H 2 Optimization of the Three-Element Type Dynamic Vibration Absorbers

2002 ◽  
Vol 124 (4) ◽  
pp. 583-592 ◽  
Author(s):  
Toshihiko Asami ◽  
Osamu Nishihara
Keyword(s):  
Optimization Design ◽  
Random Excitation ◽  
Control Device ◽  
Algebraic Solution ◽  
Primary System ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Optimum Parameters ◽  
Element Type ◽  
H2 Optimization

The dynamic vibration absorber (DVA) is a passive vibration control device which is attached to a vibrating body (called a primary system) subjected to exciting force or motion. In this paper, we will discuss an optimization problem of the three-element type DVA on the basis of the H2 optimization criterion. The objective of the H2 optimization is to reduce the total vibration energy of the system for overall frequencies; the total area under the power spectrum response curve is minimized in this criterion. If the system is subjected to random excitation instead of sinusoidal excitation, then the H2 optimization is probably more desirable than the popular H∞ optimization. In the past decade there has been increasing interest in the three-element type DVA. However, most previous studies on this type of DVA were based on the H∞ optimization design, and no one has been able to find the algebraic solution as of yet. We found a closed-form exact solution for a special case where the primary system has no damping. Furthermore, the general case solution including the damped primary system is presented in the form of a numerical solution. The optimum parameters obtained here are compared to those of the conventional Voigt type DVA. They are also compared to other optimum parameters based on the H∞ criterion.

Analytical Solutions to H∞ and H2 Optimization of Dynamic Vibration Absorbers Attached to Damped Linear Systems

2002 ◽  
Vol 124 (2) ◽  
pp. 284-295 ◽  
Author(s):  
Toshihiko Asami ◽  
Osamu Nishihara ◽  
Amr M. Baz
Keyword(s):  
Analytical Solutions ◽  
Series Solution ◽  
Numerical Solutions ◽  
Optimization Problems ◽  
Maximum Amplitude ◽  
Algebraic Solution ◽  
Primary System ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
H2 Optimization

H ∞ and H2 optimization problems of the Voigt type dynamic vibration absorber (DVA) are classical optimization problems, which have been already solved for a special case when the primary system has no damping. However, for the general case including a damped primary system, no one has solved these problems by algebraic approaches. Only the numerical solutions have been proposed until now. This paper presents the analytical solutions for the H∞ and H2 optimization of the DVA attached to the damped primary systems. In the H∞ optimization the DVA is designed such that the maximum amplitude magnification factor of the primary system is minimized; whereas in the H2 optimization the DVA is designed such that the squared area under the response curve of the primary system is minimized. We found a series solution for the H∞ optimization and a closed-form algebraic solution for the H2 optimization. The series solution is then compared with the numerical solution in order to check the accuracy in connection with the truncation error of the series. The exact solution presented in this paper is too complicated to handle by a hand-held calculator, so we proposed an approximate solution for the practical object.

Optimal design of inerter-based isolators minimizing the compliance and mobility transfer function versus harmonic and random ground acceleration excitation

2020 ◽  
pp. 107754632094017
Author(s):  
Marcial Baduidana ◽  
Aurelien Kenfack-Jiotsa
Keyword(s):  
Transfer Function ◽  
Vibration Absorber ◽  
Engineering Practice ◽  
Primary System ◽  
Optimal Parameters ◽  
Dynamic Vibration Absorber ◽  
Ground Acceleration ◽  
Dynamic Vibration ◽  
Optimum Parameters ◽  
Peak Value

This study is concerned with the problem of analysis and optimization of inerter-based systems. A main inerter system is generally composed of an inerter, a spring, and viscous damper. Series – parallel inerter system s and series inerter system s are two commonly used configurations of inerter-based system s . First , in this study , the H∞ optimum parameters of inerter-based isolators are derived to minimize the compliance and mobility transfer function of a single-degree -of-freedom system under a harmonic ground acceleration excitation. Under the optimum tuning condition, it is shown that the proposed inerter-based isolators when compared with the traditional dynamic vibration absorber provide larger suppression of the peak value of the magnitude of compliance and mobility transfer function s of the primary system. For the studied cases, more than 40% and 45% improvement can be attained in terms of minimizing the compliance and mobility transfer function s , respectively, as compared with the traditional dynamic vibration absorber for the series – parallel inerter system and 15% and 11% improvement can be attained respectively , for the series inerter system . Finally, further comparison between the inerter-based isolators and traditional dynamic vibration absorber under white noise excitation also shows that the series – parallel inerter system and series inerter system s are superior to the traditional dynamic vibration absorber . The results of the studied systems show that m ore than 23% and 16% improvement are attained in terms of minimizing the compliance and mobility transfer function s respectively , as compared with the traditional dynamic vibration absorber for the series – parallel inerter system and 26% and 13% improvement can be attained respectively , for the series inerter system . The optimal parameters for different cases are obtained. It is shown that the optimal parameters obtained using the minimized mobility transfer function are smaller than those using the compliance transfer function at all mass ratios or inertance-to-mass ratio. The results of this study can provide theoretical basis for design of the optimal inerter-based isolators in engineering practice.

