Vibration control through the robust nonlinear absorber with negative stiffness and internal resonance creation

2022 ◽  
pp. 107754632110623
Author(s):  
Peiman Harouni ◽  
Nader Khajeh Ahmad Attari ◽  
Fayaz Rahimzadeh Rofooei
Keyword(s):  
Internal Resonance ◽  
Vibration Suppression ◽  
Low Frequency ◽  
Multiple Scale ◽  
Harmonic Excitation ◽  
Negative Stiffness ◽  
Primary System ◽  
Nonlinear Absorber ◽  
Negative Stiffness Mechanism ◽  
Stiffness And Damping

In this study, a nonlinear absorber that works with a negative stiffness mechanism is suggested to mitigate vibration, and its effect on the reduction of vibration is investigated. The negative stiffness, which is inherently nonlinear, creates internal resonance; therefore, the vibration energy can be transmitted from low-frequency to high-frequency vibrating modes, causing vibration suppression. The nonlinear absorber is added to the primary nonlinear system, and when the main system is subjected to external resonance due to harmonic excitation, the negative stiffness parameter of absorber is so adjusted that autoparametric resonance occurs and vibration is reduced. First, the mathematical model of the system is presented and the governing differential equations of the motion are derived, and then, using the multiple scale method, the equations are solved for the case without, and with the 1:3 internal resonance. The responses and their stability are inspected, discussed, and compared. After that, the effect of negative stiffness and damping parameters on vibration amplitude reduction is investigated and the adequacy of the proposed absorber will be demonstrated by numerical analysis. Finally, the energy exchange between the primary system and the absorber will be demonstrated by plotting the responses in the state space and the displacement response Fourier spectrum.

The Two-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation

2005 ◽  
Vol 128 (1) ◽  
pp. 56-65 ◽  
Author(s):  
Lei Zuo ◽  
Samir A. Nayfeh
Keyword(s):  
Vibration Suppression ◽  
Single Mode ◽  
Tuned Mass Damper ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Primary System ◽  
H Infinity ◽  
Mass Damper ◽  
Mode Vibration ◽  
Two Degree Of Freedom

Whenever a tuned-mass damper is attached to a primary system, motion of the absorber body in more than one degree of freedom (DOF) relative to the primary system can be used to attenuate vibration of the primary system. In this paper, we propose that more than one mode of vibration of an absorber body relative to a primary system be tuned to suppress single-mode vibration of a primary system. We cast the problem of optimization of the multi-degree-of-freedom connection between the absorber body and primary structure as a decentralized control problem and develop optimization algorithms based on the H2 and H-infinity norms to minimize the response to random and harmonic excitations, respectively. We find that a two-DOF absorber can attain better performance than the optimal SDOF absorber, even for the case where the rotary inertia of the absorber tends to zero. With properly chosen connection locations, the two-DOF absorber achieves better vibration suppression than two separate absorbers of optimized mass distribution. A two-DOF absorber with a negative damper in one of its two connections to the primary system yields significantly better performance than absorbers with only positive dampers.

Modeling and Design of an Inertial Vibration Reflector

1997 ◽  
Vol 119 (1) ◽  
pp. 20-27
Author(s):  
R. G. Longoria ◽  
V. A. Narayanan
Keyword(s):  
Vibration Suppression ◽  
Active Vibration Control ◽  
Low Frequency ◽  
Dominant Frequency ◽  
Prototype System ◽  
Primary System ◽  
Transient Vibration ◽  
Modeling And Analysis ◽  
Reflector System ◽  
Oriented Parallel

