On the instability of the flow in an oscillating tank of fluid

1994 ◽  
Vol 268 ◽  
pp. 315-331 ◽  
Author(s):  
Philip Hall
Keyword(s):  
Standing Wave ◽  
Floquet Theory ◽  
Eigenvalue Problems ◽  
Asymptotic Methods ◽  
Linear Regime ◽  
Axis Parallel ◽  
Wave Instabilities ◽  
Oscillation Frequencies ◽  
Unsteady Boundary Layers ◽  
The Relationship

The instability of a viscous fluid inside a rectangular tank oscillating about an axis parallel to the largest face of the tank is investigated in the linear regime. The flow is shown to be unstable to both longitudinal roll and standing wave instabilities. The particular cases of low and high oscillation frequencies are discussed in detail. The relationship between the roll instability and convective or centrifugal instabilities in unsteady boundary layers is discussed. The eigenvalue problems associated with the roll and standing wave instabilities are solved using Floquet theory and a combination of numerical and asymptotic methods. The results obtained are compared to the recent experimental investigation of Bolton & Maurer (1994) which indeed provided the stimulus for the present investigation.

scholarly journals Influence of the flexibility of beams and slabs in static response and dynamic properties

2016 ◽  
Vol 9 (6) ◽  
pp. 842-855 ◽  
Author(s):  
J. R. BUENO ◽  
◽  
D. D. LORIGGIO ◽  
Keyword(s):  
Finite Element Method ◽  
Natural Frequencies ◽  
Dynamic Properties ◽  
Vibration Modes ◽  
Linear Regime ◽  
Static Response ◽  
The Finite Element Method ◽  
Standard Code ◽  
The Relationship ◽  
Brazilian Standard

Abstract This article examines numerically the flexibility influence of support beams in static response and dynamic properties of a symmetric plate formed by massive slabs of reinforced concrete in elastic linear regime, using the Finite Element Method. In the static response the variation of bending mo-ments and displacements are evaluated, which depend on the relationship between the flexibility of the slab and the beam. The evaluation of dynamic properties is held in undamped free vibration, through which the vibration modes and the values of the natural frequencies is obtained, which are compared with the limits of the Brazilian standard code for design of concrete structures. Results show that the response may show great variation due to the change in the relationship between bending stiffness of the slabs and the beams.

Synthesis of Actuation Spaces of Multi-Axis Parallel Flexure Mechanisms Based on Screw Theory

2011 ◽  
Author(s):  
C. Qiu ◽  
J. J. Yu ◽  
S. Z. Li ◽  
Hai-jun Su ◽  
Y. Z. Zeng
Keyword(s):  
Screw Theory ◽  
Design Rule ◽  
Compliance Matrix ◽  
Axis Parallel ◽  
Actuator Placement ◽  
The Relationship

This paper introduces an approach for synthesis of actuation spaces of multi-axis parallel flexure mechanisms. The concept of actuation space, first proposed by J. Hopkins and M. Culpepper, is developed from constraint and freedom space, which are two fundamental concepts in constraint-based method. Within the framework of screw theory, actuation and constraint can be represented mathematically by a wrench, and freedom can be depicted by a twist. A Compliance matrix is provided to set the relationship between constraint wrenches and actuation forces in view that such an important rule as “actuation forces are linear independent of constraint wrenches”. Developed from this design rule, a synthesis criterion of actuation space of flexure systems is promoted to select suitable actuators. As a result, this synthesis criterion enable designers to (i) formulate the actuation space systematically in the format of screws or screw system, (ii) determine actuator placement according to the requirement of minimizing the interference between actuation forces and constraint wrenches. Synthesis procedures and selective examples are discussed in details.

