Transient Growth Before Coupled-Mode Flutter

2003 ◽  
Vol 70 (6) ◽  
pp. 894-901 ◽  
Author(s):  
P. J. Schmid ◽  
E. de Langre
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Linear Stability Theory ◽  
Transient Growth ◽  
Significant Discrepancy ◽  
Two Degrees Of Freedom ◽  
Coupled Mode ◽  
Flow Induced Vibrations ◽  
The One ◽  
Analytical Approaches

Transient growth of energy is known to occur even in stable dynamical systems due to the non-normality of the underlying linear operator. This has been the object of growing attention in the field of hydrodynamic stability, where linearly stable flows may be found to be strongly nonlinearly unstable as a consequence of transient growth. We apply these concepts to the generic case of coupled-mode flutter, which is a mechanism with important applications in the field of fluid-structure interactions. Using numerical and analytical approaches on a simple system with two degrees-of-freedom and antisymmetric coupling we show that the energy of such a system may grow by a factor of more than 10, before the threshold of coupled-mode flutter is crossed. This growth is a simple consequence of the nonorthogonality of modes arising from the nonconservative forces. These general results are then applied to three cases in the field of flow-induced vibrations: (a) panel flutter (two-degrees-of-freedom model, as used by Dowell) (b) follower force (two-degrees-of-freedom model, as used by Bamberger) and (c) fluid-conveying pipes (two-degree-of-freedom model, as used by Benjamin and Pai¨doussis) for different mass ratios. For these three cases we show that the magnitude of transient growth of mechanical energy before the onset of coupled-mode flutter is substantial enough to cause a significant discrepancy between the apparent threshold of instability and the one predicted by linear stability theory.

Transient Growth Before Coupled-Mode Flutter

2002 ◽  
Author(s):  
Peter Schmid ◽  
Emmanuel de Langre
Keyword(s):  
Degrees Of Freedom ◽  
Mechanical Energy ◽  
Linear Stability Theory ◽  
Transient Growth ◽  
Significant Discrepancy ◽  
Two Degrees Of Freedom ◽  
Coupled Mode ◽  
Flow Induced Vibrations ◽  
The One ◽  
Analytical Approaches

Transient growth of energy is known to occur even in stable dynamical systems due to the non-normality of the underlying linear operator. This has been the object of growing attention in the field of hydrodynamic stability, where linearly stable flows may be found to be strongly nonlinearly unstable as a consequence of transient growth. We apply these concepts to the generic case of coupled-mode flutter, which is a mechanism with important applications in the field of fluid-structure interactions. Using numerical and analytical approaches on a simple system with two degrees of freedom and anti-symmetric coupling we show that the energy of such a system may grow by a factor of more than 10, before the threshold of coupled-mode flutter is crossed. This growth is a simple consequence of the non-orthogonality of modes arising from the non-conservative forces. These general results are then applied to three cases in the field of flow-induced vibrations: (a) panel flutter (two-degrees-of-freedom model, as used by Dowell (1995)), (b) follower force (two-degrees-of-freedom model as used by Bamberger (1981)), and (c) fluid-conveying pipes (two-degree-of-freedom model, as used by Benjamin (1961) and Paidoussis (1998)), for different mass ratios. For these three cases we show that the magnitude of transient growth of mechanical energy before the onset of coupled-mode flutter is substantial enough to cause a significant discrepancy between the apparent threshold of instability and the one predicted by linear stability theory.

scholarly journals Design, Implementation and Testing of a Novel Prototype Orthotic Knee Joint with Two Degrees of Freedom in a Patient with Medial Knee Osteoarthritis

2019 ◽  
Vol 18 (4) ◽  
pp. 524
Author(s):  
Siamak Aghajani-Fesharaki ◽  
Farzam Farahmand ◽  
Hassan Saeedi ◽  
Ehsan Abdollahy
Keyword(s):  
Knee Joint ◽  
Knee Osteoarthritis ◽  
Degrees Of Freedom ◽  
Interaction Force ◽  
Transverse Plane ◽  
Materials Testing ◽  
Keywords Knee ◽  
Two Degrees Of Freedom ◽  
Keywords Knee Joint ◽  
The One

Knee braces are a conservative treatment option for patients with knee osteoarthritis (KOA). However, no commercially available orthotic knee joint currently reflects natural knee movements. A prototype orthotic knee joint with two degrees of freedom (DOF) in the sagittal and transverse planes was developed to more closely simulate the natural motion of the knee joint. The prototype was tested on a male subject with medial KOA during a sit-to-stand task. The efficacy of the transverse plane DOF was assessed by comparing the limb-orthosis interaction force when the transverse plane was locked to mimic a one-DOF setting versus when it was unlocked. Unlocking the transverse plane eliminated the 45-Newton shearing force produced with the one-DOF setting at wide angles of flexion. The two-DOF orthotic knee joint prototype demonstrated greater conformity to natural knee movements, allowing the wearer to better tolerate bracing-related difficulties. Keywords: Knee Joint; Knee Osteoarthritis; Orthotic Devices; Braces; Rotation; Movement; Materials Testing.

Non-Stationary Responses in Externally Excited Two-Degrees-of-Freedom Nonlinear Systems with 1: 2 Internal Resonance

2004 ◽  
Vol 10 (11) ◽  
pp. 1663-1697 ◽  
Author(s):  
Anil K. Bajaj ◽  
Patricia Davies ◽  
Bappaditya Banerjee
Keyword(s):  
Internal Resonance ◽  
Degrees Of Freedom ◽  
Numerical Study ◽  
Excitation Frequency ◽  
Primary Resonance ◽  
Single Mode ◽  
Two Degrees Of Freedom ◽  
Analytical Technique ◽  
Bifurcation Points ◽  
Coupled Mode

The dynamics of two-degrees-of-freedom dynamical systems with weak quadratic nonlinearities is analyzed in the neighborhood of bifurcation points when the excitation frequency varies slowly through the region of primary resonance. The two modes of vibration are in 1: 2 subharmonic internal resonance. The slowly evolving averaged equations are numerically studied for motions initiated in the vicinity of stationary responses, and observations are made about the nature of responses of the system near the transition from single-mode to coupled-mode solutions (pitchfork points), and near jump and Hopf bifurcations in the coupled-mode solutions. An analytical technique based on the dynamic bifurcation theory is developed to explain the numerical observations for passage through the bifurcations. A numerical study is carried out to determine the effects of system parameters on the dynamics near the pitchfork bifurcation points and results are compared with analytical and numerical descriptions of dynamics.

Discussion of Probability Relations between Separated Systems

1935 ◽  
Vol 31 (4) ◽  
pp. 555-563 ◽  
Author(s):  
E. Schrödinger
Keyword(s):  
Degrees Of Freedom ◽  
Contact Transformation ◽  
Two Degrees Of Freedom ◽  
Physical Systems ◽  
Continuous Contact ◽  
Canonical Pair ◽  
Pair Matching ◽  
One To One ◽  
The One ◽  
The Way

The probability relations which can occur between two separated physical systems are discussed, on the assumption that their state is known by a representative in common. The two families of observables, relating to the first and to the second system respectively, are linked by at least one match between two definite members, one of either family. The word match is short for stating that the values of the two observables in question determine each other uniquely and therefore (since the actual labelling is irrelevant) can be taken to be equal. In general there is but one match, but there can be more. If, in addition to the first match, there is a second one between canonical conjugates of the first mates, then there are infinitely many matches, every function of the first canonical pair matching with the same function of the second canonical pair. Thus there is a complete one-to-one correspondence between those two branches (of the two families of observables) which relate to the two degrees of freedom in question. If there are no others, the one-to-one correspondence persists as time advances, but the observables of the first system (say) change their mates in the way that the latter, i.e. the observables of the second system, undergo a certain continuous contact-transformation.

scholarly journals The Effects of Knee Orthosis with Two Degrees of Freedom Joint Design on Gait and Sit-to-Stand Task in Patients with Medial Knee Osteoarthritis

2020 ◽  
Vol 20 (4) ◽  
pp. e324-331
Author(s):  
Siamak Aghajani Fesharaki ◽  
Farzam Farahmand ◽  
Hassan Saeedi ◽  
Seyed Ahmad Raeissadat ◽  
Ehsan Abdollahy ◽  
...  
Keyword(s):  
Knee Osteoarthritis ◽  
Knee Flexion ◽  
Degrees Of Freedom ◽  
Medial Knee ◽  
Two Degrees Of Freedom ◽  
Stand Test ◽  
Joint Design ◽  
Sit To Stand ◽  
The One ◽  
Knee Orthosis

