Closed-form exact solution to H(infinity) optimization of dynamic vibration absorbers: II. Application to different performance indexes for vibration isolation

2000 ◽  
Author(s):  
Toshihiko Asami ◽  
Osamu Nishihara
Keyword(s):  
Exact Solution ◽  
Closed Form ◽  
Vibration Isolation ◽  
Vibration Absorbers ◽  
Dynamic Vibration ◽  
Performance Indexes ◽  
Dynamic Vibration Absorbers

Parameters optimization of dynamic vibration absorber based on grounded stiffness, inerter, and amplifying mechanism

2021 ◽  
pp. 107754632110382
Author(s):  
Peng Sui ◽  
Yongjun Shen ◽  
Shaopu Yang ◽  
Junfeng Wang
Keyword(s):  
Analytical Solution ◽  
Vibration Isolation ◽  
Damping Ratio ◽  
Vibration Absorber ◽  
Primary System ◽  
Vibration Absorbers ◽  
Stiffness Ratio ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Dynamic Vibration Absorbers

In the field of dynamics and control, some typical vibration devices, including grounded stiffness, inerter and amplifying mechanism, have good vibration isolation and reduction effects, especially in dynamic vibration absorber (DVA). However, most of the current research studies only focus on the performance of a single device on the system, and those DVAs are gradually becoming difficult to meet the growth of performance demand for vibration control. On the basis of Voigt dynamic vibration absorber, a novel dynamic vibration absorber model based on the combined structure of grounded stiffness, inerter, and amplifying mechanism is presented, and the analytical solution of the optimal design formula is derived. First, the motion differential equation of the system is established, and the normalized amplitude amplification factor of the displacement is calculated. It is found that the system has three fixed points unrelated to the damping ratio. The optimal frequency ratio is obtained based on the fixed-point theory. In order to ensure the stability of the system, it is found that inappropriate inerter coefficient will cause the system instable when screening optimal grounded stiffness ratio. Accordingly, the best working range of inerter is determined. Finally, optimal grounded stiffness ratio and approximate optimal damping ratio are also obtained. The influence of inerter coefficient and magnification ratio on the response of the primary system is analyzed. The correctness of the derived analytical solution is verified by numerical simulation. Compared with other dynamic vibration absorbers, it is verified that presented model has superior vibration absorption performance and provides a theoretical basis for the design of a new type of dynamic vibration absorbers.

Closed-Form Exact Solution to H∞ Optimization of Dynamic Vibration Absorbers (Application to Different Transfer Functions and Damping Systems)

2003 ◽  
Vol 125 (3) ◽  
pp. 398-405 ◽  
Author(s):  
Toshihiko Asami ◽  
Osamu Nishihara
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Optimization Problem ◽  
Vibration Suppression ◽  
Transfer Functions ◽  
New Method ◽  
Algebraic Solution ◽  
Vibration Absorbers ◽  
Dynamic Vibration ◽  
Dynamic Vibration Absorbers

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.

scholarly journals Vortex-Induced Vibration Suppression of Bridges by Inerter-Based Dynamic Vibration Absorbers

2021 ◽  
Vol 2021 ◽  
pp. 1-18
Author(s):  
Junjie Chen ◽  
Michael Z. Q. Chen ◽  
Yinlong Hu
Keyword(s):  
Vibration Suppression ◽  
Vertical Displacement ◽  
Resonant Mode ◽  
Vibration Absorbers ◽  
Bridge Structure ◽  
Dynamic Vibration Absorber ◽  
Vortex Induced Vibration ◽  
Dynamic Vibration ◽  
Performance Indexes ◽  
Dynamic Vibration Absorbers

The vortex-induced vibration may cause fatigue of a bridge structure, affecting the safety of vehicles and the comfort of pedestrians. Inerter is a two-terminal device, which has been applied in many areas. This paper studies the problem of suppressing the vortex-induced vibration of a bridge by using an inerter-based dynamic vibration absorber (IDVA). The performances in terms of the suspension travel and the vertical displacement of the bridge with different IDVAs in suppressing vortex-induced vibration are compared, and the effect of the installation position of IDVA on the performance of suppressing vortex-induced vibration is shown. The performance indexes for the vertical displacement of six IDVA arrangements are obtained by using an iterative method, where the performance indexes for the vertical displacement are minimized by using the optimization toolbox in a commercial software. The result shows that the optimal installation positions and the number of suitable installation positions are affected by the resonant mode. Among the six arrangements, one arrangement is identified to have the best performance of suppressing vortex-induced vibration. All the six arrangements have reduced the suspension travel performance.

Closed-form solutions for the optimal design of inerter-based dynamic vibration absorbers

2018 ◽  
Vol 144 ◽  
pp. 41-53 ◽  
Author(s):  
Eduardo Barredo ◽  
Andrés Blanco ◽  
Jorge Colín ◽  
Victor M. Penagos ◽  
Arturo Abúndez ◽  
...  
Keyword(s):  
Optimal Design ◽  
Closed Form ◽  
Vibration Absorbers ◽  
Closed Form Solutions ◽  
Dynamic Vibration ◽  
Dynamic Vibration Absorbers

Structural Optimization of Cantilever Mechanical Elements

1986 ◽  
Vol 108 (4) ◽  
pp. 427-433 ◽  
Author(s):  
Eugene I. Rivin
Keyword(s):  
Structural Optimization ◽  
Natural Frequencies ◽  
Superior Performance ◽  
Vibration Absorbers ◽  
Stability Margins ◽  
Dynamic Vibration ◽  
Robot Arms ◽  
Limited Effectiveness ◽  
Mass Ratios ◽  
Dynamic Vibration Absorbers

Naturally limited stiffness of cantilever elements due to lack of constraint from other structural components, together with low structural damping, causes intensive and slow-decaying transient vibrations as well as low stability margins for self-excited vibrations. In cases of dimensional limitations (e.g., boring bars), such common antivibration means as dynamic vibration absorbers have limited effectiveness due to low mass ratios. This paper describes novel concepts of structural optimization of cantilever components by using combinations of rigid and light materials for their design. Two examples are given: tool holders (boring bars) and robot arms. Optimized boring bars demonstrate substantially increased natural frequencies, together with the possibility of greatly enhanced mass ratios for dynamic vibration absorbers. Machining tests with combination boring bars have been performed in comparison with conventional boring bars showing superior performance of the former. Computer optimization of combination-type robot arms has shown a potential of 10–60 percent reduction in tip-of-arm deflection, together with a commensurate reduction of driving torque for a given acceleration, and a higher natural frequencies (i.e., shorter transients). Optimization has been performed for various ratios of bending and joint compliance and various payloads.

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