地震工程学 反应谱和地震时程波的相互转化matlab编程

地震工程学作业课程名称:地震工程学______指导老师:_______翟永梅_________姓名:史先飞________学号:1232627________一、地震波生成反应谱1所示。1所取的地震波为Elcentro地震波加速度曲线，如图图1Elcentro地震波加速度曲线2所调用的Matlab程序为：%***********读入地震 记录 混凝土 养护记录下载土方回填监理旁站记录免费下载集备记录下载集备记录下载集备记录下载 ***********ElCentro;Accelerate=ElCentro(:,1)*9.8067;%单位统一为m和sN=length(Accelerate);%N读入的记录的量time=0:0.005:(N-1)*0.005;%单位s%初始化各储存向量Displace=zeros(1,N);%相对位移Velocity=zeros(1,N);%相对速度AbsAcce=zeros(1,N);%绝对加速度%***********A,B矩阵***********Damp=0.02;%阻尼比0.02TA=0.0:0.05:6;%TA=0.000001:0.02:6;%结构周期Dt=0.005;%地震记录的步长%记录计算得到的反应，MaxD为某阻尼时最大相对位移，MaxV为某阻尼最大相对速度，MaxA某阻尼时最大绝对加速度，用于画图MaxD=zeros(3,length(TA));MaxV=zeros(3,length(TA));MaxA=zeros(3,length(TA));t=1;forT=0.0:0.05:6NatualFrequency=2*pi/T;%结构自振频率计算公式化简DampFrequency=NatualFrequency*sqrt(1-Damp*Damp);%．e_t=exp(-Damp*NatualFrequency*Dt);s=sin(DampFrequency*Dt);c=cos(DampFrequency*Dt);A=zeros(2,2);A(1,1)=e_t*(s*Damp/sqrt(1-Damp*Damp)+c);A(1,2)=e_t*s/DampFrequency;A(2,1)=-NatualFrequency*e_t*s/sqrt(1-Damp*Damp);A(2,2)=e_t*(-s*Damp/sqrt(1-Damp*Damp)+c);d_f=(2*Damp^2-1)/(NatualFrequency^2*Dt);d_3t=Damp/(NatualFrequency^3*Dt);B=zeros(2,2);B(1,1)=e_t*((d_f+Damp/NatualFrequency)*s/DampFrequency+(2*d_3t+1/NatualFrequency^2)*c)-2*d_3t;B(1,2)=-e_t*(d_f*s/DampFrequency+2*d_3t*c)-1/NatualFrequency^2+2*d_3t;B(2,1)=e_t*((d_f+Damp/NatualFrequency)*(c-Damp/sqrt(1-Damp^2)*s)-(2*d_3t+1/NatualFrequency^2)*(DampFrequency*s+Damp*NatualFrequency*c))+1/(NatualFrequency^2*Dt);B(2,2)=e_t*(1/(NatualFrequency^2*Dt)*c+s*Damp/(NatualFrequency*DampFrequency*Dt))-1/(NatualFrequency^2*Dt);fori=1:(N-1)%根据地震记录,计算不同的反应Displace(i+1)=A(1,1)*Displace(i)+A(1,2)*Velocity(i)+B(1,1)*Accelerate(i)+B(1,2)*Accelerate(i+1);Velocity(i+1)=A(2,1)*Displace(i)+A(2,2)*Velocity(i)+B(2,1)*Accelerate(i)+B(2,2)*Accelerate(i+1);AbsAcce(i+1)=-2*Damp*NatualFrequency*Velocity(i+1)-NatualFrequency^2*Displace(i+1);endMaxD(1,t)=max(abs(Displace));MaxV(1,t)=max(abs(Velocity));ifT==0.0MaxA(1,t)=max(abs(Accelerate));elseMaxA(1,t)=max(abs(AbsAcce));endDisplace=zeros(1,N);%初始化各储存向量，避免下次不同周期计算时引用到前一个周期的结果Velocity=zeros(1,N);AbsAcce=zeros(1,N);t=t+1;End%***********PLOT***********closeallfigure%绘制地震记录图plot(time(:),Accelerate(:))title('PEERSTRONGMOTIONDATABASERECORD')xlabel('time(s)')ylabel('acceleration(g)')gridfigure%绘制位移反应谱plot(TA,MaxD(1,:),'-.b',TA,MaxD(2,:),'-r',TA,MaxD(3,:),':k')title('Displacement')xlabel('Tn(s)')ylabel('Displacement(m)')legend('ζ=0.02')Gridfigure%绘制速度反应谱plot(TA,MaxV(1,:),'-.b',TA,MaxV(2,:),'-r',TA,MaxV(3,:),':k')title('Velocity')xlabel('Tn(s)')ylabel('velocity(m/s)')legend('ζ=0.02')Gridfigure%绘制绝对加速度反应谱plot(TA,MaxA(1,:),'-.b',TA,MaxA(2,:),'-r',TA,MaxA(3,:),':k')title('AbsoluteAcceleration')xlabel('Tn(s)')ylabel('absoluteacceleration(m/s^2)')legend('ζ=0.02')Grid3运行的结果得到的反应谱．图2位移反应谱图3速度反应谱图4加速度反应谱一、反应谱生成地震波1所取的反应谱为上海市设计反应谱图5上海市设计反应谱2反应谱取值程序为：%% 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反应谱取值程序参照01年抗震规范functionrs_z=r_s_1(pl,zn,ld,cd,fz)%%%pl圆频率,zn阻尼比,ld烈度,cd场地类型,场地分组fz%%%%烈度选择ifld==6arfmax=0.11;endifld==7arfmax=0.23;endifld==8arfmax=0.45;endifld==9arfmax=0.90;end%%%%场地类别，设计地震分组选择ifcd==1iffz==1Tg=0.25;endiffz==2Tg=0.30;endiffz==3Tg=0.35;endendifcd==2iffz==1Tg=0.35;endiffz==2Tg=0.40;endiffz==3Tg=0.45;endendifcd==3iffz==1Tg=0.45;endiffz==2Tg=0.55;endiffz==3Tg=0.65;endendifcd==4iffz==1Tg=0.65;endiffz==2Tg=0.75;endiffz==3Tg=0.90;endend%%%%%%%%%ceita=zn;%%%%%阻尼比lmt1=0.02+(0.05-ceita)/8;iflmt1<0lmt1=0;endlmt2=1+(0.05-ceita)/(0.06+1.7*ceita);iflmt2<0.55lmt2=0.55;endsjzs=0.9+(0.05-ceita)/(0.5+5*ceita);%%%%%分段位置T1T2T3T1=0.1;T2=Tg;T3=5*Tg;T_jg=2*pi./pl;%%%%第一段0～T1ifT_jg<=T1arf_jg=0.45*arfmax+(lmt2*arfmax-0.45*arfmax)/0.1*T_jg;end%%%%第二段T1～T2ifT1t1&t(i)=t2f(i)=exp(-c*(t(i)-t2));endend%%%%%%%反应谱转换功率谱fori=1:nplSw(i)=(2*ceita/(pi*pl(i)))*r_s_1(pl(i),ceita,8,2,1)^2/(-2*log(-1*pi*log(P)/(pl(i)*Td)));Aw(i)=sqrt(4*Sw(i)*plc);end%%%%%%%%%%%%%%合成地震动at=zeros(nt,1);atj=zeros(nt,1);fori=1:nplfai(i)=rand(1)*2*pi;forj=1:ntatj(j)=f(j)*Aw(i)*real(exp(sqrt(-1)*(pl(i)*t(j)+fai(i))));endat=at+atj;end%%%%%%%计算反应谱验证是否满足rc在5%的要求,需要时程动力 