On Vibration Control Using a Bistable Snap Through Absorber From a Force Balance Perspective

2013 ◽  
Author(s):  
David R. Johnson ◽  
R. L. Harne ◽  
K. W. Wang
Keyword(s):  
Vibration Control ◽  
Primary Structure ◽  
Vibration Suppression ◽  
External Disturbance ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Force Balance ◽  
Single Frequency ◽  
System Response ◽  
Primary System

One approach to vibration control is to apply a force to a primary structure which opposes excitation, effectively canceling the external disturbance. A familiar passive example of this approach is the linear tuned mass absorber. In this spirit, the utility of a bistable attachment for attenuating vibrations, especially in terms of the high-orbit, snap through dynamic, is investigated using the harmonic balance method and experiments. Analyses demonstrate the fundamental harmonic snap through dynamic, having commensurate frequency with the single-frequency harmonic excitation, may yield displacements either substantially in-phase or out-of-phase with the primary structure. During in-phase snap through, forces are generated by the bistable oscillator which reinforce the applied loading, resulting in dramatic amplification of primary system response. During out-of-phase snap through, forces are generated which are only partially opposed to the input, leading to a measure of host structure attenuation. The experiments verify the analytical findings and also uncover nonlinear dynamics not predicted by the analysis that have slightly favorable vibration suppression performance when compared with the out-of-phase, fundamental harmonic snap through action.

A Disturbance Cancellation Perspective on Vibration Control Using a Bistable Snap-Through Attachment

2014 ◽  
Vol 136 (3) ◽  
Author(s):  
David R. Johnson ◽  
R. L. Harne ◽  
K. W. Wang
Keyword(s):  
Vibration Control ◽  
External Disturbance ◽  
Spectral Characteristics ◽  
Harmonic Balance Method ◽  
Harmonic Excitation ◽  
Single Frequency ◽  
Vibration Attenuation ◽  
Disturbance Cancellation ◽  
High Orbit ◽  
Frequency Harmonic

One approach to vibration control is to apply a force to a primary structure that opposes the excitation, effectively canceling the external disturbance. A familiar passive example of this approach is the linear-tuned mass absorber. In this spirit, the utility of a bistable attachment for attenuating vibrations, especially in terms of the high-orbit, snap-through dynamic, is investigated using the harmonic balance method and experiments. Analyses demonstrate the fundamental harmonic snap-through dynamic, having commensurate frequency with the single-frequency harmonic excitation, may generate adverse constructive forces that substantially reinforce the applied excitation, primarily at lower frequencies. However, both analyses and experiments indicate that such high-orbit dynamics may be largely destabilized by increased bistable attachment damping. Destructive forces, which substantially oppose the excitation, are unique in that they lead to a form of vibration attenuation analogous to strictly adding damping to the host structure, leaving its spectral characteristics largely unaltered. The experiments verify the analytical findings and also uncover nonlinear dynamics not predicted by the analysis, which render similar attenuation effects.

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.

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.

Vibration Control of Nonlinear Rotating Beam Using Piezoelectric Actuator and Sliding Mode Approach

2006 ◽  
Author(s):  
X. Xue ◽  
J. Tang
Keyword(s):  
Vibration Control ◽  
Piezoelectric Actuator ◽  
Vibration Suppression ◽  
Control Method ◽  
Sliding Mode ◽  
External Disturbance ◽  
Rotating Beam ◽  
System States ◽  
Euler Bernoulli Beam ◽  
Beam Transverse Vibration

In this research, we develop a general methodology for the vibration control of nonlinear rotating beam. The dynamic model of a rotating Euler-Bernoulli beam integrated with piezoelectric actuator is formulated. An integral sliding mode control design is proposed for the vibration suppression of the system with nonlinear coupling effects between the hub rotation and the beam transverse vibration. The sliding surface is constructed using part of the system states, and the rotating hub dynamics is treated as the internal dynamics of the system under the condition that the states of the zero dynamics are bounded. The robust stability of the proposed controller is also guaranteed. A series of simulation studies demonstrate that the proposed control method can effectively suppress the beam vibrations induced by the hub rotation and the external disturbance.

Dual Functional Energy Harvesting and Vibration Control: Electromagnetic Resonant Shunt Series Tuned Mass Dampers

2012 ◽  
Author(s):  
Lei Zuo ◽  
Wen Cui
Keyword(s):  
Energy Harvesting ◽  
Vibration Control ◽  
Vibration Suppression ◽  
Primary System ◽  
Dual Functional ◽  
Novel Approach ◽  
Rlc Circuit ◽  
Gradient Based ◽  
And Performance ◽  
Resonant Shunt

This paper proposes a novel approach for dual-functional energy harvesting and vibration control by integrating the tuned mass damper (TMD) and electromagnetic shunted resonant damping. The viscous dissipative element between the TMD and primary system is replaced by an electromagnetic transducer shunted with a resonant RLC circuit. An efficient gradient based method is presented for the parameter optimization in the control framework for vibration suppression and energy harvesting. A case study is performed based on the Taipei 101 TMD. It is founded that by tuning the TMD resonance and circuit resonance close to that of the primary structure, the electromagnetic resonant shunt TMD achieves the enhanced effectiveness and robustness of double-mass series TMDs, without suffering from the significantly amplified motion stroke. It is also observed that the parameters and performance optimized for vibration suppression are close to those optimized for energy harvesting, and the performances are not sensitive to the resistance of the charging circuit or electrical load.

