Optimal Design of Double-Mass Dynamic Vibration Absorbers Minimizing the Mobility Transfer Function

2018 ◽  
Vol 140 (6) ◽  
Author(s):  
Toshihiko Asami ◽  
Yoshito Mizukawa ◽  
Tomohiko Ise

Although the vibration suppression effects of precisely adjusted dynamic vibration absorbers (DVAs) are well known, multimass DVAs have recently been studied with the aim of further improving their performance and avoiding performance deterioration due to changes in their system parameters. One of the present authors has previously reported a solution that provides the optimal tuning and damping conditions of the double-mass DVA and has demonstrated that it achieves better performance than the conventional single-mass DVA. The evaluation index of the performance used in that study was the minimization of the compliance transfer function. This evaluation function has the objective of minimizing the absolute displacement response of the primary system. However, it is important to suppress the absolute velocity response of the primary system to reduce the noise generated by the machine or structure. Therefore, in the present study, the optimal solutions for DVAs were obtained by minimizing the mobility transfer function rather than the compliance transfer function. As in previous investigations, three optimization criteria were tested: the H∞ optimization, H2 optimization, and stability maximization criteria. In this study, an exact algebraic solution to the H∞ optimization of the series-type double-mass DVA was successfully derived. In addition, it was demonstrated that the optimal solution obtained by minimizing the mobility transfer function differs significantly at some points from that minimizing the compliance transfer function published in the previous report.

2003 ◽  
Vol 125 (3) ◽  
pp. 398-405 ◽  
Author(s):  
Toshihiko Asami ◽  
Osamu Nishihara

H ∞ optimization of the dynamic vibration absorbers is a classical optimization problem, and has been already solved more than 50 years ago. It is a well-known solution, but we know this solution is only an approximate one. Recently, one of the authors has proposed a new method for attaining the H∞ optimization of the absorber in linear systems. The new method enables us to obtain the exact algebraic solution of the H∞ optimization problem of the absorber. In this paper, we first apply this method to the design optimization of a viscous damped (Voigt type) absorber and a hysteretic damped absorber attached to undamped primary systems. For each absorber, six different transfer functions are taken here as performance indices to vibration suppression or isolation. As a result, we found the closed-form exact solutions to all transfer functions. The solutions obtained here are then compared with those of the approximate ones. Finally, we present the closed-form exact solutions to the hysteretic damped absorber attached to damped primary systems.


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