On the Passive Control of Friction-Induced Instability Due to Mode Coupling

2019 ◽  
Vol 141 (8) ◽  
Author(s):  
Alborz Niknam ◽  
Kambiz Farhang
Keyword(s):  
Friction Force ◽  
Parameter Space ◽  
Mode Coupling ◽  
Degrees Of Freedom ◽  
Passive Control ◽  
Original System ◽  
Contact Friction ◽  
Primary System ◽  
Combined System ◽  
Loss Of Contact

This study investigates a passive controller for a coupled two degrees-of-freedom (DOFs) oscillator to suppress friction-induced mode-coupling instability. The primary system is acted upon by a friction force of a moving belt and static coupling of the oscillator provided with an oblique spring. The combined system, original system plus absorber, response is governed by two sets of differential equations to include contact and loss of contact between the mass and the belt. Therefore, the model accounts for two sources of nonlinearity in the system: (1) discontinuity in the friction force and (2) intermittent loss of contact. Friction coefficient and absorber orientation are used to define planar parameter space for stability analysis. For various mass ratios, the parameter space is divided into stable and unstable zones by defining stability boundaries. In general, an absorber expands the stability region and provides a significant reduction in transient response overshoot and settling time. Incorporation of the absorber also prevents mass-belt separation, thereby suppressing the belt-speed-overtake by the primary mass.

Evaluation of Energy and Power Flow in a Nonlinear Energy Sink Attached to a Linear Primary Oscillator

2019 ◽  
Vol 141 (6) ◽  
Author(s):  
Christian E. Silva ◽  
Amin Maghareh ◽  
Hongcheng Tao ◽  
Shirley J. Dyke ◽  
James Gibert
Keyword(s):  
Power Flow ◽  
Degrees Of Freedom ◽  
Nonlinear Energy Sink ◽  
Primary System ◽  
Combined System ◽  
Analytical Treatment ◽  
Different Types ◽  
Energy Sink ◽  
And Performance ◽  
Nonlinear Energy

Abstract The objective of this study is to develop a novel methodology to assess the energy flow between a nonlinear energy sink (NES) and the primary system it is attached to in terms of energy orientation, which is directly related to the sign of the power present on the primary system. To extend the work done in previous studies, which have focused primarily on the analytical treatment, characterization, and performance evaluation of NES as passive nonlinear dampers for structures under different types of excitations, this study incorporates a methodology for determining whether energy is entering or leaving a primary oscillator when interacting with an NES, by means of considering the power flow of the primary oscillator. Several current measures for evaluating the effectiveness of the NES at extracting and dissipating energy irreversibly are considered through numerical simulations of systems with different damping cases of the NES. Each case provides a different dissipation scenario in the combined system, which is subjected to different types of base excitation signals such as impulse and seismic records. The methodology is further validated experimentally using a two degrees-of-freedom system with an NES attached to the second mass. Comparisons of the modeled responses versus the measured responses are provided for several physical damping realization scenarios in the NES.

Friction-Induced Vibration Due to Mode-Coupling and Intermittent Contact Loss

2018 ◽  
Vol 141 (2) ◽  
Author(s):  
Alborz Niknam ◽  
Kambiz Farhang
Keyword(s):  
Friction Force ◽  
Mode Coupling ◽  
Degrees Of Freedom ◽  
Normal Load ◽  
Contact Stiffness ◽  
Relative Mass ◽  
Mass Motion ◽  
Stick Slip ◽  
Single Mass ◽  
Intermittent Contact

A two degrees-of-freedom (2DOFs) single mass-on-belt model is employed to study friction-induced instability due to mode-coupling. Three springs, one representing contact stiffness, the second providing lateral stiffness, and the third providing coupling between tangential and vertical directions, are employed. In the model, mass contact and separation are permitted. Therefore, nonlinearity stems from discontinuity due to dependence of friction force on relative mass-belt velocity and separation of mass-belt contact during oscillation. Eigenvalue analysis is carried out to determine the onset of instability. Within the unstable region, four possible phases that include slip, stick, separation, and overshoot are found as possible modes of oscillation. Piecewise analytical solution is found for each phase of mass motion. Then, numerical analyses are used to investigate the effect of three parameters related to belt velocity, friction coefficient, and normal load on the mass response. It is found that the mass will always experience stick-slip, separation, or both. When separation occurs, mass can overtake the belt causing additional nonlinearity due to friction force reversal. For a given coefficient of friction, the minimum normal load to prevent separation is found proportional to the belt velocity.

scholarly journals An Efficient Contact Model for the Simulation of Cargo Airdrop Extraction Phase

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Leiming Ning ◽  
Jichang Chen ◽  
Mingbo Tong
Keyword(s):  
Degrees Of Freedom ◽  
Friction Model ◽  
Rigid Bodies ◽  
Contact Dynamics ◽  
Moving Frame ◽  
Contact Friction ◽  
Practical Implementation ◽  
Contact Formulation ◽  
Efficient Code ◽  
Extraction Phase