This paper presents the modeling and analysis of a novel vibration suppression device. This reflector system exerts inertial forces, induced by tuned pendular motion, to control translational vibration of a primary system. Tuning of the reflector critically depends on the parameters of the pendula and on the rotational speed at which they are spun about an axis oriented parallel to the undesired motion. Consequently, one of its most appealing attributes is this devices’s ability to be tuned to, and thus actively track, the dominant frequency of disturbance forces. The paper describes how governing equations from an integrated physical model are developed using a bond graph approach and then used to derive relations applicable in design of an inertial reflector system. It is shown how the model supports component selection and tradeoff studies as well as simulation. Experimental results from testing of a laboratory realization of a prototype system are used to verify the design and to compare with simulation of a mathematical model. The results from the laboratory demonstrate the ability of the inertial reflector to control steady and transient vibration, and the favorable results suggest extended investigation for active vibration control situations. In particular, applications in low frequency vibration mitigation are promising.

scholarly journals An Air Spring Vibration Isolator Based on a Negative-Stiffness Structure for Vehicle Seat

2021 ◽  
Vol 11 (23) ◽  
pp. 11539
Author(s):  
Cong Hung Nguyen ◽  
Cong Minh Ho ◽  
Kyoung Kwan Ahn
Keyword(s):  
Vibration Isolation ◽  
Dynamic Stiffness ◽  
Low Frequency ◽  
Negative Stiffness ◽  
Vibration Isolator ◽  
Air Spring ◽  
Nonlinear Force ◽  
Mechanical Spring ◽  
Negative Stiffness Mechanism ◽  
Vehicle Seat

This research introduces an air spring vibration isolator system (ASVIS) based on a negative-stiffness structure (NSS) to improve the vehicle seat’s vibration isolation performance at low excitation frequencies. The main feature of the ASVIS consists of two symmetric bellows-type air springs which were designed on the basis of a negative stiffness mechanism. In addition, a crisscross structure with two straight bars was also used as the supporting legs to provide the nonlinear characteristics with NSS. Moreover, instead of using a vertical mechanical spring, a sleeve-type air spring was employed to provide positive stiffness. As a result, as the weight of the driver varies, the dynamic stiffness of the ASVIS can be easily adjusted and controlled. Next, the effects of the dimension parameters on the nonlinear force and nonlinear stiffness of ASVIS were analyzed. A design process for the ASVIS is provided based on the analytical results in order to achieve high static–low dynamic stiffness. Finally, numerical simulations were performed to evaluate the effectiveness of the ASVIS. The results obtained in this paper show that the values of the seat displacement of the ASVIS with NSS were reduced by 77.16% in comparison with those obtained with the traditional air spring isolator without NSS, which indicates that the design of the ASVIS isolator with NSS allows the effective isolation of vibrations in the low-frequency region.

scholarly journals A Novel Sensor Prototype with Enhanced and Adaptive Sensitivity Based on Negative Stiffness Mechanism

Sensors ◽  
2020 ◽  
Vol 20 (16) ◽  
pp. 4644
Author(s):  
Lijun Liu ◽  
Yongzhong Nie ◽  
Ying Lei
Keyword(s):  
Low Frequency ◽  
High Sensitivity ◽  
Negative Stiffness ◽  
Micro Electro Mechanical Systems ◽  
Enhanced Sensitivity ◽  
Landslide Hazards ◽  
Negative Stiffness Mechanism ◽  
Low Sensitivity ◽  
Electric Filed ◽  
Design And Manufacture

Loess–mudstone/soil-rock interfacial landslide is one of the prominent landslide hazards that occurs in soil rock contacting zones. It is necessary to develop sensors with high sensitivity to weak and low frequency vibrations for the early warning of such interfacial landslides. In this paper, a novel monitoring sensor prototype with enhanced and adaptive sensitivity is developed for this purpose. The novelty of the sensitive sensor is based on the variable capacitances and negative stiffness mechanism due to the electric filed forces on the vibrating plate. Owing to the feedback control of adjustable electrostatic field by an embedded micro controller, the sensor has adaptive amplification characteristics with high sensitivity to weak and low frequency input and low sensitivity to high input. The design and manufacture of the proposed sensor prototype by Micro-Electro-Mechanical Systems (MEMS) with proper packaging are introduced. Post-signal processing is also presented. Some preliminary testing of the prototype and experimental monitoring of sand interfacial slide which mimics soil–rock interfacial landslide were performed to demonstrate the performance of the developed sensor prototype with adaptive amplification and enhanced sensitivity.

