An Identification Method for Orifice-Type Restrictors Based on the Closed-Form Solution of Reynolds Equation

Even though the behavior of aerostatic bearings has for long been the topic of extensive research, there are still many aspects that require further investigation. Among these, the identification of the discharge coefficients is one the most crucial. This paper presents a hybrid method to identify the discharge coefficients of aerostatic bearing orifices. The method is termed as hybrid since it exploits experimental data and the equations of the analytical model of a circular and centrally fed aerostatic pad. The obtained results demonstrate the accuracy of the method. The proposed method further offers practical advantages compared to the conventional methods.

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Validation of Nitinol SMA Characteristics Using Finite Element Analysis and Closed Form Solutions

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.856.147 ◽

2013 ◽

Vol 856 ◽

pp. 147-152

Author(s):

S.H. Adarsh ◽

U.S. Mallikarjun

Keyword(s):

Experimental Data ◽

Finite Element Analysis ◽

Finite Element ◽

Closed Form ◽

Closed Form Solution ◽

Form Solution ◽

Fe Analysis ◽

Element Analysis ◽

Complex Behaviour ◽

Closed Form Solutions

Shape Memory Alloys (SMA) are promising materials for actuation in space applications, because of the relatively large deformations and forces that they offer. However, their complex behaviour and interaction of several physical domains (electrical, thermal and mechanical), the study of SMA behaviour is a challenging field. Present work aims at correlating the Finite Element (FE) analysis of SMA with closed form solutions and experimental data. Though sufficient literature is available on closed form solution of SMA, not much detail is available on the Finite element Analysis. In the present work an attempt is made for characterization of SMA through solving the governing equations by established closed form solution, and finally correlating FE results with these data. Extensive experiments were conducted on 0.3mm diameter NiTinol SMA wire at various temperatures and stress conditions and these results were compared with FE analysis conducted using MSC.Marc. A comparison of results from finite element analysis with the experimental data exhibits fairly good agreement.

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Closed form solution of the SIR model for the COVID-19 outbreak in Italy

10.1101/2020.06.06.20124313 ◽

2020 ◽

Author(s):

Riccardo Giubilei

Keyword(s):

Experimental Data ◽

Closed Form ◽

Closed Form Solution ◽

Sir Model ◽

Form Solution ◽

Model Equations

AbstractThe CODIV-19 outbreak in early 2020 generated a tremendous effort of epidemiologists and researchers to fit the experimental data with the solutions of the SIR model equations [1] or with more sophisticated models. In this paper we show that under same hypotheses, a closed form solution exists that reasonably fits the experimental data for Italy, and the results can be extended to any other area.

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Load-carrying capacities and failure modes of scaffold-shoring systems, Part II: An analytical model and its closed-form solution

STRUCTURAL ENGINEERING AND MECHANICS ◽

10.12989/sem.2000.10.1.067 ◽

2000 ◽

Vol 10 (1) ◽

pp. 67-79 ◽

Cited By ~ 11

Author(s):

Y.L. Huang ◽

Y.G. Kao ◽

D.V. Rosowsky

Keyword(s):

Closed Form ◽

Analytical Model ◽

Failure Modes ◽

Closed Form Solution ◽

Form Solution ◽

Load Carrying

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Fractional Calculus Model of the Semilunar Heart Valve Vibrations

Volume 5: 19th Biennial Conference on Mechanical Vibration and Noise, Parts A, B, and C ◽

10.1115/detc2003/vib-48384 ◽

2003 ◽

Cited By ~ 5

Author(s):

Moustafa El-Shahed

Keyword(s):

Differential Equation ◽

Experimental Data ◽

Numerical Methods ◽

Fractional Calculus ◽

Closed Form ◽

Heart Valve ◽

Laplace Transformation ◽

Closed Form Solution ◽

Equation Of Motion ◽

Form Solution

The objective of this paper is to solve the equation of motion of semilunar heart valve vibrations. The vibrations of the closed semilunar valves were modeled with a Caputo hactional derivative of order α. With the help of Laplace transformation, closed-form solution is obtained for the equation of motion in terms of Mittag-Leffler function. An alternative Method for Semi-differential equation, when α = 0.5, is examined using MATHEMATICA. The simplicity of these solutions makes them ideal for testing the accuracy of numerical methods. This solution can be of some interest for a better fit of experimental data.

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Modeling Finite Squeeze Film Dampers

Volume 4: Turbo Expo 2002, Parts A and B ◽

10.1115/gt2002-30637 ◽

2002 ◽

Author(s):

A. El-Shafei

Keyword(s):

Closed Form ◽

Reynolds Equation ◽

Closed Form Solution ◽

Form Solution ◽

Perturbation Solution ◽

Squeeze Film ◽

Closed Form Solutions ◽

Special Cases ◽

Squeeze Film Dampers ◽

Finite Difference Solution

Most closed form solutions of Reynolds’ equation assume either a short bearing approximation or a long bearing approximation. These closed form approximations are used in rotordynamic simulation applications, otherwise a Finite Difference solution of Reynolds’ equation would be prohibitively time consuming. Recently, there have been proposed series solutions for Reynolds’ equation for special cases. In this paper, a perturbation solution to the governing equations is proposed to obtain a closed form solution of Reynolds’ equation for a finite squeeze film damper executing a circular centered orbit. The pressure field and velocity profiles are obtained. It is shown that in the limit the finite damper solution approaches either the appropriate short or long damper. This perturbation solution can be used with appropriate boundary conditions, for various damper sealing configurations, and provides insight into the damper performance.

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Universal hybrid method and approximate closed-form solution for V-notched and V-notch-cracked plate under tensile and in-plane bending

Theoretical and Applied Fracture Mechanics ◽

10.1016/j.tafmec.2020.102579 ◽

2020 ◽

Vol 108 ◽

pp. 102579

Author(s):

Benqiang Lou ◽

Nigel Barltrop

Keyword(s):

Closed Form ◽

Hybrid Method ◽

Closed Form Solution ◽

Form Solution ◽

Cracked Plate ◽

Plane Bending

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A Dishing Model for STI CMP Process

MRS Proceedings ◽

10.1557/proc-867-w5.5 ◽

2005 ◽

Vol 867 ◽

Author(s):

Shih-Hsiang Chang

Keyword(s):

Experimental Data ◽

Steady State ◽

Closed Form ◽

Contact Mechanics ◽

Closed Form Solution ◽

Form Solution ◽

Experimental Results ◽

Quantitative Prediction ◽

Comparison With Experimental Data

AbstractIt is well known that oxide dishing occurring in STI CMP leads to considerable sidewall and edge-parasitic conduction. Thus, a closed-form solution for quantitative prediction of oxide dishing is needed. A contact-mechanics-based approach to describe the steady-state oxide dishing occurring in STI CMP process is presented. The theory is validated through comparison with experimental data in the literature. Once validated, the model is used to quantify the effect of pattern geometry on oxide dishing. It is shown that the predictions of the model agree reasonably well with the experimental results measured in overpolishing time.

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