newmark的简单介绍

K=diag(k0+[k1;0])-diag(k1,-1)-diag(k1,1); C=diag(c0+[c1;0])-diag(c1,-1)-diag(c1,1); M=diag(m0); KK=K+a0*M+a1*C; N1=size(F,1); N2=size(F,2); U=zeros(N1,N2); V=zeros(N1,N2); A=zeros(N1,N2); U(:,1)=U0; V(:,1)=V0; A(:,1)=A0;

for i=1:N2-1

fe=F(:,i+1)+M*(a0*U(:,i)+a2*V(:,i)...

+a3*A(:,i))+C*(a1*U(:,i)+a4*V(:,i)+a5*A(:,i)); U(:,i+1)=inv(KK)*fe;

A(:,i+1)=a0*(U(:,i+1)-U(:,i))-a2*V(:,i)-a3*A(:,i); V(:,i+1)=V(:,i)+a6*A(:,i)+a7*A(:,i+1); end

f1=zeros(1,2001); f1(501:701)=0:-1.5:-300; f1(701:901)=-300:1.5:0; f2=zeros(1,2001);

f2(201:1201)=200*sin(20*pi/10*(0:0.01:10)); f3=zeros(1,2001);

f3(1:301)=100*ones(1,301); F=[f1;f3;f2]; m0=[2 1.5 1]'; k0=[1800 1200 600]'; c0=[180 120 60]'; U0=zeros(3,1); V0=zeros(3,1); A0=zeros(3,1); dt=0.01; b=0.25; r=0.5;

[U,V,A]=Newmark(m0,k0,c0,U0,V0,A0,dt,b,r,F); subplot(3,1,1); plot(U(2,:)); subplot(3,1,2); plot(V(2,:)); subplot(3,1,3); plot(A(2,:));