Optimum design for a novel inerter-based vibration absorber with an amplified inertance and grounded stiffness for enhanced vibration control

2021 ◽  
pp. 107754632110132
Author(s):  
Marcial Baduidana ◽  
Aurelien Kenfack-Jiotsa
Keyword(s):  
Primary Structure ◽  
Fixed Point Theory ◽  
Damping Ratio ◽  
Time History ◽  
Harmonic Excitation ◽  
Vibration Absorber ◽  
Primary System ◽  
Vibration Absorbers ◽  
Stiffness Ratio ◽  
Optimum Frequency

This article presents the results of the study of a novel inerter-based vibration absorber with an amplified inertance mechanism and grounded stiffness, to control excessive vibrational movements of an excited primary structure. The inerter vibration absorber used in this study acts as a passive tuned inerter damper. An undamped primary structure model with a single degree of freedom controlled by the proposed inerter vibration absorber is developed and used to derive the equations of motion of the coupled system. The optimum frequency ratio and the optimum damping ratio of inerter vibration absorber are found using the fixed point theory for harmonic force-excited primary structures. Then, the optimum grounded stiffness ratio is deduced. Based on the inclusion of an amplified inertance mechanism, it is found that for given inertance mass ratio, the change in the amplification ratio results in three cases for the optimum grounded stiffness ratio, that is, negative, zero, and positive. From these three cases of grounded stiffness, the inerter vibration absorber with positive grounded stiffness has demonstrated the best control performance. Under optimum parameters, the results indicate that the inerter vibration absorber in this article outperforms some existing inerter vibration absorbers under the harmonic excitation, in terms of decreases in the peak vibration response of the primary system and widens the suppression bandwidth. Finally, the further comparison among the inerter vibration absorber under random (white noise) excitation also shows that the model in this article is superior to other inerter vibration absorbers in terms of smallest mean square response and smallest variance of the time history of the primary system.

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.

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.

scholarly journals Optimal parameters of dynamic vibration absorber for linear damped rotary systems subjected to harmonic excitation

2020 ◽  
Author(s):  
Vu Duc Phuc ◽  
Tong Van Canh ◽  
Pham Van Lieu
Keyword(s):  
Vibration Suppression ◽  
Fixed Point Theory ◽  
Damping Ratio ◽  
Harmonic Excitation ◽  
Tuning Parameter ◽  
Vibration Absorber ◽  
Optimal Parameters ◽  
Dynamic Vibration Absorber ◽  
Practical Applications ◽  
Dynamic Vibration

Dynamic vibration absorber (DVA) is a simple and effective device for vibration absorption used in many practical applications. Determination of suitable parameters for DVA is of significant importance to achieve high vibration reduction effectiveness. This paper presents a   method to find the optimal parameters of a DVA attached to a linear damped rotary system excited by harmonic torque. To this end, a closed-form formula for the optimum tuning parameter is derived using the fixed-point theory based on an assumption that the damped rotary systems are lightly or moderately damped. The optimal damping ratio of DVA is found by solving a set of non-linear equations established by the Chebyshev's min-max criterion. The performance of the proposed optimal DVA is compared with that obtained by existing optimal solution in literature. It is shown that the proposed optimal parameters are possible to obtain superior vibration suppression compared to existing optimal formula. Extended simulations are carried out to examine the performance of the optimally designed DVA and the sensitivity of the optimum parameters. The simulation results show that the improvement of the vibration performance on damped rotary system can be as much as 90% by using DVA.

scholarly journals Study of Magnetic Vibration Absorber with Permanent Magnets along Vibrating Beam Structure

2013 ◽  
Vol 2013 ◽  
pp. 1-5 ◽  
Author(s):  
F. B. Sayyad ◽  
N. D. Gadhave
Keyword(s):  
Cantilever Beam ◽  
Gas Turbines ◽  
Permanent Magnets ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Vibration Absorber ◽  
Primary System ◽  
Vibration Absorbers ◽  
Vibratory System ◽  
Electrical Generator

The vibration absorbers are frequently used to control and minimize excess vibration in structural system. Dynamic vibration absorbers are used to reduce the undesirable vibration in many applications such as pumps, gas turbines, engine, bridge, and electrical generator. To reduce the vibration of the system, the frequency of absorber should be equal to the excitation frequency. The aim of this study is to investigate the effect of magnetic vibration absorber along vibrating cantilever beam. This study will aim to develop a position of magnetic vibration absorber along the cantilever beam to adopt the change in vibratory system. The absorber system is mounted on a cantilever beam acting as the primary system. The objective is to suppress the vibration of the primary system subjected to a harmonic excitation whose frequencies are varying. It can be achieved by varying the position of magnetic vibration absorber along the length of beam. The advantage of magnetic vibration absorber is that it can be easily tuned to the excitation frequency, so it can be used to reduce the vibration of system subjected to variable excitation frequency.

