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.

scholarly journals Dynamic response of multi-degree-of-freedom systems with a Coulomb friction contact under harmonic excitation

2021 ◽  
Author(s):  
Luca Marino ◽  
Alice Cicirello
Keyword(s):  
Harmonic Excitation ◽  
Degree Of Freedom ◽  
Friction Contact ◽  
Engineering Structures ◽  
Stick Slip ◽  
State Response ◽  
Mdof Systems ◽  
Analytical Response ◽  
Dynamic Performances ◽  
Stick Slip Motion

Abstract This paper investigates the steady-state response of a multi-degree-of-freedom (MDOF) system with a Coulomb contact to harmonic excitation. Although discrete MDOF models are commonly used at early design stages to analyse the dynamic performances of engineering structures, the current understanding of the friction damping effects on MDOF behaviour is still limited due to the absence of analytical solutions. In this contribution, closed-form expressions of the continuous time response, the displacement transmissibility and the phase angle of each mass of the system are derived and validated numerically for 2DOF and 5DOF systems. Moreover, the features of the analytical response are investigated, obtaining the following results: (i) the determination of the minimum amounts of friction for which the resonant peaks become finite and (ii) for which stick-slip motion can be observed at high frequencies; (iii) an equation for the evaluation of invariant points for the displacement transmissibilities; (iv) a better understanding of phenomena such as the inversions of the transmissibility curves and the onset of additional resonant peaks due to the permanent sticking of the mass in contact. All these results show that MDOF systems exhibit significantly different dynamic behaviours depending on whether the friction contact and the harmonic excitation are applied to the same or different masses.

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.

Validation Techniques for 6-DOF Vibration Data Acquisition

2012 ◽  
Vol 55 (1) ◽  
pp. 10-24 ◽  
Author(s):  
Michael Hale ◽  
Jesse Porter
Keyword(s):  
Vibration Control ◽  
Control Systems ◽  
Field Data ◽  
Dynamic Test ◽  
Degree Of Freedom ◽  
Data Validation ◽  
Standard Equipment ◽  
Vibration Data ◽  
Mdof Systems

Multiple Degree of Freedom (MDOF) excitation systems and MDOF vibration control systems continue to improve, and are now standard equipment in many dynamic test laboratories. Determination of an input specification for such MDOF systems is critically dependent on properly acquired field data. Validation of field data will be discussed and demonstrated employing the same transformation tools used in both transformation-based 6-degree-of-freedom (6-DOF) vibration control and generalized MDOF vibration specification development (VSD).

A broadband flow energy harvester induced by the wake of a bluff body

2021 ◽  
Author(s):  
Wen-An Jiang ◽  
Xin-dong Ma ◽  
Yong Wang ◽  
Mao Liu ◽  
Li-qun Chen ◽  
...  
Keyword(s):  
Bluff Body ◽  
Permanent Magnets ◽  
Energy Harvester ◽  
Analytical Data ◽  
Degree Of Freedom ◽  
Nonlinear Flow ◽  
Physical Parameters ◽  
Restoring Force ◽  
Flow Energy ◽  
Two Degree Of Freedom

Abstract Wake galloping energy harvesting have been extensively developed to scavenge flow energy from vortex-induced oscillations. Hence, the wake-galloping harvester only has a natural frequency which leads to a very narrow bandwidth. Therefore, it does not operate well under the wide region of shedding frequencies in variable wind speed. To overcome the vital issue, this paper we explored a novel two-degree-of-freedom nonlinear flow energy harvester to collect flow energy induced by the wake of a bluff body. The nonlinear restoring force is realized by using a repulsive magnetic force between two cuboid-shaped permanent magnets, and the electromechanical coupling equations is presented. Based on the method of harmonic balance, the electromechanical governing equations is decoupled, and the first order harmonic solutions are implemented. The modulation equations are established, the amplitude-frequency figures of displacement and voltage are depicted with different detuning parameters. The superiority of the presented energy harvester is contrasted with the single-degree-of-freedom linear and nonlinear cases, the results revealed that the two-degree-of-freedom nonlinear scheme can enhance the bandwidth of flow energy capture. The effect of physical parameters on the scavenged power is discussed. The accuracy and efficiency of the approximate analytical data are examined by numerical simulations.

