scholarly journals C2 Continuous Blending of Time-Dependent Parametric Surfaces

2019 ◽  
Vol 19 (4) ◽  
Author(s):  
Xiangyu You ◽  
Feng Tian ◽  
Wen Tang
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
High Efficiency ◽  
Approximate Analytical Solution ◽  
Time Dependent ◽  
Order Partial Differential Equation ◽  
Parametric Surfaces ◽  
Boundary Constraints ◽  
Surface Blending ◽  
C2 Continuity

Surface blending is widely applied in mechanical engineering. Creating a smooth transition surface of C2 continuity between time-dependent parametric surfaces that change their positions and shapes with time is an important and unsolved topic in surface blending. In order to address this issue, this paper develops a new approach to unify both time-dependent and time-independent surface blending with C2 continuity. It proposes a new surface blending mathematical model consisting of a vector-valued sixth-order partial differential equation and blending boundary constraints and investigates a simple and efficient approximate analytical solution of the mathematical model. A number of examples are presented to demonstrate the effectiveness and applications. The proposed approach has the advantages of (1) unifying time-independent and time-dependent surface blending, (2) always maintaining C2 continuity at trimlines when parametric surfaces change their positions and shapes with time, (3) providing effective shape control handles to achieve the expected shapes of blending surfaces but still exactly satisfy the given blending boundary constraints, and (4) quickly generating C2 continuous blending surfaces from the approximate analytical solution with easiness, good accuracy, and high efficiency.

Modelling of mass transport and chemical reaction in a diaphragm

1987 ◽  
Vol 52 (7) ◽  
pp. 1692-1700
Author(s):  
Martin Schleiff ◽  
Günther Lefeld ◽  
Hermann Matschiner ◽  
Otomar Špalek
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Mass Transport ◽  
Chemical Reaction ◽  
Current Density ◽  
Approximate Analytical Solution ◽  
Alkaline Electrolyte ◽  
Transport Of Ions

A mathematical model was proposed for the transport of ions in a diaphragm separating an acidic and an alkaline electrolyte. Besides an approximate analytical solution, a more exact numerical one was presented. The model permits the calculation of the position of the neutralization zone in the diaphragm, rates of transport of ions, and potential in the diaphragm. The dependence of the position of the neutralization zone on the composition of both electrolytes and on the current density was calculated for two technically important cases.

Response of Infinite Journal Gas Bearings to Harmonic Perturbations in the Rotational Speed

1977 ◽  
Vol 99 (4) ◽  
pp. 428-433 ◽  
Author(s):  
Y. Narkis ◽  
M. J. Cohen
Keyword(s):  
Analytical Solution ◽  
Rotational Speed ◽  
Approximate Analytical Solution ◽  
Critical Mass ◽  
Regions Of Interest ◽  
Time Dependent ◽  
Safe Operation ◽  
Linear Differential ◽  
Analytical Expressions ◽  
Gas Bearing

The dynamics of a long hydrodynamic gas bearing is investigated for periodic variations of the rotational speed. The analysis is divided into two regions of interest, namely: (1) for small eccentricities the system is represented by a pair of linear differential equations with time-dependent coefficients. Investigation for a sinusoidally varying rotational speed proves that an unloaded bearing can be stable, though it is known not to be stable at all constant speeds. An approximate analytical solution is given for the orbit of a stable journal whirling about its equilibrium position. (2) For higher eccentricities the nonlinear equations describing the motion of the journal center are derived. When the speed perturbation is small, the equations may be linearized, and analytical expressions are obtained for the calculation of journal response. At given speed and eccentricity resonance is reached at the critical mass of instability threshold, but even for smaller mass the amplitudes are liable to endanger safe operation of the system.

scholarly journals Approximate Analytical Solution of Advection-Dispersion Equation By Means of OHAM.

