Reflexion and transmission at a plane screen with periodically arranged circular or elliptical apertures

1973 ◽  
Vol 61 (1) ◽  
pp. 109-127 ◽  
Author(s):  
F. G. Leppington ◽  
H. Levine
Keyword(s):  
Integral Equation ◽  
Asymptotic Solution ◽  
Sound Wave ◽  
Infinite Plane ◽  
Rectangular Array ◽  
Transmission Coefficients ◽  
Single Aperture ◽  
Rigid Plane ◽  
Periodic Arrangement

A plane harmonic sound wave is considered to be incident upon a rigid plane screen that contains a periodic rectangular array of circular or elliptical apertures, and a characterization is sought for the reflexion and transmission coefficients of the scattered waves when the relationships aperture dimension [Lt ] spacing [Lt ] wavelength apply. The problem is analysed with the help of an integral equation over a single aperture and, as a consequence of the determination of the leading terms in its asymptotic solution, some prior results for more general (that is, irregular) aperture spacing are confirmed and specific features of the interaction in the periodic arrangement are established. Similar formulations are devised and given attention for the related problems in which (i) the screen is backed by a rigid infinite plane and (ii) the apertures contain rigid pistons capable of executing normal displacements compatible with an assigned and common impedance. A section is devoted to the solution, based on expansion of its kernel, for an integral equation of the first kind with a plane circular or elliptical domain.

Study of Method for Determination of Thermal Conductivity of Automotive Interior Materials

2014 ◽  
Vol 526 ◽  
pp. 46-51
Author(s):  
Li Xiong Zhang ◽  
Rong Gang Gao
Keyword(s):  
Thermal Conductivity ◽  
Conductivity Measurement ◽  
Transient Heat Conduction ◽  
Traditional Theory ◽  
Infinite Plane ◽  
Plane Source ◽  
Transient Plane Source ◽  
Wide Range ◽  
Automotive Interior

Based on the traditional theory of transient plane source for thermal conductivity measurement, this paper designed and developed a new pattern of heating and temperature sensing probe, presented the study of transient heat conduction of half-infinite plane while being heated, established a modified mathematical model of transient plane source method, and achieved the measurement of thermal conductivity of automotive interior material sample by the data processing method of mathematical iteration and liner regression using the modified transient plane source probe. According to the data of experiments, the instrument which this paper designed has a high precision of 5% and a wide range of 0.003-1W/(mK).This paper provides a practicable way for heat capacity determination of automotive interior materials.

Scattering of SH Wave on Periodic Cracks in an Infinite Plane of Piezoelectric/Piezomagnic Composite Materials

2012 ◽  
Vol 166-169 ◽  
pp. 3364-3368
Author(s):  
Wei Shi ◽  
Li Xia Ma
Keyword(s):  
Stress Intensity Factor ◽  
Integral Equation ◽  
Composite Materials ◽  
Piezoelectric Materials ◽  
Infinite Plane ◽  
Sh Wave ◽  
Scattering Problems ◽  
Sh Waves ◽  
Periodic Cracks ◽  
The Fourier Transform

In this paper, the scattering problems of SH waves on periodic cracks in an infinite of piezoelectric/piezomagnic composite materials bonded to an infinite of homogeneous piezoelectric materials is investigated, the Fourier transform techniques are used to reduce the problem to the solution of Hilbert singular integral equation, the latter is solved by Lobotto-Chebyshev and Gauss integral equation, at last, numerical results showed the effect of the frequency of wave, sizes and so on upon the normalized stress intensity factor.

scholarly journals WAVE TRANSMISSION THROUGH TRAPEZOIDAL BREAKWATERS

1978 ◽  
Vol 1 (16) ◽  
pp. 129 ◽  
Author(s):  
Ole Secher Madsen ◽  
Paisal Shusang ◽  
Sue Ann Hanson
Keyword(s):  
Energy Dissipation ◽  
Approximate Method ◽  
Cross Section ◽  
Wave Energy ◽  
Graphical Form ◽  
Dissipated Energy ◽  
Simple Method ◽  
Reflection And Transmission ◽  
Transmission Coefficients

In a previous paper Madsen and White (1977) developed an approximate method for the determination of reflection and transmission characteristics of multi-layered, porous rubble-mound breakwaters of trapezoidal cross-section. This approximate method was based on the assumption that the energy dissipation associated with the wave-structure interaction could be considered as two separate mechanisms: (1) an external, frictional dissipation on the seaward slope; (2) an internal dissipation within the porous structure. The external dissipation on the seaward slope was evaluated from the semi-theoretical analysis of energy dissipation on rough, impermeable slopes developed by Madsen and White (1975). The remaining wave energy was represented by an equivalent wave incident on a hydraulically equivalent porous breakwater of rectangular cross-section. The partitioning of the remaining wave energy among reflected, transmitted and internally dissipated energy was evaluated as described by Madsen (1974), leading to a determination of the reflection and transmission coefficients of the structure. The advantage of this previous approximate method was its ease of use. Input data requirements were limited to quantities which would either be known (water depth, wave characteristics, breakwater geometry, and stone sizes) or could be estimated (porosity) by the design engineer. This feature was achieved by the employment of empirical relationships for the parameterization of the external and internal energy dissipation mechanisms. General solutions were presented in graphical form so that calculations could proceed using no more sophisticated equipment than a hand calculator (or a slide rule). This simple method gave estimates of transmission coefficients in excellent agreement with laboratory measurements whereas its ability to predict reflection coefficients left a lot to be desired.

Complete Williams Asymptotic Expansion near the Crack Tips of Collinear Cracks of Equal Lengths in an Infinite Plane

2016 ◽  
Vol 258 ◽  
pp. 209-212 ◽  
Author(s):  
Larisa Stepanova ◽  
Pavel Roslyakov ◽  
Tatjana Gerasimova
Keyword(s):  
Plane Elasticity ◽  
Analytical Determination ◽  
Geometrical Parameters ◽  
Infinite Plane ◽  
Variable Theory ◽  
Complex Variable Theory ◽  
Plane Medium ◽  
Crack Tips ◽  
Plane Elasticity Theory

The present study is aimed at analytical determination of coefficients in crack tip expansion for two collinear finite cracks of equal lengths in an infinite plane medium. The study is based on the solutions of the complex variable theory in plane elasticity theory. The analytical dependence of the coefficients on the geometrical parameters and the applied loads for two finite cracks in an infinite plane medium is given. It is shown that the effect of the higher order terms of the Williams series expansion becomes more considerable at large distances from the crack tips. The knowledge of more terms of the stress asymptotic expansions allows us to approximate the stress field near the crack tips with high accuracy.

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