振动理论与分析7.ppt

文档介绍：Computation for differential putation for differential equation putation for differential putation for differential equation % main program t0 = 0; tN= 5; y0 = [1 0]; [t, y]=ode45(***@vib, [t0 tN],y0); subplot(1,2,1); plot(t,y); subplot(1,2,2); plot (y(:,1),y(:,2)); %sub_function function ydot= vib(t,z) x=z(1); xd=z(2); xdd=-1/3 * (8* xd+100 * x); ydot=[xd;xdd]; 10x00x 0 100x x8x3?????)(;)( ???? Example1 Input parameters Initial time t0 End time putation for differential equation x(t) dx/dt x(t) dx/dt Response time history Phase diagram example2 ?% example 2 ? t0 = 0; tN= 5; tol= 1e-7; y0 = [0 0]; ?[t, y]=ode45(***@vib2, [t0 tN],y0); ?? subplot(1,2,1); ? plot(t,y); ? subplot(1,2,2); ? plot (y(:,1),y(:,2)); function ydot= vib2(t,z) x=z(1); xd=z(2); xdd=-1/3 * (8* xd+100 * x-100); ydot=[xd;xdd]; 00x00x 100u(t) 100x x8x3?????)(;)( ????00x00x 100u(t) 100x x8x3?????)(;)( ???? Step response Example 2 STEP RESPONSE example3 ? t0 = 0; tN= 20; tol= 1e-7; y0 = [0 0]; ?[t, y]=ode45(***@vib3, [t0 tN],y0); ?? subplot(1,2,1); ? plot(t,y); ? subplot(1,2,2); ? plot (y(:,1),y(:,2)); function ydot= vib3(t,z) x=z(1); xd=z(2); xdd=-1/3 * (8* xd+100 * x-cos(2 * pi* * t)); ydot=[xd;xdd]; 00x00x 5t cos0 100x x8x3?????)(;)( .???? example3 00x00x 5t cos0 100x x8x3?????)(;)( .???? xdd=-1/3 * (8* xd+100 * x-cos( * t)); ponent Steady response Example3 Harmonic response Example4 nonlinear vibration ? t0 = 0; tN= 20; tol= 1e-7; y0 = [0 ]; ??[t, y]=ode45(***@vdpol, [t0 tN],y0); ?? subplot(1,2,1); ? plot(t,y); ? subplot(1,2,2); ? plot (y(:,1),y(:,2)); function ydot= vdpol(t,y) ydot = zeros(2,1); % a column vector ydot(1) = -y(1) * (y(2)^2-1)-y(2); ydot(2) = y(1); 0x 0xxx1x 2??????)(,)( )(????