Kinematics Analysis of a New 5 DOF Parallel-Serial Machine Tool Based on the Vector Method

2010 ◽  
Vol 450 ◽  
pp. 283-287 ◽  
Author(s):  
Rui Wang ◽  
Gang Ding ◽  
Shi Sheng Zhong
Keyword(s):  
Machine Tool ◽  
Parallel Mechanism ◽  
Kinematics Analysis ◽  
Vector Method ◽  
Velocity Transformation ◽  
Axis Parallel ◽  
Movable Platform ◽  
Parameter Coupling ◽  
The Relationship ◽  
Kinematics Parameters

A 5-axis parallel-serial machine tool is proposed, which consists of a 3-DOF parallel mechanism and a 2-DOF serial mechanism, and the kinematics analysis is discussed in detail based on the vector method. The size of the velocity transformation matrix is decreased. The problem of parameter coupling is resolved by adopting identity matrix and four-element vector. The relationship between the velocity and acceleration of the movable platform and the input parameters of the parallel mechanism is established. These algorithms are verified correct through ADAMS (Automatic Dynamic Analysis of Mechanical System) and can be referenced by kinematics analysis, dynamics analysis of parallel or parallel-serial machine tools, which have coupling kinematics parameters.

VIII.—The Schrödinger Equation with a Periodic Potential

1971 ◽  
Vol 69 (2) ◽  
pp. 125-131
Author(s):  
M. S. P. Eastham
Keyword(s):  
Differential Equation ◽  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Floquet Theory ◽  
Periodic Potential ◽  
Eigenvalue Problems ◽  
Alternative Proof ◽  
Conditional Stability ◽  
Image Position

SynopsisThe differential equationin N dimensions is considered, where q(x) is periodic. When N = 1, it is known that the conditional stability set coincides with the spectrum and that these also coincide with two other sets involving eigenvalues of associated eigenvalue problems. These results have been proved by means of the Floquet theory and the discriminant. Here an alternative proof is given which avoids the Floquet theory and which applies to the general case of N dimensions.

On a model for the motion of a contact line on a smooth solid surface

2006 ◽  
Vol 17 (3) ◽  
pp. 347-382 ◽  
Author(s):  
J. BILLINGHAM
Keyword(s):  
Solid Surface ◽  
Contact Line ◽  
Capillary Number ◽  
Asymptotic Methods ◽  
Mathematical Structure ◽  
Boundary Integral ◽  
Boundary Integral Method ◽  
Surface Thermodynamics ◽  
Water Glycerol ◽  
The Relationship

In this paper we investigate the model for the motion of a contact line over a smooth solid surface developed by Shikhmurzaev, [24]. We show that the formulation is incomplete as it stands, since the mathematical structure of the model indicates that an additional condition is required at the contact line. Recent work by Bedeaux, [4], provides this missing condition, and we examine the consequences of this for the relationship between the contact angle and contact line speed for Stokes flow, using asymptotic methods to investigate the case of small capillary number, and a boundary integral method to find the solution for general capillary number, which allows us to include the effect of viscous bending. We compare the theory with experimental data from a plunging tape experiment with water/glycerol mixtures of varying viscosities [11]. We find that we are able to obtain a reasonable fit using Shikhmurzaev's model, but that it remains unclear whether the linearized surface thermodynamics that underlies the theory provide an adequate description for the motion of a contact line.

scholarly journals A Mathematical Model with Pulse Effect for Three Populations of the Giant Panda and Two Kinds of Bamboo

2013 ◽  
Vol 2013 ◽  
pp. 1-9
Author(s):  
Xiang-yun Shi ◽  
Guo-hua Song
Keyword(s):  
Mathematical Model ◽  
Giant Panda ◽  
Floquet Theory ◽  
Sufficient Conditions ◽  
Giant Pandas ◽  
Impulsive Equations ◽  
The Relationship ◽  
Panda Habitat ◽  
Sudden Collapse ◽  
Uniformly Bounded

A mathematical model for the relationship between the populations of giant pandas and two kinds of bamboo is established. We use the impulsive perturbations to take into account the effect of a sudden collapse of bamboo as a food source. We show that this system is uniformly bounded. Using the Floquet theory and comparison techniques of impulsive equations, we find conditions for the local and global stabilities of the giant panda-free periodic solution. Moreover, we obtain sufficient conditions for the system to be permanent. The results provide a theoretical basis for giant panda habitat protection.

