{VERSION 6 0 "IBM INTEL NT" "6.0" } {USTYLETAB {CSTYLE "Maple Input" -1 0 "Courier" 0 1 255 0 0 1 0 1 0 0 1 0 0 0 0 1 }{PSTYLE "Normal" -1 0 1 {CSTYLE "" -1 -1 "" 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 }0 0 0 -1 -1 -1 0 0 0 0 0 0 -1 0 }} {SECT 0 {EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 1434 "with(plots):\nepsi lon:=1/30:\nEA:=280*77000:mg:=9.8:L:=325:mu:=mg*L/(8*EA*epsilon^3):\np lot(\{tan(kk/2)/(kk/2),1-mu*kk^2/64\},kk=Pi..3*Pi,y=-2..2):\nk:=fsolve (tan(kk/2)/(kk/2)=1-mu*kk^2/64,kk=Pi..3*Pi):\nT:=mu:\nY:=z->-1+4*z^2: \nX:=z->mu*(z+1/2)-4/3*(1+8*z^3):\nt11:=k^2/16*cos(k/2)/sin(k/4)^2:\ny 11:=z->(cos(k*z)-cos(k/2))/(2*sin(k/4)^2):\ndy11:=unapply(diff(y11(z), z),z):\nx11:=z->t11*(mu*z+64/k^3*(sin(k*z)-k*z*cos(k*z))):\nt20:=(1/2) /(mu-16/3)*(1/16*k*(k-sin(k))/sin(k/4)^4-mu*t11^2):\ny20:=z->(1-4*z^2) *t20-t11/2*y11(z):\nx20:=z->mu*(t20+t11^2/2)*z-64/3*z^3*t20-t11/2*x11( z)-k/64*(2*k*z-sin(2*k*z))/sin(k/4)^4:\nt22:=(16/3*t11^2*tan(k)/k-4/3* t11*k*cot(k/4)-1/64*k^3*(k-sin(k))/sin(k/4)^4)/(1/2*mu*k^2-10+8*tan(k) /k):\ny22:=z->2/k^2*(t22-2/3*t11^2)*(cos(2*k*z)/cos(k)-1)+7/6*t11*y11( z):\ndy22:=unapply(diff(y22(z),z),z):\nx22:=z->-8*z*y22(z)-2/k^2*(dy22 (z)-1/2*t11*dy11(z)+8*t22*z) +1/64*k*(2*k*z-sin(2*k*z))/(sin(k/4)^4)+m u*t22*z:\ndelta:=0.2:\nXX:=(s,t)->s+epsilon^2*(X(s-1/2)+delta*x11(s-1/ 2)*sin(t)+delta^2*(x20(s-1/2)+x22(s-1/2)*cos(2*t))):\nYY:=(s,t)->epsil on*(Y(s-1/2)+delta*y11(s-1/2)*sin(t)+delta^2*(y20(s-1/2)+y22(s-1/2)*co s(2*t))):\nanimate([XX(s,t),YY(s,t),s=0..1],\nt=Pi/4..(16+1)/4*Pi-2*Pi /60,frames=60,view=[0..1,-0.042..0],numpoints=50,style=line,\nthicknes s=2,color=red,titlefont=[HELVETICA,BOLD,10],\ntitle=\"Galloping overhe ad transmission lines (single span, elasto-gravity): Lindstedt-Poincar T approximation\",tickmarks=[0,0],axes=boxed);" }}}}{MARK "0 0 0" 1434 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }