Subharmonic Oscillations in an Arbitrary Tank Resulting From Axial Excitation

1968 ◽  
Vol 35 (1) ◽  
pp. 148-154 ◽  
Author(s):  
Wen-Hwa Chu
Keyword(s):  
Theoretical Result ◽  
Order Theory ◽  
Computational Effort ◽  
Characteristic Functions ◽  
Third Order ◽  
Axial Excitation ◽  
First Approximation ◽  
Rectangular Tank ◽  
Simple Geometry ◽  
Good Agreement

The problem of subharmonic liquid response in a container subjected to vertical (axial) excitation has been solved to the first approximation by the method of perturbation, employing characteristic functions. In principle, the tank can be arbitrary. However, the computational effort required to construct the characteristic functions and their derivatives may limit the application to tanks of relatively simple geometry such as a compartmented axisymmetric tank. As a check of the theoretical result, the simplest example for a rectangular tank is given, and the results are in good agreement with experiments and a third-order theory by Yarymovych.

A low-profile FSS-based high capacity chipless RFID tag for sensing and encoding applications

2021 ◽  
pp. 1-9
Author(s):  
Shahid Habib ◽  
Amjad Ali ◽  
Ghaffer Iqbal Kiani ◽  
Wagma Ayub ◽  
Syed Muzahir Abbas ◽  
...  
Keyword(s):  
Radio Frequency Identification ◽  
High Capacity ◽  
Frequency Selective Surface ◽  
Rfid Tag ◽  
Sensing Applications ◽  
Low Profile ◽  
Simple Geometry ◽  
Chipless Rfid ◽  
Frequency Identification ◽  
Good Agreement

Abstract This paper presents a polarization-independent 11-bit chipless RFID tag based on frequency-selective surface which has been designed for encoding and relative humidity (RH) sensing applications. The 10 exterior U-shaped resonators are used for item encoding whereas Kapton has been incorporated with the interior resonator for RH sensing. This radio-frequency identification (RFID) tag operates in S- and C-frequency bands. The proposed design offers enhanced fractional bandwidth up to 88% with the density of 4.46 bits/cm2. Both single- and dual-layer tags have been investigated. The simulated results are in good agreement with measured results and a comparison with existing literature is presented to show the performance. Simple geometry, high code density, large frequency signature bandwidth, high magnitude bit, high radar cross-section, and angular stability for more than 75° are the unique outcomes of the proposed design. In addition, RH sensing has been achieved by integrating the Kapton on the same RFID tag.

Analysis of the First Order and Slowly Varying Motions of an Axisymmetric Floating Body in Bichromatic Waves

2013 ◽  
Vol 135 (1) ◽  
Author(s):  
João Pessoa ◽  
Nuno Fonseca ◽  
C. Guedes Soares
Keyword(s):  
Vertical Cylinder ◽  
Vertical Axis ◽  
Second Order ◽  
The Body ◽  
Floating Body ◽  
Drift Motion ◽  
First Order ◽  
Motion Responses ◽  
Simple Geometry ◽  
Good Agreement

The paper presents an experimental and numerical investigation on the motions of a floating body of simple geometry subjected to harmonic and biharmonic waves. The experiments were carried out in three different water depths representing shallow and deep water. The body is axisymmetric about the vertical axis, like a vertical cylinder with a rounded bottom, and it is kept in place with a soft mooring system. The experimental results include the first order motion responses, the steady drift motion offset in regular waves and the slowly varying motions due to second order interaction in biharmonic waves. The hydrodynamic problem is solved numerically with a second order boundary element method. The results show a good agreement of the numerical calculations with the experiments.

scholarly journals On the Use of Recursive Evaluation of Derivatives and Padé Approximation to Solve the Blasius Problem

2016 ◽  
Vol 2016 ◽  
pp. 1-5
Author(s):  
Asai Asaithambi
Keyword(s):  
Differential Equation ◽  
Computational Effort ◽  
Navier Stokes ◽  
Series Solutions ◽  
Third Order ◽  
Navier Stokes Equation ◽  
Order Problem ◽  
Algorithmic Differentiation ◽  
Blasius Problem ◽  
Recursive Evaluation