The Multi-Degree-of-Freedom Tuned-Mass Damper for Suppression of Single-Mode Vibration Under Random and Harmonic Excitation

2003 ◽  
Author(s):  
Lei Zuo ◽  
Samir A. Nayfeh
Keyword(s):  
Decentralized Control ◽  
Vibration Suppression ◽  
Single Mode ◽  
Tuned Mass Damper ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Primary System ◽  
H Infinity ◽  
Mass Damper ◽  
Mode Vibration

Whenever a tuned-mass damper is attached to a primary system, there is potential for utilization of motion of the absorber body in more than one degree of freedom relative to the primary system. In this paper, we propose that more than one mode of vibration of an absorber body relative to a primary system be tuned to a single natural frequency of the primary system. We cast the problem of optimizing the multi-degree-of-freedom connection between the absorber body and primary structure as a decentralized control problem, and develop optimization algorithms based on the H2 and H-infinity norms to minimize the response to random and harmonic excitations, respectively. We find that a two-DOF absorber can attain better performance than the optimal SDOF absorber, even for the case where the rotary inertia of the absorber tends to be zero. With properly chosen connection locations, the two-DOF absorber can achieve better vibration suppression than two separate absorbers of optimized mass distribution. We also find that a two-DOF absorber with negative dampers in some of the connections to the primary system can obtain much better performance than absorbers with only positive dampers.

Characteristics and Optimization of Series Multiple Tuned-Mass Dampers

2007 ◽  
Author(s):  
Lei Zuo
Keyword(s):  
Total Mass ◽  
Vibration Suppression ◽  
Primary System ◽  
Mass Ratio ◽  
Dynamic Vibration Absorber ◽  
Tuned Mass Dampers ◽  
In Series ◽  
New Type ◽  
Stiffness And Damping ◽  
Better Than

Tuned-mass damper (TMD), or dynamic vibration absorber (DVA), is a very practical and effective device for vibration suppression. Various types of tuned-mass dampers have been proposed in literature, including the classic TMD, (parallel) multiple TMDs, multi-degree-of-freedom (DOF) TMD, and three-element TMD. In this paper we study the characteristics and optimization of a new type of TMD system, in which multiple absorbers are connected to the primary system in series. Structured H2 and H∞ control methods are adopted to optimize the parameters of spring stiffness and damping coefficients for random and harmonic vibration. It is found that series multiple TMDs are more effective and robust than all the other types of TMDs of the same mass ratio. The series two TMDs of total mass ratio 5% can appear to have 31%–66% more mass than the classical TMD, and it can perform better than parallel ten TMDs of the same total mass ratio. The series TMDs are also less sensitive to the parameter changes of the primary system than other TMD(s). Unlike the parallel multiple TMDs, the optimal mass distribution among absorbers in series TMDs is far from the case of equal masses, but instead the first absorber mass is much larger than the second one. Similar to the two-DOF TMD, the optimal series two TMDs also have zero damping in one of its two connections and further increased effectiveness can be obtained if negative dashpot is allowed.

scholarly journals Enhancing Vibration Isolation Performance by Exploiting Novel Spring-Bar Mechanism

2021 ◽  
Vol 11 (19) ◽  
pp. 8852
Author(s):  
Baiyang Shi ◽  
Jian Yang ◽  
Tianyun Li
Keyword(s):  
Power Flow ◽  
Vibration Isolation ◽  
Vibration Suppression ◽  
Low Frequency ◽  
Input Power ◽  
Integrated System ◽  
Negative Stiffness ◽  
Response Force ◽  
Force Transmission ◽  
Chaotic Motions

