scholarly journals H∞ Optimization of Tuned Inerter Damper with Negative Stiffness Device Subjected to Support Excitation

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Kun Ye ◽  
Patrice Nyangi
Keyword(s):  
Fixed Points ◽  
Damping Ratio ◽  
Negative Stiffness ◽  
Primary System ◽  
Stiffness Ratio ◽  
Maximum Displacement ◽  
Absolute Acceleration ◽  
Closed Form Solutions ◽  
Negative Stiffness Device ◽  
Support Excitation

In this study, H∞ optimization is conducted for a tuned inerter damper (TID) with negative stiffness device (denoted as TID_NSD) subjected to harmonic support excitation. The study shows that there are still two nonzero-frequency fixed points independent of the damping of the TID_NSD; therefore, the optimum tuning frequency and damping ratio for the TID_NSD are, respectively, derived based on the well-known fixed points theory. By imposing the zero-frequency fixed point having the same amplitude as the other two nonzero-frequency fixed points, the optimum negative stiffness ratio, which makes the primary system with a TID_NSD remain stable, is obtained. Moreover, the role of a negative stiffness device of a TID_NSD system in response control of a single degree-of-freedom (SDOF) structure is evaluated through parametric study. Also, a numerical analysis is conducted on both a SDOF and multiple DOFs structure to validate the feasibility of the derived formulas by simulations with real earthquake records. Numerical results demonstrate that the maximum displacement and the maximum absolute acceleration of the structure equipped with TID_NSD system are reduced by increasing the absolute value of negative stiffness ratio. The results also show that the optimally designed TID_NSD system outperforms the optimally designed TID system in terms of the displacement and absolute acceleration mitigation control. The closed-form solutions proposed in this study can be useful for the optimal design of the structure equipped with TID_NSD.

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 Parameters Optimization for a Kind of Dynamic Vibration Absorber with Negative Stiffness

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Yongjun Shen ◽  
Xiaoran Wang ◽  
Shaopu Yang ◽  
Haijun Xing
Keyword(s):  
Analytical Solution ◽  
Fixed Points ◽  
Numerical Solutions ◽  
Negative Stiffness ◽  
Vibration Absorber ◽  
Primary System ◽  
Stiffness Ratio ◽  
Dynamic Vibration Absorber ◽  
Dynamic Vibration ◽  
Frequency Curves

A new type of dynamic vibration absorber (DVA) with negative stiffness is studied in detail. At first, the analytical solution of the system is obtained based on the established differential motion equation. Three fixed points are found in the amplitude-frequency curves of the primary system. The design formulae for the optimum tuning ratio and optimum stiffness ratio of DVA are obtained by adjusting the three fixed points to the same height according to the fixed-point theory. Then, the optimum damping ratio is formulated by minimizing the maximum value of the amplitude-frequency curves according toH∞optimization principle. According to the characteristics of negative stiffness element, the optimum negative stiffness ratio is also established and it could still keep the system stable. In the end, the comparison between the analytical and the numerical solutions verifies the correctness of the analytical solution. The comparisons with three other traditional DVAs under the harmonic and random excitations show that the presented DVA performs better in vibration absorption. This result could provide theoretical basis for optimum parameters design of similar DVAs.

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.

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.

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.

Seismic Performance of T-Shaped CFT Column to Steel Frame Beam Connection – Experimental Study

2014 ◽  
Vol 919-921 ◽  
pp. 951-959 ◽  
Author(s):  
Yan Tao Li ◽  
Cheng Xiang Xu ◽  
Guo Feng Du
Keyword(s):  
Failure Mechanism ◽  
Damping Ratio ◽  
Local Buckling ◽  
Steel Tube ◽  
Steel Frame ◽  
Hysteretic Behavior ◽  
Stiffness Ratio ◽  
Joint Models ◽  
Panel Zone ◽  
Axial Forces

