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

244 MATLAB programs
function [ztors, zspher] = spheroidal (pois, m, wmin, wmax)
% Computes the torsional and spheroidal modes of a solid sphere, and
% plots the two determinant functions whose zero crossings define the roots
% Assumes a sphere of radius R=1 and shear wave velocity Cs=1
% Note: the modes are independent of the azimuthal index n
%
% Input arguments:
% pois = Poisson’s ratio
% m = radial index
% wmin = minimum frequency for search
% wmax = maximum frequency for search
% Output arguments:
% ztors = dimensionless frequencies, torsional modes
% zspher = dimensionless frequencies, spheroidal modes
% Actual frequencies (rad/s) are obtained multiplying by Cs/R
% where Cs is the shear wave velocity, and R is the radius
%
% For enhanced accuracy, it uses the Bessel functions of half order
% instead of the actual spherical Bessel functions. Reason:
% The factors sqrt(pi/2z) cancel out in the determinant equations
%
% Makes first a rough search in the search interval to determine approximate
% values of the roots, then refines the results using the bisection method
%
% Results agree with Eringen & Suhubi, Elastodynamics, Vol. II, pp. 814,818
dz = 0.1; % initial search step
if wmin0
f = dettors(m,zs);
ztors = zerox(f,dz,zs(1));
nz = length(ztors);
for k=1:nz
z1 = ztors(k)-dz;
z2 = ztors(k)+dz;
ztors(k) = bisect2(‘dettors’, m, z1, z2, 1.e-5,pois);
end
plot(zs,f);
axis([0 wmax -1 1]);
grid on;
pause;