SDOF Matlab Files-20191130_superposition_结构动力学_振型叠加_源码

% This script has been written to show the influence of the pulse duration % on the response of a SDOF system to a square pulse. % % THE PROBLEM % % A single degree of freedom system is being considered. % % The mass is 1kg % The stiffness is 1N/m % The damping ratio is 0.1 % % The system is subject to a force of 1 N applied as a step at time 0. The % response for varying durations of pulse is then studied. clear all close all % Define system properties k=1; m=1; xi=0.1; P=1; t_end=5; % Find the natural frequency omega_n=sqrt(k/m); omega_d=omega_n*sqrt(1-xi^2); % Calculate the response to the step at time t=0 A=xi*omega_n/omega_d*P/k; B=P/k; tstep=0.0001; t=[0:tstep:25]; u=P/k-exp(-xi*omega_n*t).*(A*sin(omega_d*t)+B*cos(omega_d*t)); f1=figure('Units','centimeters','Position',[5 5 20.99 14.05]); hold on kstep=100; for i=1:100 t_end=round(i/kstep*2*pi/omega_n,4); % Find the index of the end of the load pulse idx=int32(t_end/tstep+1); t_free=t(idx:length(t)); % time after the downward step tau=t_free-t(idx); % shifted time, to calculate the downward step P=-1; A=xi*omega_n/omega_d*P/k; B=P/k; u_down=P/k-exp(-xi*omega_n*tau).*(A*sin(omega_d*tau)+B*cos(omega_d*tau)); % Add together the two responses u_total=u; u_total(idx:end)=u_total(idx:end)+u_down; u_max(i)=max(u_total); i_max=find(u_total==u_max(i)); t_max(i)=t(i_max); t_r(i)=i/kstep; if i==1 plot(t,u_total,'LineWidth',1.5) end if i==21 plot(t,u_total,'LineWidth',1.5) end if i==41 plot(t,u_total,'LineWidth',1.5) end if i==61 plot(t,u_total,'LineWidth',1.5) end if i==81 plot(t,u_total,'LineWidth',1.5) end end grid on xlabel('Time (secs)','Interpreter','Latex','FontSize',14) ylabel('Displacement (m)','Interpreter','Latex','FontSize',14) legend('$t_{end}=0.01$','$t_{end}=0.21$','$t_{end}=0.41$','$t_{end}=0.61$','$t_{end}=0.81$','Interpreter','Latex','FontSize',14) % print(gcf,'FIGURES\Pulse_Duration_One.png','-dpng','-r300'); f2=figure('Units','centimeters','Position',[5 5 20.99 14.05]); plot(t_r,u_max,'k','LineWidth',1.5); grid on xlabel('Normalised Pulse Length $\frac{t_{end}}{T_n}$','Interpreter','Latex','FontSize',14) ylabel('Maximum Response Ratio','Interpreter','Latex','FontSize',14) legend('$\xi=0.1$','Interpreter','Latex','FontSize',14,'Location','southeast') % print(gcf,'FIGURES\Pulse_Duration_Two.png','-dpng','-r300');