Objectives: Knee bracing as a conservative treatment option for patients with medial knee osteoarthritis (KOA) is of great interest to health practitioners and patients alike. Optimal orthotic knee joint structure is essential to achieve biomechanical and clinical effectiveness. Therefore, this study aimed to identify the effects of a knee orthosis with a new two-degrees-of-freedom (DOF) joint design on selected gait parameters and in a sit-to-stand task in patients with mild-to-moderate medial KOA. Methods: This study was conducted both at the Physical Medicine and Rehabilitation Clinic in Shahid Modarres Academic Hospital and the Biomechanical Laboratory of Rehabilitation Faculty of Iran University of medical Sciences in Tehran, Iran from September 2015 to October 2017. The gait performance of 16 patients was assessed without an orthosis, using a common one-DOF (DOF) knee orthosis and using the same knee orthosis with a two-DOF orthotic joint design. The interactive shearing force between limb and brace in the shell area during a sit-to-stand test was also identified. Repeated measures analysis of variance was used to analyse the data. Results: Compared with walking with no orthosis, both orthosis conditions reduced the external knee adduction moment significantly (P ≤0.05). A significant increase between the one-DOF and two-DOF conditions in terms of walking speed (P = 0.041 and P = 0.009, respectively) and stride length (P = 0.028 and P = 0.038, respectively) was observed. In a sit-to-stand test, wearing the orthosis significantly decreased knee transverse plane range of motion (P ≤0.05). There was a 41.31 ± 8.34 Newtons reduction in knee flexion constraint force. Conclusion: The two-DOF knee orthosis was more comfortable compared to the one-DOF knee orthosis during deep knee flexion. Otherwise, the one- DOF- and two-DOF-braces performed similarly. Keywords: Knee Osteoarthritis; Orthosis; Braces; Gait Analysis; Rotations; Kinematics; Kinetics; Patient Comfort.

The scientific bases of autocontrol with vibration phase for a resonance beating-vibration system with two degrees of freedom driven by debalances

1996 ◽  
Vol 18 (2) ◽  
pp. 43-48
Author(s):  
Tran Van Tuan ◽  
Do Sanh ◽  
Luu Duc Thach
Keyword(s):  
Degrees Of Freedom ◽  
Regulation System ◽  
Vibration System ◽  
Two Degrees Of Freedom ◽  
System Operating

In the paper it is introduced a method for studying dynamics of beating-vibrators by means of digital calculation with the help of the machine in accordance with the needs by the helps of an available auto regulation system operating with high reability.

Effect of leakage and blockage on the acoustic behavior of particle filters

2019 ◽  
Vol 67 (6) ◽  
pp. 483-492
Author(s):  
Seonghyeon Baek ◽  
Iljae Lee
Keyword(s):  
Transfer Matrix ◽  
Particle Filters ◽  
Acoustic Analysis ◽  
Transmission Loss ◽  
One Dimensional ◽  
Filter System ◽  
The Difference ◽  
The One ◽  
Analytical Approaches ◽  
Good Agreement

The effects of leakage and blockage on the acoustic performance of particle filters have been examined by using one-dimensional acoustic analysis and experimental methods. First, the transfer matrix of a filter system connected to inlet and outlet pipes with conical sections is measured using a two-load method. Then, the transfer matrix of a particle filter only is extracted from the experiments by applying inverse matrices of the conical sections. In the analytical approaches, the one-dimensional acoustic model for the leakage between the filter and the housing is developed. The predicted transmission loss shows a good agreement with the experimental results. Compared to the baseline, the leakage between the filter and housing increases transmission loss at a certain frequency and its harmonics. In addition, the transmission loss for the system with a partially blocked filter is measured. The blockage of the filter also increases the transmission loss at higher frequencies. For the simplicity of experiments to identify the leakage and blockage, the reflection coefficients at the inlet of the filter system have been measured using two different downstream conditions: open pipe and highly absorptive terminations. The experiments show that with highly absorptive terminations, it is easier to see the difference between the baseline and the defects.

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