7/31/2019 Aeroelasticity - Flutter

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clear all;m = 50;l = 3;c = l/2;b = c/2;S = c*l;

e = 0.25*c;xt = 0.05*c;rt = xt/0.4;Kh = 9000;Kt = 6000;CLt = 2*pi;

St = m*xt;It = m*rt^2;wh = sqrt(Kh/m)wt = sqrt(Kt/It)D = ((m*e+St)*S*CLt)^2;E = (-2*(m*e+St)*(m*Kt+It*Kh)+4*(m*It-St^2)*e*Kh)*S*CLt;

F = (m*Kt+It*Kh)^2 - 4*(m*It-St^2)*Kh*Kt;syms x; %t bin hnh thc

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mr = solve(D*x^2+E*x+F);rho = 1.255;Vf = [sqrt(2*mr(1)/rho); sqrt(2*mr(2)/rho)];

%a vi lng v th nguynmu = m/(pi*rho*b^2*l);

R = wh/wt;ebar = e/b;rtbar = rt/b;xtbar = xt/b;

syms OhmUbar; %t bin hnh thcA = (-Ohm^2 + R^2)*(-rtbar^2*Ohm^2+rtbar^2-ebar*CLt*Ubar^2/pi/mu);B = (-xtbar*Ohm^2)*(-xtbar*Ohm^2+CLt*Ubar^2/pi/mu);% A-B l nh thc ca ma trnflutter_func = solve(A-B,Ohm);

X = [0:0.001:1]; % Khong gi tr s th vo UbarY1 = subs(flutter_func(1),X);

Y2 = subs(flutter_func(2),X);Y3 = subs(flutter_func(3),X);Y4 = subs(flutter_func(1),X);plot(X,[Y1;Y2;Y3;Y4],'LineWidth',1.5);

xlabel('U-bar');ylabel('\Omega');legend({'\Omega_1(U-bar)','\Omega_2(U-bar)','\Omega_3(U-bar)',...

'\Omega_4(U-bar)'})title('\Omega versus U-bar');grid on;