Mode Coupling-Type Instability of a Beam Subjected to Coulomb Friction

2013 ◽  
Vol 135 (6) ◽  
Author(s):  
Yasuhiro Seo ◽  
Hiroshi Yabuno ◽  
Go Kono
Keyword(s):  
Mode Coupling ◽  
Coulomb Friction ◽  
Axial Direction ◽  
Laser Printer ◽  
Beam Model ◽  
Excitation Mechanism ◽  
Cosserat Theory ◽  
Floor Surface ◽  
Excited Oscillation ◽  
Mode Coupling Instability

To analyze the excitation mechanism of self-excited oscillation in a beam that is in contact with a moving floor surface such as a cleaning blade, which is a beam mounted in a laser printer to clean the photoreceptor, we study a beam subjected to Coulomb friction and theoretically predict the occurrence of self-excited oscillation through mode-coupling instability. We present an extensible beam model, and derive its governing nonlinear equations by means of special Cosserat theory, which allows for the extensibility of the beam to be considered. The boundary conditions on the end of the beam are unique because the end of the beam makes contact with the moving floor surface. We used a discretized linearized governing equation and performed linear stability analysis. The results indicate that self-excited oscillation in the beam is produced due to both Coulomb friction and mode coupling of the bending and extension of the beam based on the extensibility in the axial direction.

Flutter-Type Instability of a Beam Subjected to Coulomb Friction

2011 ◽  
Author(s):  
Yasuhiro Seo ◽  
Go Kono ◽  
Hiroshi Yabuno
Keyword(s):  
Boundary Conditions ◽  
Linear Stability ◽  
Coulomb Friction ◽  
Continuum Model ◽  
Excitation Mechanism ◽  
Governing Equations ◽  
Cosserat Theory ◽  
Floor Surface ◽  
Excited Oscillation

To analyze the excitation mechanism of self-excited oscillation in a beam which is in contact with a moving floor surface, we deal with a beam subjected to Coulomb friction and theoretically predict the occurrence of self-excited oscillation through flutter-type instability. We introduced an extensible continuum model, and derived its governing equations by special Cosserat theory, which allows for the extensibility of the beam to be considered and boundary conditions. The boundary conditions on the end of the beam are unique, because the end of the beam contacts with the moving floor surface. Then, we discretized the system, analyzed the linear stability, and indicated that the flutter-type instability in the beam is produced due to the Coulomb friction and the extension of the extensibility.

Effect of high-frequency excitation on friction induced vibration caused by the combined action of velocity-weakening and mode-coupling

2020 ◽  
Vol 26 (9-10) ◽  
pp. 735-746 ◽  
Author(s):  
Pradyumna K Sahoo ◽  
Shyamal Chatterjee
Keyword(s):  
High Frequency ◽  
Mode Coupling ◽  
Excited Oscillation ◽  
High Frequency Excitation ◽  
Combined Action ◽  
Frequency Excitation ◽  
Mode Coupling Instability ◽  
Strength Of Excitation ◽  
Two Degree Of Freedom ◽  
Friction Induced Vibration

The present article studies the effects of both tangential and normal high-frequency excitations on a two-degree-of-freedom moving-mass-on-belt which represents a minimal model incorporating both velocity-weakening instability (so-called Stribeck effect) and mode-coupling instability (so-called binary flutter). The method of direct partition of motion is employed for studying the characteristics of the system in slow time scale. Linear stability analysis is performed near the equilibrium point of the system for both with and without sinusoidal high-frequency excitation. It is observed that the instability can be suppressed by the tangential high-frequency excitation only for a specific range of strength of excitation. However, stability does not improve under normal high-frequency excitations, though amplitude of the self-excited oscillation can be controlled to some extent. Direct numerical simulations are carried out in MATLAB SIMULINK to validate the analytical predictions.

scholarly journals Seamless Tube-Type Heater with Uniform Thickness and Temperature Distribution Based on Carbon Nanotubes Aligned by Circumferential Shearing

Materials ◽  
2019 ◽  
Vol 12 (20) ◽  
pp. 3283 ◽  
Author(s):  
Yoonchul Sohn ◽  
Dongearn Kim ◽  
Sung-Hoon Park ◽  
Sang-Eui Lee
Keyword(s):  
Temperature Distribution ◽  
Axial Direction ◽  
Circumferential Direction ◽  
Laser Printer ◽  
Seamless Tube ◽  
Uniform Temperature ◽  
Rubber Composite ◽  
Tube Type ◽  
The Difference

The uniform temperature distribution, one of the requirements for long-term durability, is essential for composite heaters. An analytical model for temperature distribution of a tube-type heater was derived, and it revealed that thickness uniformity is one order more important than intrinsic material properties such as density, heat capacity, and electrical conductivity of the heating tube. We introduced a circumferential shearing process to fabricate a flexible, seamless tube-type heating layer of carbon nanotube/silicone rubber composite with outstanding uniform distribution of thickness and temperature, which may be attributed to a shorter characteristic dimension in the circumferential direction than in the axial direction. The temperature uniformity was experimentally verified at various temperatures under heating. The difference in measured thickness and temperature in circumferential direction was within ±1.3~3.0% (for tavg = 352.7 μm) and ±1.1% (for Tavg = 138.8 °C), respectively, all over the heating tube. Therefore, the circumferential shearing process can be effective for cylindrical heaters, like a heating layer of a laser printer, which fuse toners onto papers during printing.

scholarly journals Mode coupling instability mitigation in friction systems by means of nonlinear energy sinks: Numerical highlighting and local stability analysis

2017 ◽  
Vol 24 (15) ◽  
pp. 3487-3511 ◽  
Author(s):  
Baptiste Bergeot ◽  
Sébastien Berger ◽  
Sergio Bellizzi
Keyword(s):  
Steady State ◽  
Stability Analysis ◽  
Mode Coupling ◽  
Passive Control ◽  
Singular Perturbation Theory ◽  
Geometric Singular Perturbation Theory ◽  
Complete Suppression ◽  
Slow Flow ◽  
Mode Coupling Instability ◽  
Nonlinear Energy

In this paper, we study the problem of passive control of friction-induced vibrations due to mode coupling instability in braking systems. To achieve that, the well-known two degrees of freedom Hultén’s model, which reproduces the typical dynamic behavior of friction systems, is coupled to two ungrounded nonlinear energy sinks (NES). The NES involves an essential cubic restoring force and a linear damping force. First, using numerical simulations it is shown that the suppression or the mitigation of the instability is possible and four steady-state responses are highlighted: complete suppression, mitigation through periodic response, mitigation through strongly modulated response, and no suppression of the mode coupling instability. Then the system is analyzed applying a complexification-averaging method and the resulting slow-flow is finally analyzed using geometric singular perturbation theory. This analysis allows us to explain the observed steady-state response regimes and predict some of them. The boundary values of the friction coefficient for some of the transitions between these regimes are predicted. However, the appearance of a three-dimensional super-slow flow subsystem highlights the limitation of the local linear stability analysis of the slow-flow to predict all these boundaries.

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