This study investigates the use of a spring-bar mechanism (SBM) in a vibration suppression system to improve its performance. The SBM, comprising bars and springs, is configured with a conventional linear spring-damper isolator unit. The dynamic response, force transmissibility, and vibration energy flow behaviour are studied to evaluate the vibration suppression performance of the integrated system. It is found that the SBM can introduce hardening, softening stiffness, or double-well potential characteristics to the system. By tuning the SBM parameters, constant negative stiffness is achieved so that the natural frequency of the overall system is reduced for enhanced low-frequency vibration isolation. It is also found that the proposed design yields a wider effective isolation range compared to the conventional spring-damper isolator and a previously proposed isolator with a negative stiffness mechanism. The frequency response relation of the force-excited system is derived using the averaging method and elliptical functions. It is also found that the system can exhibit chaotic motions, for which the associated time-averaged power is found to tend to an asymptotic value as the averaging time increases. It is shown that the time-averaged power flow variables can be used as uniform performance indices of nonlinear vibration isolators exhibiting periodic or chaotic motions. It is shown that the SBM can assist in reducing force transmission and input power, thereby expanding the frequency range of vibration attenuations.

Design and experiments of a quasi–zero-stiffness isolator with a noncircular cam-based negative-stiffness mechanism

2020 ◽  
Vol 26 (21-22) ◽  
pp. 1935-1947
Author(s):  
Ming Li ◽  
Wei Cheng ◽  
Ruili Xie
Keyword(s):  
Harmonic Balance ◽  
Experimental Studies ◽  
Approximation Error ◽  
Low Frequency ◽  
Harmonic Balance Method ◽  
Negative Stiffness ◽  
Restoring Force ◽  
Stiffness Characteristic ◽  
Physical Prototype ◽  
Negative Stiffness Mechanism

This article presents a quasi–zero-stiffness isolator with a cam-based negative-stiffness mechanism, where the cam has a user-defined noncircular profile to generate negative stiffness to counterbalance the positive stiffness of the vertical spring and yield the quasi–zero-stiffness characteristic around the equilibrium position. Unlike previous studies, the proposed quasi–zero-stiffness isolator has the preferable feature that the desired cubic restoring force can be directly obtained through the well-designed profile of the cam in the negative-stiffness mechanism with the friction considered during the model design, rather than through the Taylor expansion and friction-ignoring assumption, which can avoid the approximation error between the theoretical design and the specific realization. The pure-cubic nonlinear differential equation of motion of the quasi–zero-stiffness isolator is derived and solved with the harmonic balance method, followed by the discussion of the relevant dynamic characteristics. Experimental studies are carried out based on the physical prototype of the quasi–zero-stiffness isolator. The results show that the quasi–zero-stiffness isolator can greatly extend the isolation frequency bandwidth and has a much lower resonance peak. In the low-frequency band, the quasi–zero-stiffness isolator greatly outperforms the corresponding linear system but is equivalent or even inferior in the high-frequency range with the increase of excitation force.

Vibration Suppression of Flexible Structures Utilizing Internal Resonance of Liquid Sloshing in a Nearly Square Tank

2010 ◽  
Author(s):  
Takashi Ikeda
Keyword(s):  
Frequency Response ◽  
Internal Resonance ◽  
Vibration Suppression ◽  
Equations Of Motion ◽  
Flexible Structures ◽  
Harmonic Excitation ◽  
Liquid Sloshing ◽  
Maximum Efficiency ◽  
Tuned Liquid Damper ◽  
Response Curves

This paper proposes a new idea to utilize the internal resonance of two different sloshing modes in a nearly square tank when used as a tuned liquid damper (TLD). This idea results in achieving higher efficiency of vibration suppression for flexible structures subjected to horizontal harmonic excitation. Namely, the two sloshing modes (1, 0) and (0, 1) in a nearly square tank are degenerated and hence their natural frequencies are nearly equal with each other. Because the two predominant sloshing modes are nonlinearly coupled, internal resonance is expected to occur. Galerkin’s method is used to determine the modal equations of motion for liquid sloshing. Then, van der Pol’s method is used to determine the expressions of the frequency response curves. Frequency response curves and bifurcation sets are numerically calculated. From these results, the optimal values of the size and instillation angle of the tank can be determined in order to achieve maximum efficiency of vibration suppression in a flexible structure. Experiments confirmed the validity of the theoretical analysis.

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