Transient generation of elastic waves in solids by a disk-shaped normal force source

Abstract

A method for computing the transient radiation from a wide circular source, acting at a solid surface, is given for two different normal force apodizations. This method, based on a double Laplace–Hankel transform and a Cagniard inversion, allows an exact formulation of the impulse response to be obtained for two components of the displacement at any point inside the solid and is amenable to computing the field for an arbitrary time excitation. Numerical results are presented and are compared with experimental results for generation by a piezoelectric transducer.

<title>Ultrasonic field modeling for arbitrary non-contact transducer source</title>

“…Assuming the Lorentz force is decomposed spatially into N force components, the total displacement for these temporal delta force components is given by, where ⊗ denotes a convolution operation, ( ) f t is the temporal dependence of Lorentz force, ( , , 0, ) u t x y z δ = is the total displacement for these temporal delta force components of each circular source (piston or ring source), and is given by, with temporal dependence of delta function [11][12] . In same way, the solution to line coil can be deduced, but will not be given here due to limit space.…”

“…Due to the complexity of the problem, an analytical solution is only available for some simple uniform force distributions, such as uniform normal piston force and uniform radially acting ring force [1,3,[11][12] . Accordingly, transient field studies were carried out generally by the Finite Element Method (FEM) [7][8][9] .…”

Nonsteady Problem for an Elastic Half-Plane with Mixed Boundary Conditions

“…For rather small values of k, such a load may model a delta-function load, which is often used in such studies [10]. …”

“…Solutions for the displacements and stresses inside a half-space under a uniformly distributed step load were found in [14,[21][22][23] using the residue theory to invert the Laplace transform. The expressions derived in [10] are the superposition of the analytic solutions of the Lamb problem and the convolution with respect to the radial coordinate of the load distribution function and the fundamental solution. Two types of spatial distribution of load were considered and the elastic displacements resulting from a load varying with time as a delta function were calculated.…”

A model for transient ultrasonic field in solid generated by a transducer in immersion

“…Ultrasonic modelling of transducer radiation and flaw scattering is very helpful for explicit physical interpretations of the results of measurements, optimal transducer design and measurement system arrangement [1][2][3][4][5][6][7][8][9][10][11][12]. In ultrasonic imaging and automatic ultrasonic testing, the immersion mode is widely employed to remove the coupling problem and to enhance the inspection speed [13][14][15][16][17][18].…”