Transient analytic point‐source response of a layered acoustic medium: Part I

Geophysics ◽  
1985 ◽  
Vol 50 (9) ◽  
pp. 1466-1477 ◽  
Author(s):  
Martin Tygel ◽  
Peter Hubral
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Point Source ◽  
Time Domain ◽  
Plane Waves ◽  
Natural Extension ◽  
Acoustic Medium ◽  
Angle Of Incidence ◽  
The Time Domain ◽  
Plane Wave Propagation

The exact transient responses (e.g., reflection or transmission responses) of a transient point source above a stack of parallel acoustic homogeneous layers between two half‐spaces can be analytically obtained in the form of a finite integral strictly in the time domain. (The theory is presented in part II of this paper, this issue.) The transient acoustic potential of the point source is decomposed into transient plane waves, which are propagated through the layers at any angle of incidence as well in the time domain; finally, they are superposed to obtain the total point‐source response. The theory dealing with transient analytic plane wave propagation is described here. It constitutes an essential part of computing the synthetic seismogram by the new transient method proposed in part II. The plane‐wave propagation is achieved by an exact discrete recursion that automatically handles the conversion of homogeneous waves into inhomogeneous transient plane waves at layer boundaries. A particularly efficient algorithm is presented, that can be viewed as a natural extension of the popular normal‐incidence Goupillaud (1961)-type algorithm to the nonnormal incidence case.

A NONLINEAR PLANE-WAVE ALGORITHM FOR DIFFRACTIVE PROPAGATION INVOLVING SHOCKWAVES

1993 ◽  
Vol 01 (03) ◽  
pp. 371-393 ◽  
Author(s):  
P. TED CHRISTOPHER
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Frequency Domain ◽  
Time Domain ◽  
Burgers Equation ◽  
Propagation Model ◽  
Nonlinear Beam ◽  
Nonlinear Plane ◽  
Very High ◽  
Plane Wave Propagation

A new algorithm for nonlinear plane-wave propagation is presented. The algorithm uses a novel time domain representation to account for nonlinearity, while accounting for absorption in the frequency domain. The new algorithm allows for accurate representations of diffractive shockwave propagation in the framework of an existing nonlinear beam propagation model using far fewer harmonics (and thus time) than alternative algorithms based on a frequency domain solution to Burgers' equation. The new algorithm is tested against the frequency domain solution to Burgers' equation in a variety of cases and then used to model a focused ultrasonic piston transducer operating at very high source intensities.

Plane Waves Due to Combined Compressive and Shear Stresses in a Half Space

1969 ◽  
Vol 36 (2) ◽  
pp. 189-197 ◽  
Author(s):  
T. C. T. Ting ◽  
Ning Nan
Keyword(s):  
Wave Propagation ◽  
Plane Wave ◽  
Half Space ◽  
Plastic Material ◽  
Plane Waves ◽  
Shear Stresses ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Plane Wave Propagation

The plane wave propagation in a half space due to a uniformly distributed step load of pressure and shear on the surface was first studied by Bleich and Nelson. The material in the half space was assumed to be elastic-ideally plastic. In this paper, we study the same problem for a general elastic-plastic material. The half space can be initially prestressed. The results can be extended to the case in which the loads on the surface are not necessarily step loads, but with a restricting relation between the pressure and the shear stresses.

scholarly journals Propagation Modeling of Point Source Excited Magnetoinductive Waves Based on a New Plane Wave Expansion Approach

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Feng Liu ◽  
Zhijun Zhang ◽  
Lianqing Zhu ◽  
Yajun Liu
Keyword(s):  
Plane Wave ◽  
Point Source ◽  
Time Domain ◽  
Near Field ◽  
Plane Waves ◽  
Low Frequency ◽  
Square Lattice ◽  
Plane Wave Expansion ◽  
Propagation Modeling ◽  
Wave Expansion

The signal fading in wireless underground sensor networks (WUSNs), which is caused by lossy media such as soil and sand, can be reduced by applying technology of magnetoinductive (MI) propagation. This technology can effectively establish a communication at very low frequency (VLF). In contrast to the previous studies in the literature, which mostly focus on the propagation of plane waves, we propose a new approach based on the plane wave expansion (PWE) to model the near field MI waves. The proposed approach is based on excitation of a point source, which is a common case in a practical WUSN. The frequent usage of square lattice MI structure is investigated. To verify the mathematical derivation, the simulation of time domain based on the fourth-order Runge-Kutta (RK) method is carried out. Simulation results show that the new model can provide a precise prediction to the MI wave’s propagation, with the computation load being one-tenth of that of the time domain simulation. The characteristics of the propagation of the MI waves are presented and discussed. Finally, the reflection on the edge of the MI structure is reduced by analysing the terminal matching conditions and calculating a method for matching impedances.

