加振周波数ωと変位の応答倍率Md/位相角Φの関係

clear; close all;
zetas = [1,0.5,0.2,0.1,0.01];
w_wn = linspace(0,2,100);
Mds=[];
figure();
hold on;
for idx=1:length(zetas)
  zeta = zetas(idx);

  Md = 1./sqrt((1-w_wn.^2).^2+4*zeta^2.*w_wn.^2);
  plot(w_wn, Md,'DisplayName',sprintf('zeta=%.2g',zeta));
end
legend();
xlabel('加振振動数比w_wn');
ylabel('変位の応答倍率Md');
ylim([0,10]);
big;

clear; close all;
zetas = [1,0.5,0.2,0.1,0.01];
w_wn = logspace(-1,1,100);
Mds=[];
figure();
axes('XScale', 'log', 'YScale', 'log');
hold on;
for idx=1:length(zetas)
  zeta = zetas(idx);
  Md = 1./sqrt((1-w_wn.^2).^2+4*zeta^2.*w_wn.^2);
  plot(w_wn, Md,'DisplayName',sprintf('zeta=%.2g',zeta));
end
legend();
xlabel('加振振動数比w_wn');
ylabel('変位の応答倍率Md');
big;

位相角

clear; close all;
zetas = [1,0.5,0.2,0.1,0.01];
w_wn = linspace(0,2,100);
Mds=[];
figure();
hold on;
for idx=1:length(zetas)
  zeta = zetas(idx);

%   Md = 1./sqrt((1-w_wn.^2).^2+4*zeta^2.*w_wn.^2);
  phi = rad2deg(atan2(2*zeta*w_wn,1-w_wn.^2));
  plot(w_wn, phi,'DisplayName',sprintf('zeta=%.2g',zeta));
end
legend();
xlabel('加振振動数比w_wn');
ylabel('位相角Φ');
big;

clear; close all;
zetas = [1,0.5,0.2,0.1,0.01];
w_wn = linspace(0,2,100);
Mds=[];
figure();
hold on;
for idx=1:length(zetas)
  zeta = zetas(idx);

%   Md = 1./sqrt((1-w_wn.^2).^2+4*zeta^2.*w_wn.^2);
  phi = rad2deg(atan2(2*zeta*w_wn,1-w_wn.^2));
  plot(w_wn, phi,'DisplayName',sprintf('zeta=%.2g',zeta));
end
legend();
xlabel('加振振動数比w_wn');
ylabel('位相角Φ');
big;