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.

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.

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.

Optimal Design of an Inerter-Based Dynamic Vibration Absorber Connected to Ground

2019 ◽  
Vol 141 (5) ◽  
Author(s):  
Shaoyi Zhou ◽  
Claire Jean-Mistral ◽  
Simon Chesne
Keyword(s):  
Fixed Point ◽  
Optimal Design ◽  
Transient Response ◽  
Damping Ratio ◽  
Vibration Absorber ◽  
Practical Implementation ◽  
Primary System ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
The Stability

Abstract This paper addresses the optimal design of a novel nontraditional inerter-based dynamic vibration absorber (NTIDVA) installed on an undamped primary system of single degree-of-freedom under harmonic and transient excitations. Our NTIDVA is based on the traditional dynamic vibration absorber (TDVA) with the damper replaced by a grounded inerter-based mechanical network. Closed-form expressions of optimal parameters of NTIDVA are derived according to an extended version of fixed point theory developed in the literature and the stability maximization criterion. The transient response of the primary system is optimized when the coupled system becomes defective, namely having three pairs of coalesced conjugate poles, the proof of which is also spelt out in this paper. Moreover, the analogous relationship between NTIDVA and electromagnetic dynamic vibration absorber is highlighted, facilitating the practical implementation of the proposed absorber. Finally, numerical studies suggest that compared with TDVA, NTIDVA can decrease the peak vibration amplitude of the primary system and enlarge the frequency bandwidth of vibration suppression when optimized by the extended fixed point technique, while the stability maximization criterion shows an improved transient response in terms of larger modal damping ratio and accelerated attenuation rate.

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.

APPLICATION OF A TUNABLE ELECTROMAGNETIC DAMPER IN SUPPRESSION OF STRUCTURAL VIBRATION

2006 ◽  
Vol 30 (1) ◽  
pp. 41-61 ◽  
Author(s):  
Kefu Liu ◽  
Jie Liu ◽  
Liang Liao
Keyword(s):  
Damping Ratio ◽  
Step Change ◽  
Control Algorithms ◽  
Vibration Absorber ◽  
Primary System ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Exciting Frequency ◽  
On Line ◽  
Electromagnetic Damper

An electromagnetic damper is developed to construct a tunable damped dynamic vibration absorber. The developed vibration absorber can suppress vibration of a structure subjected to a harmonic force with variable frequency. The damping of the vibration absorber can be adjusted on-line to cope with variation in the exciting frequency. The electromagnetic damper is composed of an electromagnet and a copper plate attached to the absorber mass. The relationship between the damping ratio and the damper current is discussed analytically. An experiment is conducted to determine the damping coefficients. A clamped-clamped beam is used as a primary system. The damper is connected between the absorber mass and the ground. This setup is referred to as skyhook dynamic vibration absorber in this study. The performance of a skyhook dynamic vibration absorber is compared with that of a groundhook dynamic vibration absorber where a damper is connected between the primary mass and the absorber mass. Two algorithms are proposed to tune the damper on-line. The first algorithm is FFT-based while the second one is rms-based. The control algorithms are tested against three frequency varying scenarios: multi-step change, linear change, and single-step change plus impact disturbance. Merits of each of the control algorithms are demonstrated.

scholarly journals H∞ optimization of Maxwell dynamic vibration absorber with multiple negative stiffness springs

2020 ◽  
pp. 146134842097281
Author(s):  
Yan Hao ◽  
Yongjun Shen ◽  
Xianghong Li ◽  
Jun Wang ◽  
Shaopu Yang
Keyword(s):  
Fixed Point Theory ◽  
Damping Ratio ◽  
Negative Stiffness ◽  
System Stability ◽  
Vibration Absorber ◽  
Primary System ◽  
Stiffness Ratio ◽  
Dynamic Vibration Absorber ◽  
System Parameters ◽  
Dynamic Vibration

The Maxwell model with viscoelastic material and multiple negative stiffness springs is introduced into dynamic vibration absorber system, and all the system parameters are optimized in detail. The analytical solution of the primary system is exhibited according to the established motion differential equation. The dimensionless system parameters, including the optimum natural frequency ratio, the optimum damping ratio and the first optimum negative stiffness ratio of dynamic vibration absorber, are obtained based on H∞ optimization principle and the fixed-point theory. Considering system stability, the other optimum negative stiffness ratio is also determined. Furthermore, by the comparisons of the presented dynamic vibration absorber with other traditional dynamic vibration absorbers, it is found that the dynamic vibration absorber in this paper has better vibration reduction effect in the case of both harmonic and random excitation.

Dynamic Vibration Absorber Design to Suppress Boring Chatter: Absorber Parameters Identification Based on Modal Correlation

2013 ◽  
Vol 753-755 ◽  
pp. 1816-1820 ◽  
Author(s):  
Zhen Kun Hu ◽  
Ming Wang ◽  
Tao Zan
Keyword(s):  
Damping Ratio ◽  
Correlation Method ◽  
Vibration Absorber ◽  
Dynamic Vibration Absorber ◽  
Element Analysis ◽  
Simple Method ◽  
Dynamic Vibration ◽  
The Finite Element Analysis ◽  
Chatter Control ◽  
Modal Method

The dynamic vibration absorber (DVA) is generally used to suppress the machining vibration in boring processes. The DVA consists of an additional massspringdamper sub-system, and needs accurately tuning of its natural frequency and damping ratio to match the main structure for vibration control. For obtaining the optimal performance of the DVA, the parameters of the DVA used in a boring bar is identified using modal correlation method, which combines the finite element analysis method with test modal method to validate the FEMs results. The analysis results show that the modal correlation method is an effective and simple method to accurately identify the dynamic parameters of DVA and guarantee the optimal design of the DVA for boring chatter control.

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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