地震工程學(xué)-反應(yīng)譜和地震時(shí)程波的相互轉(zhuǎn)化matlab編程

------------------------------------------------------------------------地震工程學(xué)-反應(yīng)譜和地震時(shí)程波的相互轉(zhuǎn)化matlab編程地震工程學(xué)作業(yè)課程名稱:地震工程學(xué)______指導(dǎo)老師:_______翟永梅_________姓名:史先飛________學(xué)號(hào):1232627________一、地震波生成反應(yīng)譜1所取的地震波為Elcentro地震波加速度曲線，如圖1所示。圖1Elcentro地震波加速度曲線2所調(diào)用的Matlab程序?yàn)椋?***********讀入地震記錄***********ElCentro;Accelerate=ElCentro(:,1)*9.8067;%單位統(tǒng)一為m和sN=length(Accelerate);%N讀入的記錄的量time=0:0.005:(N-1)*0.005;%單位s%初始化各儲(chǔ)存向量Displace=zeros(1,N);%相對(duì)位移Velocity=zeros(1,N);%相對(duì)速度AbsAcce=zeros(1,N);%絕對(duì)加速度%***********A,B矩陣***********Damp=0.02;%阻尼比0.02TA=0.0:0.05:6;%TA=0.000001:0.02:6;%結(jié)構(gòu)周期Dt=0.005;%地震記錄的步長(zhǎng)%記錄計(jì)算得到的反應(yīng)，MaxD為某阻尼時(shí)最大相對(duì)位移，MaxV為某阻尼最大相對(duì)速度，MaxA某阻尼時(shí)最大絕對(duì)加速度，用于畫圖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;%結(jié)構(gòu)自振頻率DampFrequency=NatualFrequency*sqrt(1-Damp*Damp);%計(jì)算公式化簡(jiǎn)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)%根據(jù)地震記錄,計(jì)算不同的反應(yīng)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);%初始化各儲(chǔ)存向量，避免下次不同周期計(jì)算時(shí)引用到前一個(gè)周期的結(jié)果Velocity=zeros(1,N);AbsAcce=zeros(1,N);t=t+1;End%***********PLOT***********closeallfigure%繪制地震記錄圖plot(time(:),Accelerate(:))title('PEERSTRONGMOTIONDATABASERECORD')xlabel('time(s)')ylabel('acceleration(g)')gridfigure%繪制位移反應(yīng)譜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%繪制速度反應(yīng)譜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%繪制絕對(duì)加速度反應(yīng)譜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運(yùn)行的結(jié)果得到的反應(yīng)譜圖2位移反應(yīng)譜圖3速度反應(yīng)譜圖4加速度反應(yīng)譜反應(yīng)譜生成地震波所取的反應(yīng)譜為上海市設(shè)計(jì)反應(yīng)譜圖5上海市設(shè)計(jì)反應(yīng)譜反應(yīng)譜取值程序?yàn)椋?%規(guī)范反應(yīng)譜取值程序參照01年抗震規(guī)范functionrs_z=r_s_1(pl,zn,ld,cd,fz)%%%pl圓頻率,zn阻尼比,ld烈度,cd場(chǎng)地類型,場(chǎng)地分組fz%%%%烈度選擇ifld==6arfmax=0.11;endifld==7arfmax=0.23;endifld==8arfmax=0.45;endifld==9arfmax=0.90;end%%%%場(chǎng)地類別，設(shè)計(jì)地震分組選擇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%%%%%%反應(yīng)譜值擬加速度值rs_z=arf_jg*9.8;end生成人造地震波主程序：%%%主程序%%%%%%%%確定需要控制的反應(yīng)譜Sa（T）(T=T1,...,TM)的坐標(biāo)點(diǎn)數(shù)M，反應(yīng)譜控制容差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類場(chǎng)地，第1地震分組end%%%%%%變換的頻率差：2*pi*0.005(可以保證長(zhǎng)周期項(xiàng)5s附近有5項(xiàng)三角級(jí)數(shù))；%%%%頻率變化范圍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;%%%保證率%%%%%%人造地震動(dòng)持續(xù)時(shí)間40s，時(shí)間間隔：0.02sTd=40;dt=0.02;t=0:0.02:40;nt=length(t);%%%%%%%衰減包絡(luò)函數(shù)t1=8;%%%%上升段t2=8+24;%%%%%平穩(wěn)段;下降段則為40－32＝8sc=0.6;%%%%衰減段參數(shù)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%%%%%%%反應(yīng)譜轉(zhuǎn)換功率譜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%%%%%%%%%%%%%%合成地震動(dòng)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%%%%%%%計(jì)算反應(yīng)譜驗(yàn)證是否滿足rc在5%的要求,需要時(shí)程動(dòng)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%%%%%%%比較容差fori=1:nTyzrcrsp(i)=abs(rspa(i)-Syz(i))/max(Syz(:));endjsnum=1;whilemax(rcrsp(:))>rc%%%%%循環(huán)體函數(shù)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;%%%%%%%%%%%%%%合成地震動(dòng)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%%%%%%%計(jì)算反應(yīng)譜驗(yàn)證是否滿足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%%%%%%%比較容差fori=1:nTyzrcrsp(i)=abs(rspa(i)-Syz(i))/max(Syz(:));endjsnum=jsnum+1max(rcrsp(:))end%%%%%%%最終的反應(yīng)譜與規(guī)范譜%%%%%%%%%%%%responsespectraofcallidar%%%%%%%parameter%%Tjs=0.05:0.01:6;%%nTjs=length(Tjs);g=9.8;m=1;x0=0;v0=0;ww=