Exact Algebraic Solution of an Optimal Double-Mass Dynamic Vibration Absorber Attached to a Damped Primary System

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Toshihiko Asami
Keyword(s):  
Optimization Problems ◽  
Algebraic Solution ◽  
Vibration Absorber ◽  
Primary System ◽  
Dynamic Vibration Absorber ◽  
Excitation System ◽  
Double Mass ◽  
Series Type ◽  
Algebraic Solutions ◽  
H2 Optimization

Abstract This article presents exact algebraic solutions to optimization problems of a double-mass dynamic vibration absorber (DVA) attached to a viscous damped primary system. The series-type double-mass DVA was optimized using three optimization criteria (the H∞ optimization, H2 optimization, and stability maximization criteria), and exact algebraic solutions were successfully obtained for all of them. It is extremely difficult to optimize DVAs when there is damping in the primary system. Even in the optimization of the simpler single-mass DVA, exact solutions have been obtained only for the H2 optimization and stability maximization criteria. For H∞ optimization, only numerical solutions and an approximate perturbation solution have been obtained. Regarding double-mass DVAs, an exact algebraic solution could not be obtained in this study in the case where a parallel-type DVA is attached to the damped primary system. For the series-type double-mass DVA, which was the focus of the present study, an exact algebraic solution was obtained for the force excitation system, in which the disturbance force acts directly on the primary mass; however, an algebraic solution was not obtained for the motion excitation system, in which the foundation of the system is subjected to a periodic displacement. Because all actual vibration systems involve damping, the results obtained in this study are expected to be useful in the design of actual DVAs. Furthermore, it is a great surprise that an exact algebraic solution exists even for such complex optimization problems of a linear vibration system.

Analytical and Experimental Evaluation of an Air Damped Dynamic Vibration Absorber: Design Optimizations of the Three-Element Type Model

1999 ◽  
Vol 121 (3) ◽  
pp. 334-342 ◽  
Author(s):  
Toshihiko Asami ◽  
Osamu Nishihara
Keyword(s):  
Maxwell Model ◽  
Element Model ◽  
Original Position ◽  
Vibration Absorber ◽  
Type Model ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Spring Element ◽  
Optimum Parameters ◽  
Element Type

In this paper, we propose a dynamic vibration absorber (DVA) with an air damper consisting of a piston and a cylinder. First, it will be shown that the air damper can conveniently be represented by the Maxwell model where a spring element and a dashpot are connected in series. The air damper has no ability to return the piston to its original position. For this reason, it is necessary for the piston to be supported by a spring which is placed in parallel with the damper. The air damped DVA can then be modeled by the three-element model. Many studies have been done on the Voigt type of DVA, and the accurate expressions of optimum tuning and damping parameters have already been derived by Hahnkamm and Brock et al. However, only a few papers have been published on the three-element type of DVA, and reliable expressions for it have not been derived until now. Therefore, we began our work by trying to derive expressions for optimum parameters of the three-element type of DVA. It was clear that the optimized three-element type of DVA is superior to the conventional Voigt type of DVA. The optimum parameters which we obtained from our expressions were tested on a vibratory model. The experiments showed that the our expression is very useful for designing the air damped DVA.

An Analytical Model for the Interaction of Mass Inclusions in Heterogeneous (HG) Blankets

2011 ◽  
Vol 133 (6) ◽  
Author(s):  
A. Wagner ◽  
M. E. Johnson ◽  
K. Idrisi ◽  
D. P. Bartylla
Keyword(s):  
Elastic Layer ◽  
Analytical Approach ◽  
Low Frequency ◽  
Control Device ◽  
Effective Stiffness ◽  
Special Focus ◽  
Dynamic Vibration Absorber ◽  
Low Frequencies ◽  
Dynamic Vibration ◽  
The Masses

