expoFit.m

function [zeta] = expoFit(y,t,wn,optionPlot)
% [zeta] = expoFit(y,t,wn) returns the damping ratio calcualted by fitting
% an exponential decay to the envelop of the free-decay response.
%
% Input:
%   y: envelop of the free-decay response: vector of size [1 x N]
%   t: time vector [ 1 x N]
%   wn: target eigen frequencies (rad/Hz) :  [1 x 1]
%  optionPlot: 1 to plot the fitted function, and 0 not to plot it.
% 
% Output
%  zeta: modal damping ratio:  [1 x 1]
% 
% author: E. Cheynet  - UiB - last updated: 14-05-2020
% 

%%
% Initialisation
guess = [1,1e-2];
% simple exponentiald ecay function
myFun = @(a,x) a(1).*exp(-a(2).*x);
% application of nlinfit function
coeff = nlinfit(t,y,myFun,guess);
% modal damping ratio:
zeta = abs(coeff(2)./wn);

% alternatively: plot the fitted function
if optionPlot== 1, plot(t,myFun(coeff,t),'r'); end
end