Dynamic analysis of a uniform cantilever beam carrying a number of elastically mounted point masses with dampers

The free and forced vibration analyses of a uniform cantilever beam carryin g a number of spring-damper-mass systems with arbitrary magnitudes and loca tions were made by means of the analytical-and-numerical-combined method (A NCM). First of all, a method was presented to replace each "spring-damper-m ass" system by a massless equivalent "spring-damper" system with effective spring constant k(eff) and effective damping coefficient C-eff so that the ANCM is available for the title problem. Next, the equation of motion for t he "constrained" beam (with spring-damper-mass systems attached) was derive d by using the natural frequencies and normal mode shapes of the "unconstra ined" beam (without carrying any attachments) incorporating the expansion t heorem. Finally, the eigenvalues and the forced vibration responses of the "constrained" beam were determined by conventional numerical methods. To co nfirm the reliability of the presented theory, all the numerical results ob tained from the ANCM were compared with the corresponding ones obtained fro m the conventional finite element method (FEM) and good agreement was achie ved. The influence of the damping magnitude of each spring-damper-mass syst em on the eigenvalues and the forced vibration responses of the constrained beam was studied. Because the order of the overall property matrices for t he equation of motion of the constrained beam derived from the ANCM is much lower than that from the conventional FEM, the storing memory and the CPU time required by the ANCM are much less than those required by the FEM. (C) 2000 Academic Press.