Acoustic diffraction by multiple two‐dimensional objects; its calculation using an approximate integral method

1993 ◽  
Vol 93 (4) ◽  
pp. 2420-2421
Author(s):  
T. R. T. Nightingale
Keyword(s):  
Integral Method ◽  
Two Dimensional ◽  
Approximate Integral ◽  
Acoustic Diffraction ◽  
Approximate Integral Method

Combined Forced and Free Convection Laminar Flow over a Vertical Plate

1973 ◽  
Vol 187 (1) ◽  
pp. 191-197
Author(s):  
A. Brown
Keyword(s):  
Laminar Flow ◽  
Free Convection ◽  
Integral Method ◽  
Vertical Plate ◽  
Convection Flow ◽  
Temperature Profiles ◽  
Approximate Integral ◽  
Forced Convection Flow ◽  
Approximate Integral Method ◽  
Vertical Flat Plate

The approximate integral method of von Kármán is adapted to analyse combined forced and free convection laminar flow over a vertical flat plate at a constant temperature. This approach produces relatively simple expressions relating velocity and temperature profiles, skin friction and heat transfer to Pr and Gr/Re2 for the situation where forced convection flow is dominant over free convection. The results of the analysis compare favourably with more exact theoretical treatments and with experiment.

Combined Forced and Free Convection Laminar Flow over a Vertical Plate

1973 ◽  
Vol 187 (1) ◽  
pp. 191-197 ◽  
Author(s):  
A. Brown
Keyword(s):  
Laminar Flow ◽  
Free Convection ◽  
Integral Method ◽  
Vertical Plate ◽  
Convection Flow ◽  
Temperature Profiles ◽  
Approximate Integral ◽  
Forced Convection Flow ◽  
Approximate Integral Method ◽  
Vertical Flat Plate

The approximate integral method of von Kármán is adapted to analyse combined forced and free convection laminar flow over a vertical flat plate at a constant temperature. This approach produces relatively simple expressions relating velocity and temperature profiles, skin friction and heat transfer to Pr and Gr/Re2 for the situation where forced convection flow is dominant over free convection. The results of the analysis compare favourably with more exact theoretical treatments and with experiment.

scholarly journals An interaction integral method for evaluating T-stress for two-dimensional crack problems using the extended radial point interpolation method

2015 ◽  
Vol 18 (2) ◽  
pp. 106-113
Author(s):  
Nha Thanh Nguyen ◽  
Hien Thai Nguyen ◽  
Minh Ngoc Nguyen ◽  
Thien Tich Truong
Keyword(s):  
Integral Method ◽  
Interpolation Method ◽  
Two Dimensional ◽  
Radial Point Interpolation Method ◽  
Interaction Integral ◽  
Crack Problems ◽  
Radial Point Interpolation ◽  
T Stress ◽  
Point Interpolation Method ◽  
Point Interpolation

The so-called T-stress, or second term of the William (1957) series expansion for linear elastic crack-tip fields, has found many uses in fracture mechanics applications. In this paper, an interaction integral method for calculating the T-stress for two-dimensional crack problems using the extended radial point interpolation method (XRPIM) is presented. Typical advantages of RPIM shape function are the satisfactions of the Kronecker’s delta property and the high-order continuity. The T-stress can be calculated directly from a path independent interaction integral entirely based on the J-integral by simply the auxiliary field. Several benchmark examples in 2D crack problem are performed and compared with other existing solutions to illustrate the correction of the presented approach.

Two-dimensional analytic modeling of acoustic diffraction for ultrasonic beam steering by phased array transducers

Ultrasonics ◽  
2017 ◽  
Vol 76 ◽  
pp. 35-43 ◽  
Author(s):  
Tiansi Wang ◽  
Chong Zhang ◽  
Aleksandar Aleksov ◽  
Islam Salama ◽  
Aravinda Kar
Keyword(s):  
Phased Array ◽  
Beam Steering ◽  
Two Dimensional ◽  
Ultrasonic Beam ◽  
Analytic Modeling ◽  
Acoustic Diffraction
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