Resonance and vibration control of two-degree-of-freedom nonlinear electromechanical system with harmonic excitation

2015 ◽  
Vol 81 (4) ◽  
pp. 2003-2019 ◽  
Author(s):  
Y. A. Amer
Keyword(s):  
Vibration Control ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Electromechanical System ◽  
Two Degree Of Freedom

Vibration Control of Two-Degree-of-Freedom Structures Utilizing Sloshing in Nearly Square Tanks

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Takashi Ikeda ◽  
Yuji Harata ◽  
Shota Ninomiya
Keyword(s):  
Vibration Control ◽  
Equations Of Motion ◽  
Excitation Frequency ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Response Curves ◽  
Chaotic Motions ◽  
Installation Angle ◽  
Two Degree Of Freedom ◽  
Theoretical Results

This paper investigates the vibration control of a towerlike structure with degrees of freedom utilizing a square or nearly square tuned liquid damper (TLD) when the structure is subjected to horizontal, harmonic excitation. In the theoretical analysis, when the two natural frequencies of the two-degree-of-freedom (2DOF) structure nearly equal those of the two predominant sloshing modes, the tuning condition, 1:1:1:1, is nearly satisfied. Galerkin's method is used to derive the modal equations of motion for sloshing. The nonlinearity of the hydrodynamic force due to sloshing is considered in the equations of motion for the 2DOF structure. Linear viscous damping terms are incorporated into the modal equations to consider the damping effect of sloshing. Van der Pol's method is employed to determine the expressions for the frequency response curves. The influences of the excitation frequency, the tank installation angle, and the aspect ratio of the tank cross section on the response curves are examined. The theoretical results show that whirling motions and amplitude-modulated motions (AMMs), including chaotic motions, may occur in the structure because swirl motions and Hopf bifurcations, followed by AMMs, appear in the tank. It is also found that a square TLD works more effectively than a conventional rectangular TLD, and its performance is further improved when the tank width is slightly increased and the installation angle is equal to zero. Experiments were conducted in order to confirm the validity of the theoretical results.

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.

scholarly journals Multi-degree-of-freedom systems with a Coulomb friction contact: analytical boundaries of motion regimes

2021 ◽  
Author(s):  
Luca Marino ◽  
Alice Cicirello
Keyword(s):  
Ad Hoc ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Physical Parameters ◽  
Dimensional Parameter ◽  
Stick Slip ◽  
State Response ◽  
Mdof Systems ◽  
Two Degree Of Freedom

AbstractThis paper proposes an approach for the determination of the analytical boundaries of continuous, stick-slip and no motion regimes for the steady-state response of a multi-degree-of-freedom (MDOF) system with a single Coulomb contact to harmonic excitation. While these boundaries have been previously investigated for single-degree-of-freedom (SDOF) systems, they are mostly unexplored for MDOF systems. Closed-form expressions of the boundaries of motion regimes are derived and validated numerically for two-degree-of-freedom (2DOF) systems. Different configurations are observed by changing the mass in contact and by connecting the rubbing wall to: (i) the ground, (ii) the base or (iii) the other mass. A procedure for extending these results to systems with more than 2DOFs is also proposed for (i)–(ii) and validated numerically in the case of a 5DOF system with a ground-fixed contact. The boundary between continuous and stick-slip regimes is obtained as an extension of Den Hartog’s formulation for SDOF systems with Coulomb damping (Trans Am Soc Mech Eng 53: 107–115, 1931). The boundary between motion and no motion regimes is derived with an ad hoc procedure, based on the comparison between the overall dynamic load and the friction force acting on the mass in contact. The boundaries are finally represented in a two-dimensional parameter space, showing that the shape and the extension of the regions associated with the three motion regimes can change significantly when different physical parameters and contact configurations are considered.

Robust Control of a Flexible Arm

1994 ◽  
Vol 6 (3) ◽  
pp. 214-219
Author(s):  
Kang-Zhi Liu ◽  
◽  
Koji Higaki ◽  
Tsutomu Mita
Keyword(s):  
Robust Control ◽  
Control Theory ◽  
Vibration Control ◽  
Feedback Controller ◽  
Degree Of Freedom ◽  
Matching Method ◽  
Robust Controller ◽  
Flexible Arm ◽  
Feedforward Controller ◽  
Two Degree Of Freedom

This paper addresses the vibration control of a flexible arm with a two-degree-of-freedom robust controller. The feedback controller is designed by <I>H</I>∞ control theory to achieve robust distrubance attenuation, and the feedforward controller is designed by a signal-matching method to improve the trasient response. An experiment verifies that this methodology is effective.

scholarly journals Dynamics and Stability of a Two Degree of Freedom Oscillator With an Elastic Stop

2005 ◽  
Vol 1 (1) ◽  
pp. 94-102 ◽  
Author(s):  
Madeleine Pascal
Keyword(s):  
Periodic Solutions ◽  
Analytical Form ◽  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Periodic Motions ◽  
External Excitation ◽  
Time Duration ◽  
Existence Of Periodic Solutions ◽  
The Stability ◽  
Two Degree Of Freedom

A two degree of freedom oscillator with a colliding component is considered. The aim of the study is to investigate the dynamic behavior of the system when the stiffness obstacle changes to a finite value to an infinite one. Several cases are considered. First, in the case of rigid impact and without external excitation, a family of periodic solutions are found in analytical form. In the case of soft impact, with a finite time duration of the shock, and no external excitation, the existence of periodic solutions, with an arbitrary value of the period, is proved. Periodic motions are also obtained when the system is submitted to harmonic excitation, in both cases of rigid or soft impact. The stability of these periodic motions is investigated for these four cases.

Variable Damping and Stiffness Vibration Control With Two Magnetorheological Fluid Dampers in Series

2005 ◽  
Author(s):  
Yanqing Liu ◽  
Hiroshi Matsuhisa ◽  
Hideo Utsuno ◽  
Jeong Gyu Park
Keyword(s):  
Vibration Control ◽  
Vibration Isolation ◽  
Degree Of Freedom ◽  
Structural Vibration ◽  
Small Current ◽  
Mr Dampers ◽  
In Series ◽  
Variable Damping ◽  
Fluid Dampers ◽  
Two Degree Of Freedom

Vibration isolation methods that vary damping and stiffness have demonstrated excellent authority over system vibration, thus, potentially making them attractive for many applications. However, conventional devices for controlling variable stiffness are typically complicated and difficult to implement in most applications. To address this issue, a new method is proposed that requires two magnetorheological (MR) fluid dampers placed in series. With this configuration, variable damping and stiffness vibration control is simultaneously achieved by varying a small current to the MR dampers. This paper presents a theoretical and experimental analysis of a two degree-of-freedom system that is controlled by the MR dampers. Five different control schemes involving the variable damping and stiffness are explored. The time and frequency responses of the two degree-of-freedom system to a random input show that combined variable damping and stiffness control provides the best vibration isolation over a frequency range spanning the system’s two structural vibration modes. The experimental results agree well with the theoretical analysis.

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