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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! W$`#X $o9@ ?2 另外,为何MATLAB自带卷积分函数结果矩阵的维数会是被卷积两矩阵维数之和减1? g \ou+M# P,xJVo\ 1. 问题描述,如下图1所示: q~Al[`K M*C1QQf\N =+I-9= ^SW9J^9 2. 格林函数,如下图2所示: `M. I.Z_ &49WfctT g#Ta03\ ZLdIEBi= 3. 参考文献正确解,如下图3所示: I6gduvkXi4 3N|6?'m -yTIv*y #K/JU{" 4. 本人直接用自编卷积分MATLAB代码算的出解(如下图4)及相应代码: wh2E$b(- HgBu:x?& |`s:&<W+kp |[>yJXxEL@ clear; cMoJHC,! clc; 7$t['2j3 s:(z;cj/ %loading history #!%zf{(C+ Plhakngj dt=0.01; JfK4|{@ ti=0.0008; euW te=12; EJQT\c t=ti:dt:te; 1L!jI2~x} pt=(10*t./1.5).*(t>=0 & t<=1.5)+(20-10*t./1.5).*(t>1.5 & t<=3)+0.*(t>3); Pl-9FLJ m=length(pt); zSu,S4m_; ^4'!B
+}F %load distribution in space
r* l
c# pU[yr'D.r rp=0.1; Z",2db ri=0; )qOcx
I rc=0.1; [tElt4uG dr=0.001; TtKKU4yp r=ri:dr:rc; s&<76kwl pr=1*(r<=rp)+0*(r>rp); pd& HC n=length(pr); -YmIRocx ):}A Quy] %load function with respect to t and r Zm7,O8 [N}QCy p=pr.'*pt; WwWCNN~} &\Lu}t7Ru %green's function m~fDDQs %DA`.Z9# G=1; ]*Q,~uV^| cs=1; 7s!rer> for i=1:1:m B7YE+ for j=1:1:n (d
(>0YMv u(j,i)=heaviside(cs*t(i)-r(j))/(pi*G*sqrt(t(i)^2-(r(j)/cs)^2)); 8xG"hJR end UI%4d3 end TeO'E<@ DyA/!%g %convolution and response of displacement jUgx
;= z|Yt|W for i=1:1:m 6l &!4r@}
for j=1:1:n oA7|s1 v(j,i)=0; zK{} for k=1:1:i gW9`k,U for g=1:1:j fakad#O v(j,i)=v(j,i)+p(g,k)*u(j-g+1,i-k+1)*dr*dt; <h}x7y? end; b&
-8/t end; 53pT{2]zAi end; (/!@
-]1 end; *!{&n*N L/I ]
NA!U %plot the response history ir>+p>s. [TFp2B~)# plot(t,v(n,); o^//|]H3Y xlabel('t/s'); C*B5"s" ylabel('v/m'); c': 4e) grid on; qDhZC*"9#D title('response of point A or C'); Z glU{sU \Sv|yQUT 5. 直接用MATLAB自带卷积分算的出解(如下图5)及相应代码: ;ceg:-Zqo @$
lX%p> t~nW&]E 25 :vc0 clear; J&}1=s clc; \pTv;( "r3h+(5 %loading history o_[~{@RoR C>mFylN dt=0.01; oDJ
&{N| ti=0.0008; fX6pW%Q'6 te=12;
$#3[Z;\ t=ti:dt:te; "a33m:]J pt=(10*t./1.5).*(t>=0 & t<=1.5)+(20-10*t./1.5).*(t>1.5 & t<=3)+0.*(t>3); m_BpY9c]5 m=length(pt); f5l\3oL :}/\hz
, %load distribution in space Fp[49 ]=I2:Rb rp=0.1; .tyV=B:h ri=0; H\N}0^ea rc=0.1; 51H6
W/$ dr=0.001; o@]n<ZYo r=ri:dr:rc; `P-d. M6Oa pr=1*(r<=rp)+0*(r>rp); 6d2eWS n=length(pr); /C5py&#-I m}zXy\ %load function with respect to t and r L~by`q N_ pSIXv%1J p=pr.'*pt; lA;^c) J$sp6g>K %green function w(t1m]pF[ Z7[S698 G=1; ,:MUf]Ky cs=1; 5MZv!N for i=1:1:m [7[Qw]J for j=1:1:n \u(Gj]B#" u(j,i)=heaviside(cs*t(i)-r(j))/(pi*G*sqrt(t(i)^2-(r(j)/cs)^2)); s*Z
yr%R end jO|`aUYTf end 4^4T#f2=e ?i\V^3S n$ %convolution and response of displacement )
LTV+? TcJJ"[0 v=conv2(u,p); a2i:fz=[ |TkicgeS %plot the response history rd$T6!I G\,B*$3
rr=r(n); 8m
`Y [tpu,rpu]=meshgrid(ti:dt:2*te-dt,ri:dr:2*rc); `w8cV? [X,Y,Z]=meshgrid(linspace(min(tpu(),max(tpu()),linspace(min(rpu(),max(rpu()),linspace(min(v(),max(v())); cfg.&P> V=Y; -f1}N|hy h=contourslice(X,Y,Z,V,tpu,rpu,v,[0 0]+rr); @\xEK5SG set(h,'edgecolor','k'); @H(7Mt contourslice(X,Y,Z,V,tpu,rpu,v,[0 0]+rr); Cw kQhj? xlabel('t/s'); g}K/ba' ylabel('r/m'); ,1lW`Krx zlabel('v/m'); $= 2[Q axis([0 12 0 0.1 0 12e4]); MPyDG"B* view(0,0); SMRCG"3qwA grid on; ~i'!;'-_} title('displacement response history of point A or C');
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