applying statistical perturbation methods. It is found that the effects of damping and dis order simply superpose for a multi-span beam with strong inter-span co upling, but interact less trivially in the weak coupling case. Further more, the effect of disorder is found to be small relative to that of damping in the case of strong inter-span coupling, but of comparable m agnitude for weak coupling between spans. The adequacy of the statisti cal analysis to predict accurately localization in finite disordered b eams with boundary conditions is also examined. (C) 1995 Academic Pres s Limited.