Exact Optimization of a Three-Element Dynamic Vibration Absorber: Minimization of the Maximum Amplitude Magnification Factor

2018 ◽  
Vol 141 (1) ◽  
Author(s):  
Osamu Nishihara
Keyword(s):  
Maximum Amplitude ◽  
Resonance Curve ◽  
Element Model ◽  
Optimality Criteria ◽  
Simultaneous Equations ◽  
Vibration Absorber ◽  
Magnification Factor ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Numerical Computing

In this study, the maximum amplitude magnification factor for a linear system equipped with a three-element dynamic vibration absorber (DVA) is exactly minimized for a given mass ratio using a numerical approach. The frequency response curve is assumed to have two resonance peaks, and the parameters for the two springs and one viscous damper in the DVA are optimized by minimizing the resonance amplitudes. The three-element model is known to represent the dynamic characteristics of air-damped DVAs. A generalized optimality criteria approach is developed and adopted for the derivation of the simultaneous equations for this design problem. The solution of the simultaneous equations precisely equalizes the heights of the two peaks in the resonance curve and achieves a minimum amplitude magnification factor. The simultaneous equations are solvable using the standard built-in functions of numerical computing software. The performance improvement of the three-element DVA compared to the standard Voigt type is evaluated based on the equivalent mass ratios. This performance evaluation is highly accurate and reliable because of the precise formulation of the optimization problem. Thus, the advantages of the three-element type DVA have been made clearer.

scholarly journals Effect of Inerter in Traditional and Variant Dynamic Vibration Absorbers for One Degree-of-Freedom Systems Subjected to Base Excitations

2019 ◽  
Vol 23 (1) ◽  
pp. 9-16
Author(s):  
Dheepakram Laxmimala Barathwaaj ◽  
Sujay Yegateela ◽  
Vivek Vardhan ◽  
Vignesh Suresh ◽  
Devarajan Kaliyannan
Keyword(s):  
Damping Ratio ◽  
Maximum Amplitude ◽  
Vibration Absorber ◽  
Primary System ◽  
Base Excitation ◽  
Mass Ratio ◽  
Magnification Factor ◽  
Dynamic Vibration Absorber ◽  
Optimum Frequency ◽  
Dynamic Vibration

Abstract In this paper, closed-form optimal parameters of inerter-based variant dynamic vibration absorber (variant IDVA) coupled to a primary system subjected to base excitation are derived based on classical fixed-points theory. The proposed variant IDVA is obtained by adding an inerter alone parallel to the absorber damper in the variant dynamic vibration absorber (variant DVA). A new set of optimum frequency and damping ratio of the absorber is derived, thereby resulting in lower maximum amplitude magnification factor than the inerter-based traditional dynamic vibration absorber (traditional IDVA). Under the optimum tuning condition of the absorbers, it is proved both analytically and numerically that the proposed variant IDVA provides a larger suppression of resonant vibration amplitude of the primary system subjected to base excitation. It is demonstrated that adding an inerter alone to the variant DVA provides 19% improvement in vibration suppression than traditional IDVA when the mass ratio is less than 0.2 and the effective frequency bandwidth of the proposed IDVA is wider than the traditional IDVA. The effect of inertance and mass ratio on the amplitude magnification factor of traditional and variant IDVA is also studied.

Closed-Form Solutions to the Exact Optimizations of Dynamic Vibration Absorbers (Minimizations of the Maximum Amplitude Magnification Factors)

2002 ◽  
Vol 124 (4) ◽  
pp. 576-582 ◽  
Author(s):  
Osamu Nishihara ◽  
Toshihiko Asami
Keyword(s):  
Exact Solutions ◽  
Closed Form ◽  
Maximum Amplitude ◽  
Primary System ◽  
Magnification Factor ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Classic Problem ◽  
Resonance Frequencies ◽  
Minimum Amplitude

A typical design problem for which the fixed-points method was originally developed is that of minimizing the maximum amplitude magnification factor of a primary system by using a dynamic vibration absorber. This is an example of usual cases for which their exact solutions are not obtained by the well-known heuristic approach. In this paper, more natural formulation of this problem is studied, and algebraic closed-form exact solutions to both the optimum tuning ratio and the optimum damping coefficient for this classic problem are derived under assumption of undamped primary system. It is also proven that the minimum amplitude magnification factor, resonance and anti-resonance frequencies are entirely algebraic.