A high-fidelity cargo airdrop simulation requires the accurate modeling of the contact dynamics between an aircraft and its cargo. This paper presents a general and efficient contact-friction model for the simulation of aircraft-cargo coupling dynamics during an airdrop extraction phase. The proposed approach has the same essence as the finite element node-to-segment contact formulation, which leads to a flexible, straightforward, and efficient code implementation. The formulation is developed under an arbitrary moving frame with both aircraft and cargo treated as general six degrees-of-freedom rigid bodies, thus eliminating the restrictions of lateral symmetric assumptions in most existing methods. Moreover, the aircraft-cargo coupling algorithm is discussed in detail, and some practical implementation details are presented. The accuracy and capability of the present method are demonstrated through four numerical examples with increasing complexity and fidelity.

Transient Response of MDOF Systems With Inerters to Nonstationary Stochastic Excitation

2017 ◽  
Vol 84 (10) ◽  
Author(s):  
Sami F. Masri ◽  
John P. Caffrey ◽  
Hui Li
Keyword(s):  
Degrees Of Freedom ◽  
Broad Band ◽  
Primary System ◽  
Mean Square ◽  
Stochastic Excitation ◽  
Mass Ratio ◽  
Tuning Parameters ◽  
Mdof Systems ◽  
Mean Square Response ◽  
Arbitrary Location

Explicit, closed-form, exact analytical expressions are derived for the covariance kernels of a multi degrees-of-freedom (MDOF) system with arbitrary amounts of viscous damping (not necessarily proportional-type), that is equipped with one or more auxiliary mass damper-inerters placed at arbitrary location(s) within the system. The “inerter” is a device that imparts additional inertia to the vibration damper, hence magnifying its effectiveness without a significant damper mass addition. The MDOF system is subjected to nonstationary stochastic excitation consisting of modulated white noise. Results of the analysis are used to determine the dependence of the time-varying mean-square response of the primary MDOF system on the key system parameters such as primary system damping, auxiliary damper mass ratio, location of the damper-inerter, inerter mass ratio, inerter node choices, tuning of the coupling between the damper-inerter and the primary system, and the excitation envelope function. Results of the analysis are used to determine the dependence of the peak transient mean-square response of the system on the damper/inerter tuning parameters, and the shape of the deterministic intensity function. It is shown that, under favorable dynamic environments, a properly designed auxiliary damper, encompassing an inerter with a sizable mass ratio, can significantly attenuate the response of the primary system to broad band excitations; however, the dimensionless “rise-time” of the nonstationary excitation substantially reduces the effectiveness of such a class of devices (even when optimally tuned) in attenuating the peak dynamic response of the primary system.

A Comparative Study of Mass Based Vibration Dampers

2017 ◽  
Author(s):  
Mohamed Gharib ◽  
Mansour Karkoub
Keyword(s):  
Comparative Study ◽  
Passive Control ◽  
Initial Conditions ◽  
Free Vibrations ◽  
Decay Rates ◽  
Coupled Systems ◽  
Primary System ◽  
Operating Personnel ◽  
Control Techniques ◽  
Dynamic Structures

Undesired vibrations in structures, buildings, and machines lead to reduction in the life of the system and greatly affects the safety of the occupying or operating personnel. In addition, economic and time losses could result from needed repairs or reconstruction. Many control techniques, active and passive, have been devised over the years to reduce/eliminate the vibrations in the aforementioned systems. Passive vibration control techniques are favorable over the active ones due to their simplicity, ease of implementation, cost, and power consumption. In dynamic structures, such as large buildings, passive control techniques are favored over their active counterparts. The most common types of passive control devices are tuned mass and impact dampers. The advocates of each of these devices boasts advantages of the others; however, there have been no systematic studies to compare and quantify the effectiveness of each of these types of devices as well as their suitability for specific applications. In this paper, a comparative study between the tuned mass dampers and impact dampers is conducted. A one-story structure is used to show the effectiveness of each of these devices in absorbing the vibrations of the structure. The coupled systems are modeled and simulated under free vibrations. The time responses are acquired using the same geometric parameters, excitation, and initial conditions. The comparisons are based on the settling time and amplitude decay rates of the primary system using each damper type. The numerical results show that both dampers can produce similar dampening effects if the parameters are optimized; however, correlating the dampers parameters is a challenging problem in the field of vibration and control.

