Influence of inerters on the vibration control effect of series double tuned mass dampers: Two layouts and analytical study

Abstract

Summary In this paper, two configurations of series double tuned mass damper with inerters (SDTMDI) are investigated: grounded type (G‐SDTMDI) and inserted type (I‐SDTMDI). For the former layout, two inerters relate each tuned mass to the ground, while they are inserted between any two adjacent masses in the latter layout. Implementing on a harmonically forced primary system of single degree of freedom, their optimal design is conducted by using an extended version of fixed points theory. The present study suggests that for a given total tuned mass, the vibration control effect of G‐SDTMDI is solely controlled by the total inertance, because of which one of the two grounded inerters can be removed, and the vibration control performance will not be influenced under the condition that the amount of inertance remains unchanged. Meanwhile, the control effect delivered by I‐SDTMDI is dictated by the inerter relating the primary system and its adjacent tuned mass. Finally, it is analytically and numerically proven that grounded inerters can render the vibration control effect more pronounced, featured by a decreased peak amplitude and an enlarged frequency bandwidth of vibration reduction. The only potential detrimental effect observed is by incorporating an inerter between the host structure and its adjacent tuned mass. In this case, the vibration amplitude of host structure is amplified, and the effective plateau of vibration reduction is narrowed.

Statistical seismic performance assessment of tuned mass damper inerter

“…The optimal design of classic TMD, primarily codified by Den Hartog, is well-established using the fixed points theory. 3,6 Due to manufacturing, transportation, installation, and maintenance costs, the mass ratio (μ) is frequently preselected as a constant, usually lower than 5% of the controlled modal mass; and the frequency and damping ratios are considered as design variables. It is analytically and numerically proven that the mass ratio has a profound effect on the vibration suppression of an optimal TMD.…”

“…Some of the recently proposed methods to overcome these deficiencies include but are not limited to using unusual mass ratio, 7 active TMD (ATMD), 10 semi-active TMD (SATMD), 11,12 hybrid TMDs, 13 and multiple TMDs (MTMD), 8 with their pros and cons being debated extensively. 6 F I G U R E 1 (a) Basic concept of classic TMD, 3 (b) basic concept of TMDI, 4 and (c) ideal inerter, inertance constant b, and its relationship to force 5 One of the more recent alternatives is TMD with inerter (TMDI) depicted in Figure 1b. 4 An inerter, shown in Figure 1c, is a two-terminal element with negligible mass, whose reaction force is related to the relative acceleration between the two terminals with a proportionality coefficient known as inertance (b).…”

Analytical, Numerical and Experimental Study of an Enhanced Nonlinear Energy Sink

“…The passive control technique is widely used because of its simple structure, low cost, and easy realization [3]. Among them, linear absorbers are most commonly researched and used in engineering fields, such as tuned mass dampers [4] and tuned liquid damping [5]. The resonance peak was reduced by linear absorbers, significantly.…”

Application of Tuned Mass Damper to Mitigation of the Seismic Responses of Electrical Equipment in Nuclear Power Plants

“…Salvi et al [18] studied the effects of the soil-structure interaction on the low and high frequencies of multi-story frame structures. In addition, Elias et al [19] investigated the effectiveness of multi-mode control while using multiple tuned mass dampers (MTMD) [20][21][22][23][24]. Lu et al [25] and Elias et al [26] proposed optimal TMD design methods to reduce the dynamic displacement of a nonlinear building under unknown earthquake excitations.…”