Optimum design of linear multiple tuned mass dampers subjected to white-noise base acceleration considering practical configurations

This study investigates the application of multiple tuned mass dampers (MTMDs) for situations wherein multiple small-sized tuned mass dampers (TMDs) are required to be installed owing to practical reasons such as a space limitation, for transportation, and for ease of handling. This paper presents an optimum design and analysis of linear MTMDs with various practical configurations on a single-degree-of-freedom (SDOF) primary structure subjected to a zero-mean white-noise base-acceleration excitation. Six practical configurations are developed and comparatively analyzed, each of which is constrained with linearly distributed frequency ratios, uniformly distributed damping coefficients, linearly distributed mass ratios, and combinations thereof. Two different optimization techniques were adopted in this study. The first minimizes the nominal performance objective function while the second minimizes the mean value of the objective function while assuming that the associated structural parameters are perturbative. All the optimized parameters and plots are presented in a non-dimensional form in order to provide results that are useful for practical design. Among the six cases investigated, a three-parameter optimum solution based on frequency and damping ratios showed sufficiently satisfactory control performance and is recommended for practical design. Furthermore, this study provides the contour maps that enable designers to accommodate the moving TMD units within a permissible stroke limit.