Numerical Analysis of the Performance of an Adjustable Thermoacoustically-Driven Thermo-Acoustic Refrigerator

2019 ◽  
Author(s):  
A. C. Alcock ◽  
S. Balonji ◽  
L. K. Tartibu
Keyword(s):  
Standing Wave ◽  
Sound Wave ◽  
Coefficient Of Performance ◽  
Cooling Power ◽  
Performance Parameters ◽  
Design Environment ◽  
Resonator Length ◽  
Low Amplitude ◽  
The Relationship ◽  
Initial Results

Abstract Thermo-acoustic refrigeration could potentially become an alternative option to current traditional refrigeration systems provided that the issue related to its efficiency is addressed. One of the incentives for developing this technology is the opportunity it establishes with respect to the use of a sustainable heat source to induce cooling. Many existing works have pointed out the relationship between the geometrical configuration of the device and its performance. Mainly, the stack geometry and position have been the focus of these previous works. In this work, a standing-wave ThermoAcoustically-Driven Thermo-Acoustic Refrigerator with an adjustable resonator has been developed. Hence the device is made of two portions, joined with an adjustable duct, namely a simple standing-wave thermo-acoustic engine that converts heat into a sound wave and a simple thermo-acoustic refrigerator where heat pumping takes place. The Design Environment for Low-amplitude ThermoAcoustic Energy Conversion (DELTAEC) was used to model and analyze the influence of the adjustment of the resonator on the cooling performance. Parameters like the temperature difference across the stack, the frequency of the acoustic sound wave generated, the cooling power and the coefficient of performance have been studied. The initial results reported in this study show the possibility to change the performance of practical TADTAR by adjusting the resonator length.

Periodic solutions for functional differential equations with sign-changing nonlinearities

2010 ◽  
Vol 140 (3) ◽  
pp. 597-616 ◽  
Author(s):  
John R. Graef ◽  
Lingju Kong
Keyword(s):  
Differential Equations ◽  
Periodic Solutions ◽  
Eigenvalue Problems ◽  
Functional Differential Equations ◽  
Degree Theory ◽  
Topological Degree Theory ◽  
First Order ◽  
Functional Differential ◽  
Linear Integral ◽  
The Relationship

We establish some eigenvalue criteria for the existence of non-trivial T-periodic solutions of a class of first-order functional differential equations with a nonlinearity f(x). The nonlinear term f(x) can take negative values and may be unbounded from below. Conditions are determined by the relationship between the behaviour of the quotient f(x)/x for x near 0 and ±∞ and the smallest positive characteristic value of an associated linear integral operator. This linear operator plays a key role in the proofs of the results and its construction is non-trivial. Applications to related eigenvalue problems are also discussed. The analysis mainly relies on the topological degree theory.

scholarly journals Researched on the bias stability of the HRG affected by the temperature and the standing wave azimuth

2020 ◽  
pp. 002029402095246
Author(s):  
Wanliang Zhao ◽  
Hao Yang ◽  
Lijun Song ◽  
Xiangyu Yu ◽  
Fucheng Liu ◽  
...  
Keyword(s):  
Standing Wave ◽  
Control Mode ◽  
Bias Error ◽  
Field Environment ◽  
Bias Stability ◽  
Temperature Experiment ◽  
System Temperature ◽  
Hardware Circuit ◽  
The Relationship ◽  
Main Operating

The force-to-rebalanced control mode is the main operating mechanism of the HRG, and the standing wave azimuth of the resonator points to the 0° direction. But the bias of the HRG is very sensitive to the change of external physical field environment and it is urgent to improve the bias stability. The relationship between the bias of the HRG and the standing wave azimuth is periodic. When the standing wave azimuth and the damping axis are aligned, the bias error of the HRG will be greatly reduced, and the bias stability of the HRG affected by the temperature can also be improved by changing the azimuth of standing wave. In this paper, the control algorithm and the hardware circuit of the HRG are designed to control the HRG at any standing wave azimuths. The control of the HRG in different standing wave azimuths is realized, and the system temperature experiment is carried out. The experimental results show that the bias of the HRG are significantly different at different standing wave azimuths, and the bias stability of the HRG affected by the temperature can be improved 3 times by changing the standing wave azimuth.

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