The heterogeneous (HG) blanket is a passive treatment used to reduce the low frequency transmission of sound through partitions. HG blankets, glued onto a structure, consist of an elastic medium with embedded mass inhomogeneities that mechanically replicate a mass-spring-damper system to reduce efficient radiating structural modes at low frequencies. The elastic layer typically used has sound absorption properties to create a noise control device with a wide bandwidth of performance. The natural frequency of an embedded dynamic vibration absorber is determined by the mass of the inhomogeneity as well as by its effective stiffness due to the interaction of the mass inclusion with the elastic layer. A novel analytical approach has been developed to describe in detail the interaction of the mass inclusions with the elastic layer and the interaction between the masses by evaluating special elastomechanical concepts. The effective stiffness is predicted by the analytical approach based on the shape of the mass inclusions as well as on the thickness and material properties of the layer. The experimental validation is included and a simplified direct equation to calculate the effective stiffness of a HG blanket is proposed. Furthermore, the stress field inside the elastic material will be evaluated with focus on the stresses at the base to assess the modeling of one or more masses placed on top of the elastic layer as dynamic vibration absorbers. Finally, the interaction between two (or more) masses placed onto the same layer is studied with special focus on the coupling of the masses at low distances between them.

scholarly journals Suspension parameter design of underframe equipment considering series stiffness of shock absorber

2020 ◽  
Vol 12 (5) ◽  
pp. 168781402092264
Author(s):  
Jie Chen ◽  
Yangjun Wu ◽  
Xiaolong He ◽  
Limin Zhang ◽  
Shijie Dong
Keyword(s):  
Simulation Software ◽  
Dynamics Simulation ◽  
Ride Quality ◽  
Railway Vehicle ◽  
Vibration Absorber ◽  
Dynamic Vibration Absorber ◽  
Suspension Parameters ◽  
Dynamic Vibration ◽  
Beam System ◽  
Element Type

In this article, a vertical rigid–flexible coupling model between the vehicle and the equipment is established. Considering the series stiffness of hydraulic shock absorbers, the underframe equipment is like a three-element-type Maxwell model dynamic vibration absorber. The carbody is approximated by an elastic beam and the three-element-type dynamic vibration absorber for general beam system was studied by fixed-point theory. The analytical solution of the optimal suspension parameters for the beam system subjected to harmonic excitation is obtained. The dynamic vibration absorber theory is applied to reduce the resonance of the carbody and to design the suspension parameters of the underframe equipment accordingly. Then, the railway vehicle model was established by multi-body dynamics simulation software, and the vibration levels of the vehicle at different speeds were calculated. A comparative analysis was made between the vehicles whose underframe equipment was suspended by the three-element-type dynamic vibration absorber model and the Kelvin–Voigt-type dynamic vibration absorber model, respectively. The results show that, compared with the vehicle whose underframe equipment is suspended by the Kelvin–Voigt-type dynamic vibration absorber model, the vehicle whose underframe equipment is suspended by the three-element-type dynamic vibration absorber model can achieve a much better ride quality and root mean square value of the vibration acceleration of the carbody. The carbody elastic vibration can be reduced and the vehicle ride quality can be improved effectively using the designed absorber.

scholarly journals Attenuation of Motorcycle Handle Vibration Using Dynamic Vibration Absorber

2018 ◽  
Vol 217 ◽  
pp. 01006
Author(s):  
Muhammad Iyad Al-Maliki Saifudin ◽  
Nabil Mohamad Usamah ◽  
Zaidi Mohd Ripin
Keyword(s):  
Vibration Absorber ◽  
Primary System ◽  
Additional Source ◽  
Dynamic Vibration Absorber ◽  
Vibration Absorption ◽  
The Road ◽  
Dynamic Vibration ◽  
Attenuation Level ◽  
Road Surface Roughness ◽  
Extended Exposure

Motorcycle riders are exposed to hand-transmitted vibration of the hand-arm system due to the vibration of the handle and extended exposure can result in numbness and trembling. One feasible solution to attenuate the handle vibration is by using a dynamic vibration absorber (DVA). In this work a DVA is designed and mounted on the motorcycle handle in order to reduce the vibration at the handle by transferring the vibration from the primary system handle to the secondary mass. Removal of elastomeric material at the DVA mounting locations, symmetry of secondary mass and the direction of DVA attachment influence the vibration absorption. A series of tests conducted show that the vibration on the handle is mainly induced by the engine and there is additional source of vibration from the road surface roughness. Installation of DVA at different locations on the handle resulted in various attenuation levels at different speed in the x and z directions. the attenuation level is between 59-68 % in the biodynamic x-directions for speed at 30-50 kmh-1.

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