Interaction Between Two Bodies Translating in an Inviscid Fluid

1991 ◽  
Vol 35 (01) ◽  
pp. 1-8
Author(s):  
L. Landweber ◽  
A. T. Chwang ◽  
Z. Guo
Keyword(s):  
Translational Motion ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Circular Cylinders ◽  
Integral Approach ◽  
Inviscid Fluid ◽  
Added Masses ◽  
Two Bodies ◽  
Good Agreement

The equations of motion of two bodies in translational motion in an inviscid fluid at rest at infinity are expressed in Lagrangian form. For the case of one body stationary and the other approaching it in a uniform stream, an exact, closed-form solution in terms of added masses is obtained, yielding simple expressions for the velocity of the moving body as a function of its relative position and for the interaction forces. This solution is applied to the case of a rectangular cylinder approaching a cylindrical one, for which the added-mass coefficients had been previously obtained in a companion paper by an integral-equation procedure. In order to compare results with those in the literature, and to evaluate the accuracy of the present procedures, results were calculated for a pair of circular cylinders by these methods as well as by successive images. Very good agreement was found. Comparison with published results showed good agreement with the added mass but very poor agreement on the forces, including disagreement as to whether the forces were repulsive or attractive. The discrepancy is believed to be due to the omission of terms in the Bernoulli equation which was used to obtain the pressure distribution and then the force on a body. The Lagrangian formulation is believed to be preferable to the pressure-integral approach because it yields the hydrodynamic force directly in terms of the added masses and their derivatives, thus requiring the calculation of many fewer coefficients.

scholarly journals Added Mass and Damping of a Vibrating Rod in Confined Viscous Fluids

1976 ◽  
Vol 43 (2) ◽  
pp. 325-329 ◽  
Author(s):  
S. S. Chen ◽  
M. W. Wambsganss ◽  
J. A. Jendrzejczyk
Keyword(s):  
Experimental Data ◽  
Experimental Study ◽  
Cylindrical Shell ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Viscous Fluids ◽  
Series Of Experiments ◽  
Theoretical Results ◽  
Good Agreement

This paper presents an analytical and experimental study of a cylindrical rod vibrating in a viscous fluid enclosed by a rigid, concentric cylindrical shell. A closed-form solution for the added mass and damping coefficient is obtained and a series of experiments with cantilevered rods vibrating in various viscous fluids is performed. Experimental data and theoretical results are in good agreement.

Dynamic Responses of Two Parallel Circular Cylinders in a Liquid

1975 ◽  
Vol 97 (2) ◽  
pp. 78-83 ◽  
Author(s):  
Shoei-Sheng Chen
Keyword(s):  
Approximate Solution ◽  
Equations Of Motion ◽  
Closed Form Solution ◽  
Added Mass ◽  
Form Solution ◽  
Dynamic Responses ◽  
Circular Cylinders ◽  
Steady State Responses ◽  
Fluid Coupling ◽  
State Responses

The problem of two parallel circular cylinders vibrating in a liquid is studied analytically. First, the equations of motion including fluid coupling are derived using the added mass concept. Then, a closed form solution and an approximate solution are obtained for free vibration. Finally, the steady-state responses of two cylinders subjected to harmonic excitations are presented. The results of this study illustrate the significance of the interaction of two structures in a liquid.

Fourth-order fractional diffusion model of thermal grooving: integral approach to approximate closed form solution of the Mullins model

2018 ◽  
Vol 13 (1) ◽  
pp. 6 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Integration Method ◽  
Closed Form Solution ◽  
Multiple Integral ◽  
Fractional Diffusion ◽  
Form Solution ◽  
Balance Method ◽  
Integral Approach ◽  
Integration Technique ◽  
Multiple Integration ◽  
Space Coordinate

A multiple integration technique of the integral-balance method allowing solving high-order subdiffusion diffusion equations is presented in this article. The new method termed multiple-integral balance method (MIM) is based on multiple integration procedures with respect to the space coordinate. MIM is a generalization of the widely applied Heat-balance integral method of Goodman and the double integration method of Volkov. The method is demonstrated by a solution of the linear subdiffusion model of Mullins for thermal grooving by surface diffusion.

