A mathematical model of the Lamb wave reflection at a two-dimensional rectangular notch

2019 ◽  
Vol 58 (SG) ◽  
pp. SGGB08
Author(s):  
Junya Ishihara ◽  
Masashi Ishikawa ◽  
Hideo Nishino
Keyword(s):  
Mathematical Model ◽  
Lamb Wave ◽  
Wave Reflection ◽  
Two Dimensional ◽  
Rectangular Notch

Two Dimensional Unsteady State Mathematical Model for dispersion of Chlorine in Water in a Channel

2011 ◽  
Vol 3 (8) ◽  
pp. 503-505
Author(s):  
Jaipal Jaipal ◽  
◽  
Rakesh Chandra Bhadula ◽  
V. N Kala V. N Kala
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Unsteady State

Study on Grinding Force in Two-Dimensional Ultrasonic Grinding Nano-Ceramics

2010 ◽  
Vol 42 ◽  
pp. 204-208 ◽  
Author(s):  
Xiang Dong Li ◽  
Quan Cai Wang
Keyword(s):  
Mathematical Model ◽  
Ultrasonic Vibration ◽  
Contact Time ◽  
Reaction Force ◽  
Grinding Force ◽  
Two Dimensional ◽  
Indentation Fracture ◽  
Ultrasonic Grinding ◽  
The Impact ◽  
Ultrasonic Vibration Assisted Grinding

In this paper, the characteristic of grinding force in two-dimensional ultrasonic vibration assisted grinding nano-ceramic was studied by experiment based on indentation fracture mechanics, and mathematical model of grinding force was established. The study shows that grinding force mainly result from the impact of the grains on the workpiece in ultrasonic grinding, and the pulse power is much larger than normal grinding force. The ultrasonic vibration frequency is so high and the contact time of grains with the workpiece is so short that the pulse force will be balanced by reaction force from workpiece. In grinding workpiece was loaded by the periodical stress field, which accelerates the fatigue fracture.

Two-dimensional discrete mathematical model of tumor-induced angiogenesis

2009 ◽  
Vol 30 (4) ◽  
pp. 455-462
Author(s):  
Gai-ping Zhao ◽  
Er-yun Chen ◽  
Jie Wu ◽  
Shi-xiong Xu ◽  
M. W. Collins ◽  
...  
Keyword(s):  
Mathematical Model ◽  
Two Dimensional ◽  
Discrete Mathematical Model

A Numerical Study of Unsteady Natural Convection in a Rectangular Enclosure: The Effect of Compressibility

2004 ◽  
Author(s):  
K. M. Akyuzlu ◽  
Y. Pavri ◽  
A. Antoniou
Keyword(s):  
Mathematical Model ◽  
Stokes Equations ◽  
Numerical Study ◽  
Vertical Wall ◽  
Ideal Gas ◽  
Working Fluid ◽  
Two Dimensional ◽  
Algebraic Equations ◽  
Rectangular Enclosure ◽  
Circulation Patterns

A two-dimensional, mathematical model is adopted to investigate the development of buoyancy driven circulation patterns and temperature contours inside a rectangular enclosure filled with a compressible fluid (Pr=1.0). One of the vertical walls of the enclosure is kept at a higher temperature then the opposing vertical wall. The top and the bottom of the enclosure are assumed insulated. The physics based mathematical model for this problem consists of conservation of mass, momentum (two-dimensional Navier-Stokes equations) and energy equations for the enclosed fluid subjected to appropriate boundary conditions. The working fluid is assumed to be compressible through a simple ideal gas relation. The governing equations are discretized using second order accurate central differencing for spatial derivatives and first order forward finite differencing for time derivatives where the computation domain is represented by a uniform orthogonal mesh. The resulting nonlinear equations are then linearized using Newton’s linearization method. The set of algebraic equations that result from this process are then put into a matrix form and solved using a Coupled Modified Strongly Implicit Procedure (CMSIP) for the unknowns (primitive variables) of the problem. A numerical experiment is carried out for a benchmark case (driven cavity flow) to verify the accuracy of the proposed solution procedure. Numerical experiments are then carried out using the proposed compressible flow model to simulate the development of the buoyancy driven circulation patterns for Rayleigh numbers between 103 and 105. Finally, an attempt is made to determine the effect of compressibility of the working fluid by comparing the results of the proposed model to that of models that use incompressible flow assumptions together with Boussinesq approximation.

Analysis and modeling of an inverted pendulum system

2021 ◽  
Author(s):  
Keyword(s):  
Mathematical Model ◽  
Nonlinear System ◽  
Inverted Pendulum ◽  
System Analysis ◽  
Dimensional System ◽  
Two Dimensional ◽  
System Operation ◽  
Pendulum System ◽  
Inverted Pendulum System ◽  
Two Dimensional System

A nonlinear system, which consists of an inverted pendulum mounted on a cart with an electric drive, is considered. A mathematical model is created, its analysis and modeling of the investigated two-dimensional system operation is carried out. Keywords mathematical model; inverted pendulum; system analysis; state space

MATHEMATICAL MODEL OF TWO-DIMENSIONAL LAYERED PRESSURE FLOW IN THE AUGER CHANNEL

2018 ◽  
Author(s):  
А.В. ГУКАСЯН ◽  
В.С. КОСАЧЕВ ◽  
Е.П. КОШЕВОЙ
Keyword(s):  
Mathematical Model ◽  
Analytical Solution ◽  
Cross Section ◽  
Dynamic Pressure ◽  
Two Dimensional ◽  
Flow Dynamic ◽  
Pressure Flow ◽  
Rectangular Channels ◽  
Wide Range ◽  
Pressure Characteristics

Получено аналитическое решение двумерного слоистого напорного течения в канале шнека, позволяющее моделировать расходно-напорные характеристики прямоугольных каналов шнековых прессов с учетом гидравлического сопротивления формующих устройств и рассчитывать расходно-напорные характеристики экструдеров в широком диапазоне геометрии витков как в поперечном сечении, так и по длине канала. Obtained the analytical solution of two-dimensional layered pressure flow in the screw channel, allow to simulate the flow-dynamic pressure characteristics of rectangular channels screw presses taking into account the hydraulic resistance of the forming device and calculate the mass flow-dynamic pressure characteristics of the extruders in a wide range of the geometry of the coils, as in its cross section and along the length of the channel.

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