The Blasius problem is one of the well-known problems in fluid mechanics in the study of boundary layers. It is described by a third-order ordinary differential equation derived from the Navier-Stokes equation by a similarity transformation. Crocco and Wang independently transformed this third-order problem further into a second-order differential equation. Classical series solutions and their Padé approximants have been computed. These solutions however require extensive algebraic manipulations and significant computational effort. In this paper, we present a computational approach using algorithmic differentiation to obtain these series solutions. Our work produces results superior to those reported previously. Additionally, using increased precision in our calculations, we have been able to extend the usefulness of the method beyond limits where previous methods have failed.

Comparison of Numerical and Perturbation Solutions of Two-Dimensional Nonlinear Water-Wave Problems

1976 ◽  
Vol 20 (03) ◽  
pp. 160-170
Author(s):  
Nils Salvesen ◽  
C. von Kerczek
Keyword(s):  
Perturbation Theory ◽  
Numerical Solutions ◽  
Order Perturbation ◽  
Order Perturbation Theory ◽  
Wave System ◽  
Two Dimensional ◽  
Third Order ◽  
Flow Past ◽  
Wave Problems ◽  
Good Agreement

Numerical solutions of the nonlinear problem of the steady two-dimensional potential flow past a submerged line vortex are obtained using the finite-difference iterative technique previously presented by the authors. These solutions are compared in detail with third-order perturbation theory solutions. It is found that very good agreement is obtained for cases of positive circulation of the vortex with strength large enough to produce downstream waves whose steepness is within 15 percent of the maximum possible steepness of irrotational free waves. These computed waves are as steep as the steepest waves obtained in a certain experiment involving the flow past a two-dimensional hydrofoil. For negative circulation, there is substantial difference between the numerical results and third-order perturbation theory. The failure of the perturbation theory is discussed. Details of the far-downstream wave system obtained by the numerical method are compared with other numerical solutions and very high-order perturbation theory solutions of the free-wave problem. Very good agreement is obtained in most cases.

A Two-Dimensional Potential Flow Model of the Wave Field Generated by a Semisubmerged Body in Heaving Motion

1988 ◽  
Vol 32 (02) ◽  
pp. 83-91
Author(s):  
X. M. Wang ◽  
M. L. Spaulding
Keyword(s):  
Free Surface ◽  
Boundary Conditions ◽  
Potential Flow ◽  
Flow Model ◽  
Second Order ◽  
Two Dimensional ◽  
Third Order ◽  
The Third ◽  
Potential Flow Model ◽  
Good Agreement

A two-dimensional potential flow model is formulated to predict the wave field and forces generated by a sere!submerged body in forced heaving motion. The potential flow problem is solved on a boundary fitted coordinate system that deforms in response to the motion of the free surface and the heaving body. The full nonlinear kinematic and dynamic boundary conditions are used at the free surface. The governing equations and associated boundary conditions are solved by a second-order finite-difference technique based on the modified Euler method for the time domain and a successive overrelaxation (SOR) procedure for the spatial domain. A series of sensitivity studies of grid size and resolution, time step, free surface and body grid redistribution schemes, convergence criteria, and free surface body boundary condition specification was performed to investigate the computational characteristics of the model. The model was applied to predict the forces generated by the forced oscillation of a U-shaped cylinder. Numerical model predictions are generally in good agreement with the available second-order theories for the first-order pressure and force coefficients, but clearly show that the third-order terms are larger than the second-order terms when nonlinearity becomes important in the dimensionless frequency range 1≤ Fr≤ 2. The model results are in good agreement with the available experimental data and confirm the importance of the third order terms.