2018 ◽  
Vol 7 (1) ◽  
pp. 15-20
Author(s):  
D J Prajapati ◽  
N B Desai
Keyword(s):  
Analytical Solution ◽  
Dispersion Equation ◽  
Graphical Representation ◽  
Approximate Analytical Solution ◽  
Time Dependent ◽  
Analysis Method ◽  
Optimal Homotopy Analysis Method ◽  
Advection Dispersion ◽  
Homotopy Analysis ◽  
Input Source

This work deals with the analytical solution of advection dispersion equation arising in solute transport along unsteady groundwater flow in finite aquifer. A time dependent input source concentration is considered at the origin of the aquifer and it is assumed that the concentration gradient is zero at the other end of the aquifer. The optimal homotopy analysis method (OHAM) is used to obtain numerical and graphical representation.

scholarly journals Comprehensive Parameters Identification and Dynamic Model Validation of Interior-Mount Line-Start Permanent Magnet Synchronous Motors

Machines ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 4 ◽  
Author(s):  
Luqman S. Maraaba ◽  
Zakariya M. Al-Hamouz ◽  
Abdulaziz S. Milhem ◽  
Ssennoga Twaha
Keyword(s):  
Mathematical Model ◽  
Permanent Magnet ◽  
High Efficiency ◽  
Experimental Tests ◽  
Induction Machines ◽  
Test Methods ◽  
Operating Conditions ◽  
Test Method ◽  
Permanent Magnet Synchronous Motors ◽  
Synchronous Motors

The application of line-start permanent magnet synchronous motors (LSPMSMs) is rapidly spreading due to their advantages of high efficiency, high operational power factor, being self-starting, rendering them as highly needed in many applications in recent years. Although there have been standard methods for the identification of parameters of synchronous and induction machines, most of them do not apply to LSPMSMs. This paper presents a study and analysis of different parameter identification methods for interior mount LSPMSM. Experimental tests have been performed in the laboratory on a 1-hp interior mount LSPMSM. The measurements have been validated by investigating the performance of the machine under different operating conditions using a developed qd0 mathematical model and an experimental setup. The dynamic and steady-state performance analyses have been performed using the determined parameters. It is found that the experimental results are close to the mathematical model results, confirming the accuracy of the studied test methods. Therefore, the output of this study will help in selecting the proper test method for LSPMSM.

Numerical Approximations to Solution of Biochemical Reaction Model

2011 ◽  
Vol 9 (1) ◽  
Author(s):  
Ahmet Yildirim ◽  
Ahmet Gökdogan ◽  
Mehmet Merdan
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Transformation Method ◽  
Reaction Model ◽  
Biochemical Reaction ◽  
Graphical Form ◽  
Kutta Method ◽  
Transform Method ◽  
Runge Kutta Method ◽  
Differential Transform

In this paper, approximate analytical solution of biochemical reaction model is used by the multi-step differential transform method (MsDTM) based on classical differential transformation method (DTM). Numerical results are compared to those obtained by the fourth-order Runge-Kutta method to illustrate the preciseness and effectiveness of the proposed method. Results are given explicit and graphical form.

New Approximate Analytical Solution of the Diode-Resistance Equation

2021 ◽  
pp. 153665
Author(s):  
José A. Gazquez ◽  
Manuel Fernandez-Ros ◽  
Blas Torrecillas ◽  
José Carmona ◽  
Nuria Novas
Keyword(s):  
Analytical Solution ◽  
Approximate Analytical Solution ◽  
Resistance Equation

Modal Analysis of the Axial Compressor Blade: Advanced Time-Dependent Electronic Interferometry and Finite Element Method

2020 ◽  
Vol 0 (0) ◽  
Author(s):  
Mykhaylo Tkach ◽  
Serhii Morhun ◽  
Yuri Zolotoy ◽  
Irina Zhuk
Keyword(s):  
Experimental Data ◽  
Mathematical Model ◽  
Finite Element ◽  
High Reliability ◽  
Axial Compressor ◽  
Time Dependent ◽  
Experimental Setup ◽  
Vibration Modes ◽  
Compressor Blades ◽  
Isoparametric Finite Element

AbstractNatural frequencies and vibration modes of axial compressor blades are investigated. A refined mathematical model based on the usage of an eight-nodal curvilinear isoparametric finite element was applied. The verification of the model is carried out by finding the frequencies and vibration modes of a smooth cylindrical shell and comparing them with experimental data. A high-precision experimental setup based on an advanced method of time-dependent electronic interferometry was developed for this aim. Thus, the objective of the study is to verify the adequacy of the refined mathematical model by means of the advanced time-dependent electronic interferometry experimental method. The divergence of the results of frequency measurements between numerical calculations and experimental data does not exceed 5 % that indicates the adequacy and high reliability of the developed mathematical model. The developed mathematical model and experimental setup can be used later in the study of blades with more complex geometric and strength characteristics or in cases when the real boundary conditions or mechanical characteristics of material are uncertain.

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