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.

A Framework for Efficiency Evaluation of Multi-Degree-of-Freedom Gear Trains

1996 ◽  
Vol 118 (4) ◽  
pp. 556-560 ◽  
Author(s):  
C. Innocenti
Keyword(s):  
Experimental Data ◽  
Finite Number ◽  
Degree Of Freedom ◽  
Gear Train ◽  
Efficiency Evaluation ◽  
Suggested Approach ◽  
New Approach ◽  
Gear Trains ◽  
Two Degree Of Freedom

The paper proposes a new approach to the efficiency evaluation of any one- or multi-degree-of-freedom gear trains. The suggested approach generalizes the known procedures developed for two-degree-of-freedom gear trains. It is based on the determination of a vector whose components are the torques delivered to the shafts of the gear train. Furthermore the paper shows that, for a notable category of gear trains, such a vector can have only a finite number of directions, which implies that a limited number of experimental data suffices for estimating the efficiency at any operational condition. Examples of application of the proposed methodology are provided.

Experimental Determination of the Complete Dynamical Properties of a Two-Degree-Of-Freedom Model Having Nearly Coincident Natural Frequencies

1967 ◽  
Vol 9 (5) ◽  
pp. 402-413 ◽  
Author(s):  
R. W. Traill-Nash ◽  
G. Long ◽  
C. M. Bailey
Keyword(s):  
Experimental Investigation ◽  
Experimental Determination ◽  
Natural Frequencies ◽  
Degree Of Freedom ◽  
Influence Coefficients ◽  
Stiffness Properties ◽  
Modes Of Vibration ◽  
Dynamical Properties ◽  
Two Degree Of Freedom

Existing techniques of resonance testing have shown a marked inability to find the principal modes, natural frequencies and levels of damping in a structure which possesses two or more close natural frequencies (1)§. This paper describes an experimental investigation on a two-degree-of-freedom model of a technique which makes use of dynamical influence coefficients (or receptances) measured at a number of stations on the structure (2) (3) (4) (5). The measured coefficients are used to calculate natural frequencies and modes of vibration, and the mass, damping and stiffness properties of the system. Several model configurations having different natural frequency separations were tested and no special difficulty resulted when natural frequencies were close or even coincident.

A New Algorithm for the Determination of the Workspace of Complex Planar Kinematic Chains

1995 ◽  
Author(s):  
Pascal Lê-Huu ◽  
Clément M. Gosselin
Keyword(s):  
Numerical Solution ◽  
Inverse Kinematics ◽  
Degree Of Freedom ◽  
Topological Graph ◽  
Kinematic Chains ◽  
Cartesian Space ◽  
Hybrid Manipulator ◽  
Three Degree Of Freedom ◽  
Two Degree Of Freedom

Abstract A new algorithm for the determination of the workspace of complex planar kinematic chains is presented in this paper. This algorithm is completely general since it can deal with any kind of topological graph and any set of parameters defined in a convention of notation. It uses the numerical solution of the inverse kinematics and is based on a wavefront expansion in the Cartesian space. Three examples are presented here, and lead to a dexterity mapping for two two-degree-of-freedom multi-loop manipulators and a three-degree-of-freedom hybrid manipulator.

The Steady-State Response of a Two-Degree-of-Freedom Bilinear Hysteretic System

1965 ◽  
Vol 32 (1) ◽  
pp. 151-156 ◽  
Author(s):  
W. D. Iwan
Keyword(s):  
Approximate Solution ◽  
Steady State ◽  
Degree Of Freedom ◽  
Finite Limit ◽  
Steady State Response ◽  
Varying Parameters ◽  
Hysteretic System ◽  
State Response ◽  
The Stability ◽  
Two Degree Of Freedom

The method of slowly varying parameters is used to obtain an approximate solution for the steady-state response of a two-degree-of-freedom bilinear hysteretic system. The stability of the system is investigated and it is shown that such a system exhibits unbounded amplitude resonance when the level of excitation is increased beyond a certain finite limit.

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