Substructure coupling approach to parameterization of passive dynamic auxiliary systems

A physical structure might show undesired forced vibrations when excited by a specific force signal. Moreover, if the resulting deflections influence the acting force, undesired self-excited vibrations can result. In such cases a usual approach is to modify the structure by mounting passive tuned mass dampers (TMD). Different strategies are available to design such TMD. The different approaches have in common, that the original structure is approximated as a single degree of freedom (SDOF) system. This approximation limits the applicability of the design strategies. This paper attempts to solve the abovementioned drawback. Based on a frequency domain substructure coupling approach, it is proposed to apply a sequential quadratic programming algorithm to determine effective parameters of TMD. The approach considers the multiple degrees of freedom (MDOF) character of the original structure. The new method is evaluated by means of a simple finite element model of a simplified milling machine assembly. By means of this analytical example, it is shown that both SDOF TMD and MDOF TMD can be parameterized by the new method. The practical applicability is proven by designing a STMD for a linear axis test bench. Finally, limitations of the method and reasonable subsequent research tasks are discussed.