dva_kelvin_voigt

function [maxAmp,X] = dva_kelvin_voigt(x,p)

% Author: Rebecca Corman
% Date: January 27, 2014
% FUNCTION: dva_kelvin_voigt
% INPUTS:
% x - vector of design parameters, these parameters will vary with
% optimization
% p - set of fixed parameters, these parameters will not change with
% optimization
% OUTPUTS:
% maxAmp - maximum amplitude of mass, m1
% X - array of position of mass, m1
%
% This function takes inputs of design variables and fixed parameters and
% calculates the response of a mass-spring system to a forcing function at
% frequency omega using the Kelvin-Voigt model.


% Set parameters
mu = p.mu;
r = p.r;

% Design Variables
beta = x(1);
zeta = x(2);



X = zeros(size(r)); % Initialize X

for i=1:length(r)    
    % non-dimensional amplitude:
    X(i) = sqrt(((2*zeta*r(i))^2+(r(i)^2-beta^2)^2)/...
        ((2*zeta*r(i))^2*(r(i)^2-1+mu*r(i)^2)^2+...
        (mu*r(i)^2*beta^2-(r(i)^2-1)*(r(i)^2-beta^2))^2));
end

% objective function:
maxAmp = max(X);

end