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用MATLAB自带卷积分函数计算弹性半空间在一三角脉冲荷载下自由表面的竖向位移,与文献正确结果相差10的5次方倍,但自己编写卷积分代码,反而得到文献结果。请大家帮我看下问题出在哪?谢谢! 8X I? > ]8a3x 另外,为何MATLAB自带卷积分函数结果矩阵的维数会是被卷积两矩阵维数之和减1? 9JWa$iBH@ }=|!:kiE 1. 问题描述,如下图1所示: <ERB.d! H<QT3RF2 P)uDLFp] +n7?S~R$ 2. 格林函数,如下图2所示: ]r-C1bKD` TO-nD> !o>H1#2l Nr0
(E 3. 参考文献正确解,如下图3所示: 0jzbG]pc:E UK{irU|\ Q//,4>JKf 9W8]8sUeG 4. 本人直接用自编卷积分MATLAB代码算的出解(如下图4)及相应代码: NBF MN% jr)7kP@ ;3
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sO5?aB& clear; [j"9rO" + clc; &|aqP
\Q5 (4@lKKiU%H %loading history 0Hs|*:Y1D 4Td{;Y="yF dt=0.01; *c)uGz'cD
ti=0.0008; }'OHE(s te=12; ~Aq5XI%i t=ti:dt:te; oxj3[</'k pt=(10*t./1.5).*(t>=0 & t<=1.5)+(20-10*t./1.5).*(t>1.5 & t<=3)+0.*(t>3); Q.Aw2 m=length(pt); )?2e
[|~2X> %load distribution in space 5VO;s1 9
C{;h rp=0.1; 2Sq_Tw3^ ri=0; HAYMX:% rc=0.1; QW_agm dr=0.001; {ls+dx/ r=ri:dr:rc; SSBg?H 'T pr=1*(r<=rp)+0*(r>rp); yIb,,!y9{ n=length(pr); KvQ,;A t |W) %load function with respect to t and r 1shBY@mlq x"4} isp< p=pr.'*pt; < pTTo QR">.k4QJ %green's function +Ug/rtK4 m uW!xY G=1; &ff&Y.q~ cs=1; \#'TNmS for i=1:1:m ^Cv^yTj;& for j=1:1:n Gq#~vr u(j,i)=heaviside(cs*t(i)-r(j))/(pi*G*sqrt(t(i)^2-(r(j)/cs)^2)); jxgj,h"}9` end "&Qctk`<P end i{^Z1;Yl Zc"B0_&?:7 %convolution and response of displacement ( #Z` P%Ay3cR+E for i=1:1:m N:VX!w for j=1:1:n sP'0Sl~NU v(j,i)=0; !}M, for k=1:1:i *FR$vLGn for g=1:1:j Q6C-4ja v(j,i)=v(j,i)+p(g,k)*u(j-g+1,i-k+1)*dr*dt; .7ayQp end; V2|3i}V" end; 2h
{q h end; K:y^OAZfV end; ~9Cz6yF ]J2:194 %plot the response history MVCl.o '[ P}&<ie, plot(t,v(n,); Z<b"`ty. xlabel('t/s'); ']ood! ylabel('v/m'); IO.<q,pP!_ grid on; -m 5}#P89 title('response of point A or C'); @LD6:gy %bb~Y" 5. 直接用MATLAB自带卷积分算的出解(如下图5)及相应代码: h7_)%U<J2 R@T6U:1 |-2}j2' 7q9gngT1LA clear; ~H@+D}J? clc; _q>SE1j+W= @=]8^?$t
0 %loading history T9y;OG %NHYW\sKX dt=0.01; \Mx
JH[ ti=0.0008; j;P+_Hfe/E te=12; t]_S t=ti:dt:te; iT)WR90 pt=(10*t./1.5).*(t>=0 & t<=1.5)+(20-10*t./1.5).*(t>1.5 & t<=3)+0.*(t>3); }3/~x m=length(pt); *8g<R =F%RLpNU4 %load distribution in space EH9Hpo JSMPyj rp=0.1; &y_? rH ri=0; zDBD .5R; rc=0.1; h#f&|*Q5m dr=0.001; m24v@?* r=ri:dr:rc; \MYU<6{u pr=1*(r<=rp)+0*(r>rp); ij)Cm]4(2 n=length(pr); M StX*Zw j64 4V|z %load function with respect to t and r 99ASIC! <DiOWi p=pr.'*pt; 'wQy]zm$ c]m! G'L_/ %green function ;lfWuU%R ]O{_O&w G=1; $Lq:=7&LRn cs=1; LdTIR] for i=1:1:m a?<?5 for j=1:1:n U}P,EP%p u(j,i)=heaviside(cs*t(i)-r(j))/(pi*G*sqrt(t(i)^2-(r(j)/cs)^2)); 7!d$M{0" end U~QMR-bz end yz)ESQ~va ,Aa|Bd]b
%convolution and response of displacement VO9f~>`( lBiovT v=conv2(u,p); kEAhTh&g* dq8+m(7k %plot the response history {[3YJkrM zzf7S%1I rr=r(n); 8tZ};="F [tpu,rpu]=meshgrid(ti:dt:2*te-dt,ri:dr:2*rc); |3@=CE7G [X,Y,Z]=meshgrid(linspace(min(tpu(),max(tpu()),linspace(min(rpu(),max(rpu()),linspace(min(v(),max(v())); IA4+ad'\E V=Y; ZlM_m
>,o h=contourslice(X,Y,Z,V,tpu,rpu,v,[0 0]+rr); 8eww7k^R set(h,'edgecolor','k'); 8kbBz contourslice(X,Y,Z,V,tpu,rpu,v,[0 0]+rr); hZF(/4Z2 xlabel('t/s'); Q&wYc{TUbm ylabel('r/m'); +u#Sl)F zlabel('v/m'); zlMlMyG4 axis([0 12 0 0.1 0 12e4]); 4<yK7x view(0,0); (HSw%e grid on; "`]'ZIx[R/ title('displacement response history of point A or C');
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