The focus of this research program is T-shaped CFT central column to steel frame beam connection. 3 joints with strong columns-weak beams and 1 joint with strong beams-weak columns 1:2 scale specimens were tested under constant axial loads and cyclic horizontal loads. Overall impact of axial force ratio and beam to column linear stiffness ratio on joint failure mechanism, hysteretic behavior, deformation ductility, and energy dissipation capability was investigated. Results showed that the failure mechanism for specimens with strong columns-weak beams was local buckling of the steel beam flanges and formation of the plastic hinges. There was minimum damage on the concrete column and joint panel zone. For a specimen with strong beams-weak columns, there was local buckling fracture on steel tube above and below the joint panel zone. Crushing of the core concrete was also observed with formation of the column hinges. It was found that both axial forces and beam to column linear stiffness ratio had impacts on joint capacity and ductility behavior of the specimens. Experiment results showed that the joint models had deformation ductility factor between 3.39 and 3.91 and viscous damping ratio between 0.46 and 0.51.

Negative Stiffness Device for Seismic Protection of Structures

2013 ◽  
Vol 139 (7) ◽  
pp. 1124-1133 ◽  
Author(s):  
A. A. Sarlis ◽  
D. T. R. Pasala ◽  
M. C. Constantinou ◽  
A. M. Reinhorn ◽  
S. Nagarajaiah ◽  
...  
Keyword(s):  
Negative Stiffness ◽  
Seismic Protection ◽  
Negative Stiffness Device

Optimization of Dynamic Vibration Absorbers for Suppressing Sound Radiation of Plate Structures

2020 ◽  
Vol 143 (2) ◽  
Author(s):  
Guanghe Huo ◽  
Zhaobo Chen ◽  
Yinghou Jiao ◽  
Xuezhi Zhu
Keyword(s):  
Fixed Points ◽  
Frequency Ratio ◽  
Vibration Suppression ◽  
Damping Ratio ◽  
Sound Radiation ◽  
Thin Plates ◽  
Optimal Frequency ◽  
Radiation Control ◽  
Dynamic Vibration ◽  
Analytical Expressions

Abstract Dynamic vibration absorber (DVA) is a practical tool used for sound and vibration suppression in the specific frequency band. The parameters of DVAs should be optimally tuned to obtain the best sound and vibration suppression application effects. When the DVAs are used for structural vibration reduction, DVAs’ two parameters which are the optimal frequency ratio and damping ratio have simple analytical expressions. However, the concise analytical expressions of the DVAs that are used for suppressing the structural sound radiations have not been reported. First, this paper investigates the characteristics of DVAs in suppressing sound radiation from thin plates. Second, the fixed points’ phenomenon of the sound radiations of the plate carrying DVAs is revealed. In addition, the classical fixed points’ theory is extended into the optimization process of the DVAs that are used for sound radiation control of the plate. The analytical expression of the optimal frequency ratio, as well as the damping ratio optimization method of the DVA, is simultaneously proposed. Third, the installation position of DVAs is also presented to obtain a better acoustic radiation effect. Finally, the numerical simulations are performed to verify the availability of the method. It is showed that the best sound radiation control effect could be obtained by adopting the optimization means proposed in this paper.

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.

Experimental Study on the Performance of the Laminated Steel Isolators

2013 ◽  
Vol 423-426 ◽  
pp. 1603-1607
Author(s):  
Yao Guo Xie ◽  
Ping He ◽  
Xian Qiang Qu ◽  
Hong Bin Cui
Keyword(s):  
Experimental Study ◽  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Damping Ratio ◽  
Dynamic Performance ◽  
Performance Testing ◽  
Stiffness Ratio ◽  
Static Stiffness ◽  
Comparison Of The Results

Through the analysis and comparison of the results of static and dynamic performance testing of a series of laminated steel pieces isolators used in the vibration isolation of warships, in the number and thickness of laminated steel pieces of the same circumstances, laminated steel arc and preload of test samples had a certain impact on the values ​​of static stiffness, dynamic stiffness, damping ratio as well as dynamic and static stiffness ratio.

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