地震工程学反应谱和地震时程波的相互转化matlab编程样本

地震工程学作业课程名称：地震工程学______指引教师:_______翟永梅_________姓名：史先飞________学号：1232627________一、地震波生成反映谱1所取地震波为Elcentro地震波加速度曲线，如图1所示。图1Elcentro地震波加速度曲线2所调用Matlab程序为：%***********读入地震记录***********ElCentro;Accelerate=ElCentro(:,1)*9.8067;%单位统一为m和sN=length(Accelerate);%N读入记录量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；%构造周期Dt=0.005；%地震记录步长%记录计算得到反映，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；%构造自振频率DampFrequency=NatualFrequency*sqrt(1-Damp*Damp)；%计算公式化简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)%依照地震记录,计算不同反映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种周期成果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%绘制位移反映谱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%绘制速度反映谱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%绘制绝对加速度反映谱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运营成果得到反映谱图2位移反映谱图3速度反映谱图4加速度反映谱反映谱生成地震波所取反映谱为上海市设计反映谱图5上海市设计反映谱反映谱取值程序为：%%规范反映谱取值程序参照抗震规范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%%%%烈度选取ifld==6arfmax=0.11;endifld==7arfmax=0.23;endifld==8arfmax=0.45;endifld==9arfmax=0.90;end%%%%场地类别，设计地震分组选取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～T2ifT1<T_jg&T_jg<=T2arf_jg=lmt2*arfmax;end%%%%第三段T2~T3ifT2<T_jg&T_jg<=T3arf_jg=((Tg/T_jg)^sjzs)*lmt2*arfmax;end%%%%第四段T3～6.0ifT3<T_jg&T_jg<=6.0arf_jg=(lmt2*0.2^sjzs-lmt1*(T_jg-5*Tg))*arfmax;end%%%%第五段6.0～if6.0<T_jgarf_jg=(lmt2*0.2^sjzs-lmt1*(6.0-5*Tg))*arfmax;end%%%%%%反映谱值拟加速度值rs_z=arf_jg*9.8;end生成人造地震波主程序：%%%主程序%%%%%%%%拟定需要控制反映谱Sa（T）(T=T1,...,TM)坐标点数M，反映谱控制容差rcTyz=[0.04:0.016:0.1,0.15:0.05:3.0,3.2:0.05:5.0]；rc=0.06；nTyz=length(Tyz);ceita=0.035;%%%阻尼比：0.035fori=1:nTyzSyz(i)=r_s_1(2*pi/Tyz(i),ceita,8,2,1)；%%%%8度，2类场地，第1地震分组end%%%%%%变换频率差：2*pi*0.005(可以保证长周期项5s附近有5项三角级数)；%%%%频率变化范畴N1=30，30*0.005*2*pi;N2=3000，5000*0.005*2*piplc=2*pi*0.005;pl=30*0.005*2*pi:0.005*2*pi:10000*0.005*2*pi;npl=length(pl);P=0.9；%%%保证率%%%%%%人造地震动持续时间40s，时间间隔：0.02sTd=40；dt=0.02;t=0:0.02:40;nt=length(t);%%%%%%%衰减包络函数t1=8；%%%%上升段t2=8+24；%%%%%平稳段；下降段则为40－32＝8sc=0.6；%%%%衰减段参数fori=1:ntift(i)<=t1f(i)=(t(i)/t1)^2;endift(i)>t1&t(i)<t2f(i)=1;endift(i)>=t2f(i)=exp(-c*(t(i)-t2));endend%%%%%%%反映谱转换功率谱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%%%%%%%计算反映谱验证与否满足rc在5%规定,需要时程动力分析%%%%%%%%%%%%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(1)blxs1(xsxs)=blxs(1);endforsxsx=1:nTyz-1if(2*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%%%%%%%计算反映谱验证与否满足rc在5%规定%%%%%%%%%%%%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%%%%%%%最后反映谱与规范谱%%%%%%%%%%%%responsespectraofcallidar%%%%%%%parameter%%Tjs=0.05:0.01:6;%%nTjs=length(Tjs);g=9.8;m=1;x0=0;v0=0;ww=2*pi./Tyz;