Derivation of Position-Probability Density for the Transient Nano-Tunnel Problem in SET

2010 ◽  
Author(s):  
Sheam-Chyun Lin ◽  
Hsien-Chang Shih ◽  
Fu-Sheng Chuang ◽  
Ming-Lun Tsai ◽  
Harki Apri Yanto ◽  
...  
Keyword(s):  
Probability Density ◽  
Error Function ◽  
Closed Form Solution ◽  
Form Solution ◽  
Single Electron ◽  
Mathematical Operation ◽  
Similarity Parameter ◽  
Set Up ◽  
Position Probability ◽  
Good Agreement

This theoretical investigation intends to study the nano-tunnel problem of the single electron transistor (SET), which is one of the most important components in the nano-electronics industry. With a combined effort of quantum mechanics and similarity parameter, the partial differential equation of transient position-probability density is attained and can be applied to predict the electron’s position inside the nano tunnel. Also, an appropriate set of the initial and the boundary conditions is set up in accordance to the actual electron behavior for solving this PDE of probability density function. Thereafter, a simple, closed-form solution for the probability density is obtained and expressed in terms of the error function for a new similarity variable η. Note that this analytic similarity solution is easy to perform the calculation and suitable for any further mathematical operation, such as the optimization applications. In addition, it is shown that these predications are reasonable and in good agreement to the physical meanings, which are evaluated from both microscopic and macroscopic viewpoints. In conclusions, this is an innovative approach by using the Schro¨dinger equation directly to solve the nano-tunnel problem. Moreover, with the aids of this analytic position-probability-density solution, it is illustrated that the free single electron in the SET’s tunnel can only appear at some specified regions, which are defined by a dimensionless parameter η within a range of 0 ≤ η ≤ 2. This result can be served as a valuable design reference for setting the practical manufacture requirement.

Axially Symmetric Radial Flow of Rigid/Linear-Hardening Materials

1979 ◽  
Vol 46 (2) ◽  
pp. 322-328 ◽  
Author(s):  
D. Durban
Keyword(s):  
Radial Flow ◽  
Closed Form Solution ◽  
Wire Drawing ◽  
Form Solution ◽  
Flow Rule ◽  
Axially Symmetric ◽  
Linear Hardening ◽  
Stress Components ◽  
Von Mises ◽  
Good Agreement

A closed-form solution has been discovered for axially symmetric radial flow of rigid/linear-hardening materials. It is assumed that the materials obey the von Mises flow rule and that the flow field is in steady state. Explicit expressions for the stress components and the radial velocity are given. The applicability of the solution to wire drawing or extrusion is discussed. Some approximate formulas are derived and shown to be in good agreement, within their range of validity, with experimental results for drawing.

Using Isochronous Method to Calculate Creep Damage in Pressure Vessel Components: Part 2

2017 ◽  
Author(s):  
Chithranjan Nadarajah ◽  
Benjamin F. Hantz ◽  
Sujay Krishnamurthy
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Pressure Vessel ◽  
Closed Form Solution ◽  
Creep Damage ◽  
Form Solution ◽  
Creep Model ◽  
Stress Strain ◽  
Element Analysis ◽  
Good Agreement

This paper is Part 2 of two papers illustrating how isochronous stress strain curves can be used to calculate creep stresses and damage for pressure vessel components. Part 1 [1], illustrated the use of isochronous stress strain curves to obtain creep stresses and damages on two simple example problems which were solved using closed form solution. In Part 2, the isochronous method is implemented in finite element analysis to determine creep stresses and damages on pressure vessel components. Various different pressure vessel components are studied using this method and the results obtained using this method is compared time explicit Omega creep model. The results obtained from the isochronous method is found to be in good agreement with the time explicit Omega creep model.

scholarly journals Added Masses and Forces on Two Bodies Approaching Central Impact in an Inviscid Fluid

1992 ◽  
Vol 36 (02) ◽  
pp. 99-122
Author(s):  
L. Landweber ◽  
A. Shahshahan
Keyword(s):  
Integral Equation ◽  
Exact Solution ◽  
Infinite Series ◽  
Numerical Differentiation ◽  
The Other ◽  
Asymptotic Formulas ◽  
Inviscid Fluid ◽  
Interaction Forces ◽  
Added Masses ◽  
Two Bodies