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.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1991 ◽  
Author(s):  
Hashem Ashrafiuon
Keyword(s):  
Dynamic Models ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Different Levels

Abstract This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. The design parameters are computed and compared for the rigid, static, and dynamic models of the base as well as different levels of base flexibility.

scholarly journals Optimal Design of a Damped Single Degree of Freedom Platform for Vibration Suppression in Harmonically Forced Undamped Systems

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Jimmy S. Issa
Keyword(s):  
Objective Function ◽  
Frequency Response Function ◽  
Damping Ratio ◽  
Optimal Solution ◽  
Vibration Absorber ◽  
Primary System ◽  
Mass Ratio ◽  
Optimal Damping ◽  
Mass Ratios ◽  
Invariant Points

Vibration reduction in harmonically forced undamped systems is considered using a new vibration absorber setup. The vibration absorber is a platform that is connected to the ground by a spring and damper. The primary system is attached to the platform, and the optimal parameters of the latter are obtained with the aim of minimizing the peaks of the primary system frequency response function. The minimax problem is solved using a method based on invariant points of the objective function. For a given mass ratio of the system, the optimal tuning and damping ratios are determined separately. First, it is shown that the objective function passes through three invariant points, which are independent of the damping ratio. Two optimal tuning ratios are determined analytically such that two of the three invariant points are equally leveled. Then, the optimal damping ratio is obtained such that the peaks of the frequency response function are equally leveled. The optimal damping ratio is determined in a closed form, except for a small range of the mass ratio, where it is calculated numerically from two nonlinear equations. For a range of mass ratios, the optimal solution obtained is exact, because the two peaks coincide with the two equally leveled invariant points. For the remaining range, the optimal solution is semiexact. Unlike the case of the classical absorber setup, where the absorber performance increases with increasing mass ratios, it is shown that an optimal mass ratio exists for this setup, for which the absorber reaches its utmost performance. The objective function is shown in its optimal shape for a range of mass ratios, including its utmost shape associated with the optimal mass ratio of the setup.

Optimum Vibration Absorbers for Linear Damped Systems

1981 ◽  
Vol 103 (4) ◽  
pp. 908-913 ◽  
Author(s):  
S. E. Randall ◽  
D. M. Halsted ◽  
D. L. Taylor
Keyword(s):  
Damping Ratio ◽  
Maximum Amplitude ◽  
Vibration Absorber ◽  
Vibration Absorbers ◽  
Mass Ratio ◽  
Linear Vibration ◽  
Optimal Linear ◽  
Damped Systems ◽  
Independent Parameters ◽  
Qualitative Discussion

This paper presents computational graphs that determine the optimal linear vibration absorber for linear damped primary systems. Considered as independent parameters are the main system damping ratio and the mass ratio examined over the range 0 to 0.50 and 0.01 to 0.40, respectively. The remaining nondimensional parameters were optimized using numerical methods based on minimum-maximum amplitude criteria. With independent parameters specified the computational graphs can be used to find the response amplitudes as well as the optimal absorber characteristics. This procedure is illustrated in a design example. A qualitative discussion of the sensitivity to parameter errors is presented.

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.

Optimal Design of Vibration Absorber Systems Supported by Elastic Base

1992 ◽  
Vol 114 (2) ◽  
pp. 280-283
Author(s):  
H. Ashrafiuon
Keyword(s):  
Optimal Design ◽  
Damping Ratio ◽  
Equations Of Motion ◽  
Elastic Base ◽  
Design Parameters ◽  
Primary System ◽  
Vibration Absorbers ◽  
Equivalent Damping ◽  
System Equations ◽  
Flexible Models

This paper presents the effect of foundation flexibility on the optimum design of vibration absorbers. Flexibility of the base is incorporated into the absorber system equations of motion through an equivalent damping ratio and stiffness value in the direction of motion at the connection point. The optimum values of the uncoupled natural frequency and damping ratio of the absorber are determined over a range of excitation frequencies and the primary system damping ratio. Optimal design parameters are computed and compared for the rigid, and flexible models of the base as well as different levels of base flexibility.

Sign in / Sign up

Export Citation Format

Share Document