Analysis and optimization of multiple tuned mass dampers with coulomb dry friction

The optimum design and analysis of frictional multiple tuned mass dampers (FMTMDs) are presented in this study, where Coulomb dry friction is incorporated as an energy dissipation mechanism. To deal with the nonlinearity of the Coulomb dry friction force, which is a source of difficulty in the optimization process, this study adopted a statistical linearization that replaces the original nonlinear system with an equivalent linear system, and found an optimum design that minimized the root mean square (RMS) displacement of the primary structure. The equivalent damping ratio of a tuned mass damper (TMD) unit significantly decreased with the increase in number of TMDs. Four practical configurations were formulated and comparatively analyzed, by constraining the frequency ratios and the coefficient of friction (COF). Among the four investigated cases, a particular solution described using only three parameters is recommended for use in design, because it is simple and sufficiently accurate. We also analyzed the input sensitivity of nonlinear frequency responses of FMTMDs in order to provide general design guidance.