Optimum Design of Vibration Absorbers for Structurally Damped Timoshenko Beams

A procedure in designing optimal Dynamic Vibration Absorbers (DVA) for a structurally damped beam system subjected to an arbitrary distributed harmonic force excitation, is presented. The Timoshenko beam theory is used to assess the effects of rotatory inertia and shear deformation. The method provides flexibility of choosing the number of absorbers depending upon the number of significant modes which are to be suppressed. Uniform cross-sectional area is considered for the beam and each absorber is modeled as a spring-mass-damper system. For each absorber with a selected mass, the optimum stiffness and damping coefficients are determined in order to minimize the beam dynamic response at the resonant frequencies for which they are operated. For this purpose, absorbers each tuned to a different resonance, are used to suppress any arbitrarily number of resonances of the beam. The interaction between absorbers is also accounted for in the analysis. The optimum tuning and damping ratios of the absorbers, each tuned to the mode of concern, are determined numerically by sloving a min-max problem. The Direct Updated Method is used in optimization procedure and the results show that the optimum values of the absorber parameters depend upon various factors, namely: the position of the applied force, the location where the absorbers are attached, the position at which the beam response should be minimized, and also the beam characteristics such as boundary conditions, rotatory inertia, shear deformation, structural damping, and cross sectional geometry. Through the given examples, the feasibility of using proposed study is demonstrated to minimize the beam dynamic response over a broad frequency range. The resulting curves giving the non-dimensional absorber parameters can he used for practical applications, and some interesting conclusions can be drown from the study of them.