Reflections and Conclusions

2017 ◽  
pp. 626-653
Keyword(s):  
Mode Coupling ◽  
Degrees Of Freedom ◽  
Subsequent Development ◽  
Eyewitness Testimony ◽  
Design Criteria ◽  
Dynamic Design ◽  
Two Degrees Of Freedom ◽  
Long Span ◽  
Gate Design

In this chapter, reflection on the discovery of gate instability mechanisms is provided. Stemming from Ishii's encounter as an undergraduate with the Wachi gate failure and his subsequent development of the theory for eccentricity instability, a framework for future analyses of other gate instabilities was established. The study of two degrees-of-freedom instabilities of long-span gates created a paradigm for mode coupling in hydraulic gate vibrations. The Folsom failure occurred with eyewitness testimony claiming to have heard and felt vibration. The path to understanding the mechanism that could produce vibration of the Folsom gate was the realization that the skinplate can be easily excited to undergo streamwise vibration. To counteract such vibration, dynamic design criteria for Tainter gates are needed. A draft formulation of dynamic guidelines for Tainter gate design is developed. We hope for feedback from those who use the guidelines to provide for the continuing improvement of the guidelines.

scholarly journals Structural Reanalysis Based on FRFs Using Sherman–Morrison–Woodbury Formula

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Jun Ren ◽  
Qianghao Zhang
Keyword(s):  
Degrees Of Freedom ◽  
Salient Feature ◽  
Original System ◽  
Modal Testing ◽  
Structural Dynamic ◽  
Structural Dynamic Modification ◽  
Modal Model ◽  
Dynamic Modification ◽  
One Step ◽  
Stiffness And Damping

Structural dynamic modification is a popular approach to obtain desire frequencies and dynamic characteristics. It has been observed that reanalyzing the modified structure usually involves complicated calculations when modifications are concerned with numerous degrees of freedom (DOFs), especially adding substructures to these DOFs. This paper proposed a method to reanalyze the frequency response functions (FRFs) of structures with multiple co-ordinates modifications. Two different cases are taken into consideration in the modifications, including adding (or decreasing) masses, stiffness, and damping, as well as adding spring-mass substructures, which makes the method more practical. This method is developed by employing Sherman–Morrison and Woodbury (SMW) formula based on the FRFs related to the modifications coordinates of the original system. The advantage of this method is that neither a physical model nor a modal model is required; instead, it needs only the FRFs, which can be directly measured by experimental modal testing. Another salient feature of this proposed strategy is that the FRFs of the modified structure can be calculated in only one step. Validation of this proposed method is demonstrated using various numerical examples. It is shown that the method is very effective and can be considered for real applications.

Design and Realtime Implementation of an Adaptive Variation Absorber for Uncertain Mechanical Systems Subjected to Unknown Disturbances

2004 ◽  
Vol 10 (1) ◽  
pp. 55-84
Author(s):  
Raffi Derkhorenian ◽  
Nader Jalili ◽  
D M Dawson
Keyword(s):  
Degrees Of Freedom ◽  
Controller Design ◽  
Linear Time ◽  
Vibration Absorber ◽  
Primary System ◽  
Control Input ◽  
Adaptation Algorithm ◽  
Single Input Single Output ◽  
Linear Time Invariant ◽  
Single Output

In this paper we describe the design and implementation of a nonlinear adaptive disturbance rejection approach for single-input-single-output linear-time-invariant uncertain systems subject to sinusoidal disturbances with unknown amplitude and frequency. This is an extension of our earlier study to a more complicated plant, a two-degrees-of-freedom (2DOF) system representing a vibration absorber setting. The controller design is based on a single Lyapunov function incorporating both the error states and the update laws and, hence, global stability and improved transient performance are readily achieved. Utilizing only the system output, a virtual control input is used in place of non-measurable and unknown signals. The performance of the adaptation algorithm is demonstrated through real-time simulations, both for regulation and tracking, on a 2DOF system representing an active vibration absorber setup. It is shown that when the primary system is subjected to an unknown sinusoidal disturbance, the proposed controller in the absorber subsection completely suppresses the primary system vibration in the presence of unknown disturbance.

scholarly journals Multidimensional entanglement transport through single-mode fiber

2020 ◽  
Vol 6 (4) ◽  
pp. eaay0837 ◽  
Author(s):  
Jun Liu ◽  
Isaac Nape ◽  
Qainke Wang ◽  
Adam Vallés ◽  
Jian Wang ◽  
...  
Keyword(s):  
Hilbert Spaces ◽  
Mode Coupling ◽  
Degrees Of Freedom ◽  
Single Mode ◽  
Single Mode Fiber ◽  
Entangled States ◽  
Spatial Mode ◽  
Alternative Approach ◽  
Spatial Modes ◽  
State Tomography

The global quantum network requires the distribution of entangled states over long distances, with substantial advances already demonstrated using polarization. While Hilbert spaces with higher dimensionality, e.g., spatial modes of light, allow higher information capacity per photon, such spatial mode entanglement transport requires custom multimode fiber and is limited by decoherence-induced mode coupling. Here, we circumvent this by transporting multidimensional entangled states down conventional single-mode fiber (SMF). By entangling the spin-orbit degrees of freedom of a biphoton pair, passing the polarization (spin) photon down the SMF while accessing multiple orbital angular momentum (orbital) subspaces with the other, we realize multidimensional entanglement transport. We show high-fidelity hybrid entanglement preservation down 250 m SMF across multiple 2 × 2 dimensions, confirmed by quantum state tomography, Bell violation measures, and a quantum eraser scheme. This work offers an alternative approach to spatial mode entanglement transport that facilitates deployment in legacy networks across conventional fiber.

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