Transient analytic point‐source response of a layered acoustic medium: Part II

Geophysics ◽  
1985 ◽  
Vol 50 (9) ◽  
pp. 1478-1487 ◽  
Author(s):  
Martin Tygel ◽  
Peter Hubral
Keyword(s):  
Point Source ◽  
Plane Waves ◽  
Integral Solution ◽  
Acoustic Medium ◽  
Transient Solution ◽  
Full Wave ◽  
Starting Point ◽  
Infinite Integral ◽  
The Time Domain ◽  
Root Operator

In part I (this issue) analytic methods are described for propagating directly in the time domain the full wave field of transient plane waves at arbitrary incidence angles through parallel acoustic homogeneous layers. The theory of part I is used here to compute transient point‐source responses by way of integrating the transient plane‐wave responses over various (real and nonreal) incidence angles. At first the complete transient point‐source reflection (transmission) responses are formulated with the help of the transient Sommerfeld‐Weyl integral that was developed previously by us. This leads to a transient solution in form of an infinite integral over incidence angles involving an (angle‐dependent) integrand that is a time‐convolution between a transient reflectivity (transmissivity) function and an inverse transient analytic square root operator. The transient Sommerfeld‐Weyl integral solution is then proven to be causal. This causality provides the starting point for formulating exact transient point‐source responses in terms of integrals over a finite range of incidence angles only.

Time Domain Simulations on a Single Point Moored Submerged Sphere of Variable Radius

2005 ◽  
Author(s):  
Joa˜o M. B. P. Cruz ◽  
Anto´nio J. N. A. Sarmento
Keyword(s):  
Wave Propagation ◽  
Time Domain ◽  
Physical Phenomenon ◽  
Single Point ◽  
Vertical Direction ◽  
Equation Of Motion ◽  
Hydrodynamic Coefficients ◽  
Energy Converter ◽  
Submerged Sphere ◽  
The Time Domain

This paper presents a different approach to the work developed by Cruz and Sarmento (2005), where the same problem was studied in the frequency domain. It concerns the same sphere, connected to the seabed by a tension line (single point moored), that oscillates with respect to the vertical direction in the plane of wave propagation. The pulsating nature of the sphere is the basic physical phenomenon that allows the use of this model as a simulation of a floating wave energy converter. The hydrodynamic coefficients and diffraction forces presented in Linton (1991) and Lopes and Sarmento (2002) for a submerged sphere are used. The equation of motion in the angular direction is solved in the time domain without any assumption about its output, allowing comparisons with the previously obtained results.

scholarly journals Effects of Central Tube on Shape of Modal Duct of a Helicoid in a Simple Expansion Chamber

2018 ◽  
Vol 2018 ◽  
pp. 1-6
Author(s):  
Daniel Omondi Onyango ◽  
Robert Kinyua ◽  
Abel Nyakundi Mayaka
Keyword(s):  
Wave Propagation ◽  
Acoustic Wave ◽  
Plane Wave ◽  
Acoustic Pressure ◽  
Three Dimensional ◽  
The Other ◽  
Expansion Chamber ◽  
Central Tube ◽  
Simple Expansion ◽  
Plane Wave Propagation

The shape of the modal duct of an acoustic wave propagating in a muffling system varies with the internal geometry. This shape can be either as a result of plane wave propagation or three-dimensional wave propagation. These shapes depict the distribution of acoustic pressure that may be used in the design or modification of mufflers to create resonance at cut-off frequencies and hence achieve noise attenuation or special effects on the output of the noise. This research compares the shapes of acoustic duct modes of two sets of four pitch configurations of a helicoid in a simple expansion chamber with and without a central tube. Models are generated using Autodesk Inventor modeling software and imported into ANSYS 18.2, where a fluid volume from the complex computer-aided-design (CAD) geometry is extracted for three-dimensional (3D) analysis. Mesh is generated to capture the details of the fluid cavity for frequency range between 0 and 2000Hz. After defining acoustic properties, acoustic boundary conditions and loads were defined at inlet and outlet ports before computation. Postprocessed acoustic results of the modal shapes and transmission loss (TL) characteristics of the two configurations were obtained and compared for geometries of the same helical pitch. It was established that whereas plane wave propagation in a simple expansion chamber (SEC) resulted in a clearly defined acoustic pressure pattern across the propagation path, the distribution in the configurations with and without the central tube depicted three-dimensional acoustic wave propagation characteristics, with patterns scattering or consolidating to regions of either very low or very high acoustic pressure differentials. A difference of about 80 decibels between the highest and lowest acoustic pressure levels was observed for the modal duct of the geometry with four turns and with a central tube. On the other hand, the shape of the TL curve shifts from a sinusoidal-shaped profile with well-defined peaks and valleys in definite multiples of π for the simple expansion chamber, while that of the other two configurations depended on the variation in wavelength that affects the location of occurrence of cut-on or cut-off frequency. The geometry with four turns and a central tube had a maximum value of TL of about 90 decibels at approximately 1900Hz.

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