Nearfield of Time Harmonic Scalar‐Wave Beams

1968 ◽  
Vol 44 (3) ◽  
pp. 735-739
Author(s):  
H. N. Kritikos
Keyword(s):  
Scalar Wave ◽  
Time Harmonic ◽  
Harmonic Scalar

Switching on a two-dimensional time-harmonic scalar wave in the presence of a diffracting edge

Wave Motion ◽  
2011 ◽  
Vol 48 (3) ◽  
pp. 197-213 ◽  
Author(s):  
D.P. Hewett ◽  
J.R. Ockendon ◽  
D.J. Allwright
Keyword(s):  
Two Dimensional ◽  
Scalar Wave ◽  
Time Harmonic ◽  
Harmonic Scalar

The scattering of a scalar wave by a semi-infinite rod of circular cross section

1955 ◽  
Vol 247 (934) ◽  
pp. 499-528 ◽  
Keyword(s):  
Boundary Condition ◽  
Circular Cross Section ◽  
Scattering Coefficient ◽  
Wave Number ◽  
Infinite Cylinder ◽  
Angle Of Incidence ◽  
Pressure Amplitude ◽  
Average Pressure ◽  
Scalar Wave ◽  
Harmonic Scalar

The form of the exact solution for the scattering of a plane harmonic scalar wave by a semi-infinite circular cylindrical rod of diameter 2 a is found when the boundary condition is u — 0 or du/dv — 0,where u represents the scalar field and v is the normal to the rod. When the angle of incidence is n, i.e. the angle between the direction of propagation of the incident wave and the normal (out of the rod) to the end is , the average pressure amplitude on the end of the rod and the scattering coefficient are found for the boundary condition 0. Graphs are given showing the behaviour of these quantities for the range 0 < < 10, where k is the wave-number. When ka reaches 10, the quantities have almost become constant. For small values of ka the scattering coefficient is shown to be {ka)2', it appears from the numerical results that this is, in fact, a fairly close approximation for ka <2. It is further shown that the average pressure amplitude on the end for other angles of incidence is approximately the product of the average pressure amplitude for an angle of incidence of n and the amplitude of the symmetric mode (ka < 3-83) which the incident field would produce inside a hollow semi-infinite cylinder occupying the same position as the rod. When the boundary condition is u — 0 and ka is small it is proved that the scattered field is the same as that due to a semi-infinite hollow cylinder longer by an amount 0-la approximately. A similar result does not hold for the boundary condition 0. The theory is extended to the case when a pressure pulse falls on a circular rod. It is found that the pressure on the end drops almost to its final value in the time taken for a wave to travel the diameter of the rod, and that the average pressure during this process is given, at time by (0-9154-0-745(2— a0tja)2}I approximately, where a0 is the speed of sound. Tables, in the range 0(0-25)10 of ka, of the ‘split’ functions which arise in connexion with a semi-infinite cylinder are given.

Focusing Time-Harmonic Scalar Fields in Complex Scenarios: A Comparison

2013 ◽  
Vol 12 ◽  
pp. 1029-1032 ◽  
Author(s):  
Domenica A. M. Iero ◽  
Tommaso Isernia ◽  
Lorenzo Crocco
Keyword(s):  
Scalar Fields ◽  
Time Harmonic ◽  
Harmonic Scalar

Calculating the response of waveguides to base excitation using the wave and finite element method

2021 ◽  
pp. 107754632098131
Author(s):  
Jamil Renno ◽  
Sadok Sassi ◽  
Wael I Alnahhal
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Transfer Functions ◽  
Travelling Waves ◽  
Model Free ◽  
Time Harmonic ◽  
Element Approach ◽  
Response Transfer ◽  
Free Wave Propagation ◽  
Element Method

The prediction of the response of waveguides to time-harmonic base excitations has many applications in mechanical, aerospace and civil engineering. The response to base excitations can be obtained analytically for simple waveguides only. For general waveguides, the response to time-harmonic base excitations can be obtained using the finite element method. In this study, we present a wave and finite element approach to calculate the response of waveguides to time-harmonic base excitations. The wave and finite element method is used to model free wave propagation in the waveguide, and these characteristics are then used to find the amplitude of excited waves in the waveguide. Reflection matrices at the boundaries of the waveguide are then used to find the amplitude of the travelling waves in the waveguide and subsequently the response of the waveguide. This includes the displacement and stress frequency response transfer functions. Numerical examples are presented to demonstrate the approach and to discuss the numerical efficiency of the proposed method.

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