Rail Dynamic Vibration Absorber Design and Vibration Reduction Analysis

2011 ◽  
Vol 42 (11) ◽  
pp. 15-19
Author(s):  
Linya Liu ◽  
Bin Zhang ◽  
Jin Wang
Keyword(s):  
Finite Element ◽  
Degrees Of Freedom ◽  
Element Model ◽  
Vertical Displacement ◽  
Vibration Absorber ◽  
Vertical Acceleration ◽  
Dynamic Vibration Absorber ◽  
Finite Element Software ◽  
Dynamic Vibration ◽  
Damped System

The rail between two adjacent fasteners is regarded as the research object, and the rail is simplified as the main vibration system of undamped single degree of freedom, which supports the elastic components. The dynamic vibration absorber is simplified as a spring and damped system of 3-DOF(three degrees of freedom), to establish a mathematical model of rail dynamic vibration absorber. Through relevant theories, the parameter values of dynamic vibration absorber can be deduced when it achieves the best absorption effect. In accordance with the parameters, the scantlings of the structure of the dynamic vibration absorber can also be designed. Through the finite element software, the finite element model CRTS _ Ballastless Track system is established; with consideration of the value of irregularity, we load it variously. Analysis results showed that: compared to the rail and track where the dynamic vibration absorber is not installed, the maximum vertical displacement of the rail and track where a dynamic vibration absorber is installed was reduced by 65% and 67% respectively, the maximum vertical acceleration decreased by 75% and 70% and around, which reveals that the rail dynamic vibration absorber has a good vibration-reducing effect.

scholarly journals Design of a hybrid proportional electromagnetic dynamic vibration absorber for control of idling engine vibration

2019 ◽  
Vol 234 (1) ◽  
pp. 56-70
Author(s):  
Tao Fu ◽  
Subhash Rakheja ◽  
Wen-Bin Shangguan
Keyword(s):  
Magnetic Force ◽  
Element Model ◽  
Geometric Parameters ◽  
Vibration Absorber ◽  
Electromagnetic Actuator ◽  
Primary System ◽  
Frequency Range ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Engine Vibration

A hybrid proportional electromagnetic dynamic vibration absorber consisting of an electromagnetic actuator and an elastic element is proposed for control of engine vibration during idling. The design of the proportional electromagnetic actuator is realized considering the geometric parameters of the core to achieve nearly constant magnetic force over a broad range of its dynamic displacement but proportional to square of the current. The dynamic characteristics of the electromagnetic dynamic vibration absorber are analyzed analytically and experimentally. The effects of various geometric parameters of the actuator such as the slopes and width/height, and the air gaps on the resulting magnetic force characteristics are evaluated using a finite element model and verified experimentally. A methodology is proposed to achieve magnetic force proportional to current and consistent with the disturbance frequency. The hybrid proportional electromagnetic dynamic vibration absorber is subsequently applied to a single-degree-of-freedom primary system with an acceleration feedback control algorithm for attenuation of primary system vibration in a frequency band around the typical idling vibration frequencies. The effectiveness of the hybrid proportional electromagnetic dynamic vibration absorber is evaluated through simulations and laboratory experiments under harmonic excitations in the 20–30 Hz frequency range. Both the simulation and measurements show that the hybrid proportional electromagnetic dynamic vibration absorber can yield effective attenuation of periodic idling vibration in the frequency range considered.

Design of Viscous Dynamic Vibration Absorber for a Vertical-Axis Wind Turbine

2012 ◽  
Author(s):  
Georges Kouroussis ◽  
Lassaad Ben Fekih ◽  
Jean-Yves Bottieau ◽  
Olivier Verlinden
Keyword(s):  
Wind Turbine ◽  
Low Cost ◽  
Vibration Reduction ◽  
Vertical Axis ◽  
Element Model ◽  
Mode Shapes ◽  
Vibration Absorber ◽  
Vertical Axis Wind Turbine ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration

This paper presents the investigations brought to fruition for the design of a dynamic vibration absorber (DVA) for vertical-axis wind turbine. A first step is devoted to the experimental analysis of the structure, by seeking its modal behaviour in low frequency range. A numerical model of the turbine system consisting of finite elements is developed. Their dynamics and geometrical characteristics are updated, by fitting the first three bending numerical mode shapes with the experimental ones. Finally, a mathematical model of DVA is implemented and the vibration reduction is evaluated with the help of the updated finite element model, considering the modal decomposition of the structure. The results exhibit significant vibration reduction performance evidencing this kind of device. A tuneable anti-vibration device is then designed, with a purpose of simplicity and low-cost production. The possible non-linearity of the DVA is also studied, by comparing behaviours of linear and quadratic selected dampers.

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