Dynamic Analysis of a Functionally Greded Sandwich Beam Traversed by a Moving Mass Based on a Refined Third-Order Theory

2021 ◽  
pp. 301-315
Author(s):  
Le Thi Ngoc Anh ◽  
Tran Van Lang ◽  
Vu Thi An Ninh ◽  
Nguyen Dinh Kien
Keyword(s):  
Dynamic Analysis ◽  
Sandwich Beam ◽  
Order Theory ◽  
Moving Mass ◽  
Third Order

Numerical algorithm for predicting wheel flange wear in trams – Validation in a curved track

2019 ◽  
Vol 234 (10) ◽  
pp. 1156-1169
Author(s):  
Bartosz Łuczak ◽  
Bartosz Firlik ◽  
Tomasz Staśkiewicz ◽  
Wojciech Sumelka
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Computational Effort ◽  
Wheel Wear ◽  
Curved Track ◽  
Method Accuracy ◽  
Elliptic Contact ◽  
Method Analysis ◽  
Good Agreement ◽  
Element Method

In tram operations, flange wear is predominant due to the low-radius curves and inappropriate technical conditions of the infrastructure; hence, investigations should be focused on the interaction between the wheel flange and the rail gauge corner. Moreover, the calculation methods based on the Hertzian model (elliptic contact patch) provide less accurate results due to the contact occurrence in the wheel flange region. This paper presents a methodology of a finite element method to predict the tram wheel wear in complex motions. The new procedure is based on the Abaqus software and several other sub-procedures written in Python and Fortran. Multibody simulations were used to determine the wheel–rail alignment. In this method, accuracy was chosen at the expense of the computational effort. The main steps are: preparation of models and ride scenarios, multibody simulation for calculating the wheel–rail alignment for different track scenarios and multiple runs of finite element method analysis to determine the wear magnitude. The proposed methodology presents a good agreement with the measurements and can be considered as guidelines for a proper configuration of the flange-designing experimental setup where the influence of the technical conditions of the infrastructure should be introduced adequately.

On an Approximate Method of Calculating Pressures on Non-lifting Head Shapes at Supersonic Speeds

1955 ◽  
Vol 6 (1) ◽  
pp. 31-45
Author(s):  
H. K. Zienkiewicz
Keyword(s):  
Method Of Characteristics ◽  
Order Theory ◽  
Stagnation Pressure ◽  
Slender Body Theory ◽  
Pressure Losses ◽  
The Method Of Characteristics ◽  
Curvature Approximation ◽  
Body Theory ◽  
Theory And Experiment ◽  
Good Agreement

SummarySlender-body theory is used to derive the ogive of curvature approximation for very slender, pointed, convex head shapes at supersonic speeds. Results of application of this approximation, together with the λ-method for circular arc ogives, to a variety of non-slender head shapes show very good agreement with the method of characteristics, van Dyke's second-order theory and experiment. Good agreement with the method of characteristics and with experiment is obtained even in cases when the stagnation pressure losses across the nose shock wave are not negligible.

scholarly journals PRESBURGER ARITHMETIC, RATIONAL GENERATING FUNCTIONS, AND QUASI-POLYNOMIALS

2015 ◽  
Vol 80 (2) ◽  
pp. 433-449 ◽  
Author(s):  
KEVIN WOODS
Keyword(s):  
Generating Functions ◽  
Counting Function ◽  
Order Theory ◽  
Characteristic Functions ◽  
Presburger Arithmetic ◽  
First Order ◽  
First Order Theory ◽  
Rational Generating Function ◽  
Rational Generating Functions

AbstractPresburger arithmetic is the first-order theory of the natural numbers with addition (but no multiplication). We characterize sets that can be defined by a Presburger formula as exactly the sets whose characteristic functions can be represented by rational generating functions; a geometric characterization of such sets is also given. In addition, ifp= (p1, . . . ,pn) are a subset of the free variables in a Presburger formula, we can define a counting functiong(p) to be the number of solutions to the formula, for a givenp. We show that every counting function obtained in this way may be represented as, equivalently, either a piecewise quasi-polynomial or a rational generating function. Finally, we translate known computational complexity results into this setting and discuss open directions.

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