scholarly journals Dual-Functional Energy-Harvesting and Vibration Control: Electromagnetic Resonant Shunt Series Tuned Mass Dampers

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
Lei Zuo ◽  
Wen Cui
Keyword(s):  
Energy Harvesting ◽  
Vibration Control ◽  
Vibration Suppression ◽  
Primary System ◽  
Tuned Mass Dampers ◽  
Dual Functional ◽  
Rlc Circuit ◽  
Double Mass ◽  
Gradient Based ◽  
Resonant Shunt

This paper proposes a novel retrofittable approach for dual-functional energy-harvesting and robust vibration control by integrating the tuned mass damper (TMD) and electromagnetic shunted resonant damping. The viscous dissipative element between the TMD and primary system is replaced by an electromagnetic transducer shunted with a resonant RLC circuit. An efficient gradient based numeric method is presented for the parameter optimization in the control framework for vibration suppression and energy harvesting. A case study is performed based on the Taipei 101 TMD. It is found that by tuning the TMD resonance and circuit resonance close to that of the primary structure, the electromagnetic resonant-shunt TMD achieves the enhanced effectiveness and robustness of double-mass series TMDs, without suffering from the significantly amplified motion stroke. It is also observed that the parameters and performances optimized for vibration suppression are close to those optimized for energy harvesting, and the performance is not sensitive to the resistance of the charging circuit or electrical load.

Active Parameter Control of Nonlinear Vibrating Structures

1989 ◽  
Vol 56 (3) ◽  
pp. 658-666 ◽  
Author(s):  
S. F. Masri ◽  
R. K. Miller ◽  
T. J. Dehghanyar ◽  
T. K. Caughey
Keyword(s):  
Vibration Control ◽  
Primary Structure ◽  
Control Method ◽  
Direct Method ◽  
Primary System ◽  
System A ◽  
On Line ◽  
Reliability And Robustness ◽  
Related Paper ◽  
Active Control Method

A simple, yet efficient method is presented for the on-line vibration control of nonlinear, multidegree-of-freedom systems responding to arbitrary dynamic environments. The procedure uses nonlinear auxiliary mass dampers with adjustable motion-limiting stops located at selected positions throughout a given nonlinear system. A mathematical model of the system to be controlled is not needed for implementing the control algorithm. The degree of the primary structure oscillation near each vibration damper determines the damper’s actively-controlled gap size and activation time. By using control energy to adjust the damper parameters instead of directly attenuating the motion of the primary system, a significant improvement is achieved in the total amount of energy expended to accomplish a given level of vibration control. In a related paper, the direct method of Lyapunov is used to establish that the response of the controlled nonlinear primary structure is Lagrange stable. Numerical simulation studies of several example systems, as well as an experimental study with a mechanical model, demonstrate the feasibility, reliability, and robustness of the proposed semi-active control method.

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.

Parametric Studies of the Vibration Control Effects of a Nonlinear Damper System under Multi-Axis Excitations

2013 ◽  
Vol 712-715 ◽  
pp. 1682-1685
Author(s):  
Zheng Lu
Keyword(s):  
Numerical Simulations ◽  
Vibration Control ◽  
Primary Structure ◽  
Coefficient Of Restitution ◽  
Primary System ◽  
Mass Ratio ◽  
System Parameters ◽  
Shaped Container ◽  
Weight Penalty ◽  
Parametric Studies

This paper studies the influence of system parameters to the vibration control effects of a nonlinear damper system under multi-axis excitations. The nonlinear damper system is composed of a particle damper and a primary structure. Based on numerical simulations, it is shown that: increasing the mass ratio can improve the dampers effectiveness, but only up to a certain level; applying particles with a high value of the coefficient of restitution can result in a broader range of acceptable response levels; a lightly-damped primary system can achieve a considerable reduction in its response with a small weight penalty; and that a cylindrically-shaped container provides a higher level of effectiveness than a rectangularly-shaped one.

Semi-Analytical Modeling and Vibration Control of a Geometrically Nonlinear Plate

2017 ◽  
Vol 17 (04) ◽  
pp. 1771003 ◽  
Author(s):  
Atta Oveisi ◽  
Tamara Nestorović ◽  
Ngoc Linh Nguyen
Keyword(s):  
Harmonic Balance ◽  
Vibration Suppression ◽  
External Disturbance ◽  
Nonlinear Partial Differential Equation ◽  
Harmonic Balance Method ◽  
Single Mode ◽  
Piezo Actuator ◽  
Control Law ◽  
Geometrically Nonlinear ◽  
Relationship Of

This paper presents the dynamic modeling of a piezolaminated plate considering geometrical nonlinearities. The piezo-actuator and piezo-sensor are connected via proportional derivative feedback control law. The Hamilton’s principle is used to extract the strong form of the equation of motion with the reflection of the higher order strain terms by means of the strain–displacement relationship of the von Karman type. Then the nonlinear partial differential equation (PDE) obtained is converted to a nonlinear algebraic equation by employing the combination of harmonic balance method and single-mode Galerkin’s technique. Finally, the vibration suppression performance and sensitivity of the dynamic response is evaluated for various control parameters and magnitudes of external disturbance.

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