Abstract Summary
Vibration absorption has been studied for over a century by systems and dynamics specialists from variety of different perspectives. Actively tuned class occupies a large place in the literature. The tuning operation imparts increased efficacy of the absorber when removing the undesired oscillations by “sensitizing” the absorber substructure to attract vibratory energy upon itself while leaving the main body of the structure relatively quiet. The concept of “actively tuned absorber” has been implemented to date with considerable success. It has been shown and is broadly accepted that an ideal absorber for tonal excitation needs to be “resonant” at the frequency of the excitation. With that point in mind, one can build a tuned resonant absorber which could remove the oscillations at its point of attachment to the main structure. That is, a “collocated” vibration absorber at the point of suppression. The main theme of the present study arises when the absorber to main structure attachment point and the point of desired suppression happen to be separated from one another, i.e., “non collocated” vibration suppression operation. Similar absorber tuning philosophy as described above would lead to an undesired consequence, namely the inclusion of a part of the main structure (together with the attached absorber) to be jointly “resonant” to execute complete removal of the oscillations. In recent literature this partition is named “resonant substructure”. This philosophy brings about two critical challenges: (a) How to identify this “resonant substructure” (b) How to actively and properly sensitize it for the incoming excitation frequencies? Both of these topics have attracted attention in recent years from various angles especially on the lumped mass constructs. However, the scientific findings are very weak, to say the least, when it comes to implementing the same concepts to continua (such as beams, plates etc.). This conceptual dichotomy between the lumped mass structures and the continua is the main topic of this paper. So, we wish to extend the well understood “non collocated vibration absorption (NCVA)” operation to be deployed on a simple continuum (say an oscillating beam). This seemingly straightforward task being harnessed with the lumped mass experience of the NCVA’s suddenly presents a dichotomy in the form of uncertainty for both problems (a) and (b). The authors wish to lay out the complexities of the problem and establish the non triviality of the lumped mass to continua transition of the NCVA procedure. On this occasion, we also wish to formulate a generalized benchmark problem to be solved. In brief, main difficulty arises from the fact that when a point is designated for suppression on a lumped mass construct, the main objective is to create a negating force via a sensitized “resonant absorber subsection”. Once this mission is accomplished the point of suppression acts like a fictitious ground, and the entire system becomes decoupled with that ground being in the middle. In a continuum, however, such a decoupling effect disappears as the “fictitious ground” (with zero transverse oscillations) still transmits some influence from one side to the