An integral-equation procedure has been developed to determine interaction forces on two bodies approaching central impact in an inviscid fluid. The accuracy of the results from that procedure is evaluated by applying it to a pair of circles and a pair of spheres for which exact solutions are available. A second purpose was to refine the procedure so that accurate solutions could be obtained at closer distances between the bodies. In the first part of this work, the classical theory is extended by deriving truncation corrections for the infinite series representing the exact solution and asymptotic formulas for computing interaction forces at small gaps. In the second part, two problems were resolved: one on the treatment of the sharp peaks of the integrands when the gap between the bodies was small, the other on reducing the errors in the numerical differentiation required to evaluate the forces. Results for various combinations of circle pairs, for equal spheres, and for an elliptical cylinder approaching a circular one are presented. A new relation between the interaction forces on a wall and on a body moving normal to it is presented. Addendum published in 1994 Volume 38, Issue 2 (June), pages 172–173, is included.

scholarly journals Diffusion models of heat and momentum with weakly singular kernels in the fading memories: How the integral-balance method can be applied?

2015 ◽  
Vol 19 (3) ◽  
pp. 947-957 ◽  
Author(s):  
Jordan Hristov
Keyword(s):  
Closed Form ◽  
Closed Form Solution ◽  
Form Solution ◽  
Diffusion Models ◽  
Integral Approach ◽  
Fading Memory ◽  
Weakly Singular Kernels ◽  
Weakly Singular ◽  
Liouville Derivative ◽  
Singular Kernels

This work presents an attempt to apply the heat-balance integral approach to diffusion models with fading memories with weakly singular kernels resulting in closed-form solutions. The main steps are exemplified by solutions where the fading memory is represented by Volterra integrals and by a time-fractional Riemann-Liouville derivative. The examples address sole elastic (damping) effects and cases where the viscous diffusivity should be taken into account. As examples polynomial approximation is applied, demonstrating how to avoid problems in determination of the exponent of the general parabolic profile, but without freedom to optimize the final closed-form solution. In general, this is a new implementation of an old idea and related methods to new models and we hope the demonstrated technique could be useful in solutions of practical problems.

scholarly journals Developed Mathematical Model for Indeterminate Elements with Variable Inertia and Curved Elements with Constant Cross-Section

2019 ◽  
Vol 2019 ◽  
pp. 1-11
Author(s):  
Mohamed A. El Zareef ◽  
Mohamed E. El Madawy ◽  
Mohamed Ghannam
Keyword(s):  
Mathematical Models ◽  
Numerical Integration ◽  
Cross Section ◽  
Closed Form Solution ◽  
Form Solution ◽  
Optimum Number ◽  
Fe Model ◽  
Constant Cross Section ◽  
Structural Elements ◽  
Good Agreement

Issues such as analysis of indeterminate structural elements that have variable inertia as well as a curved shape still have no closed form solution and are considered one of the major problems faced by design engineers. One method to cope with these issues is by using suitable the finite element (FE) software for analyzing these types of elements. Although it saves time, utilization of FE programs still needs professional users and not all engineers are familiar with it. This paper has two main objectives; first, to develop simple mathematical models for analyzing indeterminate structural elements with variable inertia and that have a curved shape with constant cross section, this model is much easier to be used by engineers compared to the FE model. For simplicity and saving time, a MATLAB program is developed based on investigated mathematical models. The force method combined with numerical integration technique is used to develop these models. The developed mathematical models are verified using the suitable FE software; good agreement was observed between the mathematical and the FE model. The second objective is to introduce a mathematical formula to determine the accurate number of divisions that would be used in the mathematical models. The study proves that the accuracy of analysis depends on the number of divisions used in the numerical integration. The optimum number of divisions is obtained by comparing the output results for both FE and developed mathematical models. The developed mathematical models show a good agreement with FE results with faster processing time and easier usage.

On the Analytical Solution of Externally Pressurized Porous Gas Journal Bearings

1978 ◽  
Vol 100 (3) ◽  
pp. 442-444 ◽  
Author(s):  
B. C. Majumdar
Keyword(s):  
Analytical Solution ◽  
Pressure Distribution ◽  
Closed Form ◽  
Closed Form Solution ◽  
Journal Bearings ◽  
Form Solution ◽  
Performance Characteristics ◽  
Gas Bearing ◽  
Good Agreement

A closed form solution of pressure distribution which leads to the determination of bearing performance characteristics of an externally pressurized porous gas bearing without journal rotation is obtained. A good agreement with a similar available solution confirms the validity of the method.

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