4 BRETSCHNEIDER SPECTRUM DEFINITION4 Bretschneider Spectrum DefinitionThe formula for the Bretschneider (one-sided) ocean wave spectrum is5S(ω) =ω4m164H2 551/3e− ωm/4ω4ωwhere ω is frequency in radians per second, ωmis the modal (most likely) frequencygiven wave, and H1/3is the significant wave height. Make a single figure that shoBretschneider spectrum (S as a function of ω) for these cases:SeaState 2π/ωm, sec H1/3, m2 6.3 0.33 7.5 0.94 8.8 1.95 9.7 3.36 12.4 5.0Here is the MATLAB code I used and the resulting figure:%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% 2.017 Homework 1. Bretschnieder Spectrum.% FSH MIT Mechanical Engineeringclear all;figure(1);clf;hold off; hold on; % note: hold is on so we can% figures% show the data from the table in the problemSSvec = [2 3 4 5 6] ; % sea stateswmvec = 2*pi*ones(size(SSvec)) ./ [6.3 7.5 8.8 9.7 12.4] ;% modal frequenciesHsigvec = [0.3 0.9 1.9 3.3 5.0] ; % significant wave heights% vector of frequencies for the spectrum calculationwvec = [.1:.01:2];% step through the different seastatesfor i = 1:length(wmvec),wm = wmvec(i) ;Hsig = Hsigvec(i) ;SS = SSvec(i) ;5of anyws the%%%%overlay4 BRETSCHNEIDER SPECTRUM DEFINITION 6 for j = 1:length(wvec), w = wvec(j) ; S(j) = 5/16 * wm^4 / w^5 * Hsig^2 * exp(-5 * wm^4 / 4 / w^4) ; end; % check that we got the right formula! disp(sprintf(... ’Square Root of Integral of Area of S: %g; 4*Hsig: %g’, ... sqrt(sum(S)*mean(diff(wvec))), 1/4*Hsig)); % add on the curves and some labels plot(wvec,S,’LineWidth’,2); if SS > 3, text(wm-.18,max(S),sprintf(’SS %g’, SS)); end; end; % finish off the plot grid; title(’Sea Wave Spectra for Sea States 2-6’); xlabel(’frequency \omega, rad/s’); ylabel(’S(\omega)’); print -deps hw1_bret.eps %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%4 BRETSCHNEIDER SPECTRUM DEFINITION 7 Sea Wave Spectra for Sea States 2−6 4.5S(ω) 4 3.5 3 2.5 2 1.5 1 0.5 0 SS 4 SS 5 SS 6 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8 2 frequency ω, rad/sMIT OpenCourseWarehttp://ocw.mit.edu 2.017J Design of Electromechanical Robotic Systems Fall 2009 For information about citing these materials or our Terms of Use, visit:
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