Eduardo Kausel-Fundamental solutions in elastodynamics_ a compendium-Cambridge University Press (2006)

212 MATLAB programs
function [] = Cavity3D(r, pois)
% Spherical (3-D) cavity in a full, homogeneous space
% subjected to a harmonic/impulsive pressure p
% Arguments:
% r = R/R0 = (distance to receiver)/(radius of cavity)
% pois = Poisson’s ratio
%
% This program assumes p0=1 (unit pressure), and r0=1 (radius of cavity)
% Basic parameters
a2 = (2-2*pois)/(1-2*pois);
a = sqrt(a2); % Cp/Cs
R0 = 1;
% Radius of cavity
R = r*R0;
% Receiver
rho = 1;
% mass density
Cs = 1;
% S-wave velocity
Cp = a*Cs;
% P-wave velocity
mu = rho*Csˆ2; % shear modulus
% Frequency and time vectors
nf = 1024;
wmax = 16*pi;
dw = wmax/nf;
w = [dw:dw:wmax];
tmax = 6;
% maximum dimensionless time
nt = 200;
% No. of time steps
dt = tmax/nt; % time step
T = [0:nt]*dt; % dimensionless, delayed time (= t*Cp/R)
% Response in frequency domain
fac = 0.25*R0/mu; % assuming p=1 here
w0 = w*R0/Cp;
w1 = w0*r;
G0 = 1+i*w0;
G1 = 1+i*w1;
G = fac*(G0./(G0-0.25*a2*w0.ˆ2)); % Cavity wall at R0
plot(w,real(G));
hold on;
plot(w,imag(G),‘r’);
grid on;
tit = sprintf(...
‘T.F. for pressure in spherical cavity, R/R0=%5.4f, \\nu=%5.2f’,...
r, pois);
titx = ‘Frequency (rad/s)’;
title (tit);
xlabel(titx);
H = G.*exp(-i*(r-1)*w0).*G1./G0/rˆ2; %Receiver at R
plot(w,real(H),‘:’);
plot(w,imag(H),‘r:’);