Using Component Mode Synthesis and Static Shapes for Tuning TMDs

The application of the component mode synthesis (CMS) method to calculate the optimum tuned mass‐damper parameters is extended by adding a number of static mode shapes to the formulation. It is shown that the addition of these modes can result in a better accuracy of the responses. A three‐dimensional floor model is used to illustrate this technique. In addition, the tuning parameters are compared to values found using the customary equivalent single degree of freedom (SDOF) model for optimization. It is shown that when several mass dampers are tuned to a single mode, the equivalent SDOF model for optimization cannot generate the optimum parameters for these tuned mass dampers. It is also found that using the CMS method with the addition of the static mode shape can result in significant reduction in the computational effort for the system response. It is also concluded that when n number of tuned mass dampers are used to reduce the level of vibration of a single mode, the optimality criterion is expected to produce $n+1$ number of equal peaks in the response curve near that natural frequency.