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%%%%%%%%%%%%responsespectraofcallidar%%%%%%%parameterg=9.8;m=1;x0=0;v0=0;ww=2*pi./Tyz;%%%%%%%%loadag=at;%%%%%%%修改%%%%%%%solutionfory=1:nTyzz=0.037;w=ww(y);c=2*z*w;k=w^2;fori=1:nt-1p(i)=-ag(i+1)+ag(i);a0=m\(-ag(i)-c*v0-k*x0);kk=k+(dt^2)\(6*m)+dt\(3*c);pp=p(i)+m*(dt\(6*v0)+3*a0)+c*(3*v0+2\(dt*a0));dx=kk\pp;dv=dt\(3*dx)-3*v0-2\(dt*a0);x1=x0+dx;x0=x1;v1=v0+dv;v0=v1;as(i)=a0;as(i)=as(i)+ag(i);vs(i)=v0;xs(i)=x0;endmaxas(y)=max(as);maxvs(y)=max(vs);maxxs(y)=max(xs);endfori=1:nTyzrspa(i)=maxas(i);end%%%%%%%比较容差fori=1:nTyzrcrsp(i)=abs(rspa(i)-Syz(i))/max(Syz(:));endjsnum=1;whilemax(rcrsp(:))>rc%%%%%循环体函数blxs=Syz./rspa;forxsxs=1:nplif2*pi/pl(xsxs)=Tyz(sxsx))&(2*pi/pl(xsxs)<=Tyz(sxsx+1))blxs1(xsxs)=blxs(sxsx)+(blxs(sxsx+1)-blxs(sxsx))*(2*pi/pl(xsxs)-Tyz(sxsx))/(Tyz(sxsx+1)-Tyz(sxsx));endendif2*pi/pl(xsxs)>Tyz(nTyz)blxs1(xsxs)=blxs(nTyz);endendAw=Aw.*blxs1;%%%%%%%%%%%%%%合成地震动at=zeros(nt,1);atj=zeros(nt,1);fori=1:nplforj=1:ntatj(j)=f(j)*Aw(i)*real(exp(sqrt(-1)*(pl(i)*t(j)+fai(i))));endat=at+atj;end%%%%%%%计算反应谱验证是否满足rc在5%的要求%%%%%%%%%%%%responsespectraofcallidar%%%%%%%parameterg=9.8;m=1;x0=0;v0=0;ww=2*pi./Tyz;%%%%%%%%loadag=at;%%%%%%%修改%%%%%%%solutionfory=1:nTyzz=0.037;w=ww(y);c=2*z*w;k=w^2;fori=1:nt-1p(i)=-ag(i+1)+ag(i);a0=m\(-ag(i)-c*v0-k*x0);kk=k+(dt^2)\(6*m)+dt\(3*c);pp=p(i)+m*(dt\(6*v0)+3*a0)+c*(3*v0+2\(dt*a0));dx=kk\pp;dv=dt\(3*dx)-3*v0-2\(dt*a0);x1=x0+dx;x0=x1;v1=v0+dv;v0=v1;as(i)=a0;as(i)=as(i)+ag(i);vs(i)=v0;xs(i)=x0;endmaxas(y)=max(as);maxvs(y)=max(vs);maxxs(y)=max(xs);endfori=1:nTyzrspa(i)=maxas(i);end%%%%%%%比较容差fori=1:nTyzrcrsp(i)=abs(rspa(i)-Syz(i))/max(Syz(:));endjsnum=jsnum+1max(rcrsp(:))end%%%%%%%最终的反应谱与规范谱%%%%%%%%%%%%responsespectraofcallidar%%%%%%%parameter%%Tjs=0.05:0.01:6;%%nTjs=length(Tjs);g=9.8;m=1;x0=0;v0=0;ww=2*pi./Tyz;%%%%%%%%loadag=at;%%%%%%%修改%%%%%%%solutionfory=1:nTyzz=0.037;w=ww(y);c=2*z*w;k=w^2;fori=1:nt-1p(i)=-ag(i+1)+ag(i);a0=m\(-ag(i)-c*v0-k*x0);kk=k+(dt^2)\(6*m)+dt\(3*c);pp=p(i)+m*(dt\(6*v0)+3*a0)+c*(3*v0+2\(dt*a0));dx=kk\pp;dv=dt\(3*dx)-3*v0-2\(dt*a0);x1=x0+dx;x0=x1;v1=v0+dv;v0=v1;as(i)=a0;as(i)=as(i)+ag(i);vs(i)=v0;xs(i)=x0;endmaxas(y)=max(as);maxvs(y)=max(vs);maxxs(y)=max(xs);endfori=1:nTyzrspa(i)=maxas(i)/g;rspa_S(i)=r_s_1(2*pi/Tyz(i),ceita,8,2,1)/g;endsubplot(2,1,1);plot(t,at);subplot(2,1,2);plot(Tyz,rspa);holdon;plot(Tyz,rspa_S);生成的人造地震波如图所示。4．图6人造地震波和初始反应谱