Generalized Den Hartog tuned mass damper system for control of vibrations in structures

Abstract

The Den Hartog method is one of old, but efficient methods for the design of tuned mass damper (TMD) systems for passive control vibrations in buildings subjected to earthquake excitations.However, Den Hartog, in his model, did not include the main mass (structure) damping in deriving the equations for computing the optimum design parameters for the TMD system (damping and frequency ratios).In this work an attempt is made to generalize the Den Hartog method to include the effect of the structure damping in the derived equations.The dynamic equations for a TMD system attached to SDOF structure with damping are derived.Then, using the complex numbers technique, the equation for maximum displacement of the structure when subjected to harmonic excitation is derived.The numerical optimization technique is used to compute the optimum values of TMD parameters that will minimize the maximum displacement of the structure.Finally, the curve fitting procedure with trial functions is used to obtain equations for computing the optimum frequency ratio and optimum damping ratio for a TMD system.