| syms m x t y |
| rho=2323; |
| h=0.3048; |
| E=2756010∧6; |
| mu=0.15; |
| B=8; |
| K=136; |
| N=20; |
| Massofvehicle=3200; |
| coeffofrollingfriction=0.015; |
| Contacttires=2; |
| areaofcontact=0.0025; |
| v=(1005)/18; %assumng 100kmph |
| b0=.508/2; |
| a0=0.254/2; |
| d0=1.22/2; |
| q0= MassofvehiclecoeffofrollingfrictionContacttires/(areaofcontactv)%-7.7810∧3; |
| %distributed load of vehicle |
| y1=3.2; |
| y2=4.8; |
| %piezo |
| d31=-27410∧(-12); %V/m |
| hc=0.055; |
| lp=0.14; |
| bp=0.14; |
| hp=0.01; |
| e33=30.0610∧(-9); % F/m |
| S11=16.510∧(-12); %m∧2/N |
| S12=-5.7410∧(-12); %m∧2/N |
| xp=8;%tenative |
| yp=0.5;%centre of piezo |
| R =80010∧3; |
| xp1=xp-0.5lp; |
| xp2=xp+0.5lp; |
| yp1=yp-0.5bp; |
| yp2=yp+0.5bp; |
| %pavement structuring |
| D=Eh/(12(1-mu∧2)); |
| am=msym(pi)/B; |
| a1=sym(pi)/9.8814; %supposed to be B |
| vc=sqrt((2(a1∧2)D+2sqrt((a1∧4)D∧2+KD))/(rhoh)); |
| Lm=sqrt(am∧4+K/D); |
| Bm=((v∧2)rhoh/(2D))-am∧2; |
| Tm=sqrt(0.5(Lm-Bm)); |
| Pm=sqrt(0.5(Lm+Bm)); |
| v0=sqrt((4Dam∧2)/(rhoh)); |
| o=(2v∧2-v0∧2)/(2sqrt((vc∧2-v∧2)(v∧2+vc∧2-v0∧2))); %gamma m |
| deg=180/pi; |
| cm1=((osin(a0Pm)cosh(a0Tm)+cos(a0Pm)sinh(a0Tm))); |
| sm1=(-ocos(a0Pm)sinh(a0Tm)+sin(a0Pm)cosh(a0Tm)); |
| cm2=((exp(-a0Tm))(osin(a0Pm)-cos(a0Pm))); |
| sm2=((-exp(-a0Tm))(ocos(a0Pm)+sin(a0Pm))); |
| CM2=((exp(-d0Tm))(cm1cos(d0Pm)+sm1sin(d0Pm))); |
| SM2=((exp(-d0Tm))(sm1cos(d0Pm)-cm1sin(d0Pm))); |
| CM1=((exp(d0Tm))(cm1cos(d0Pm)-sm1sin(d0Pm))+CM2); |
| SM1=((exp(d0Tm))(cm1sin(d0Pm)+sm1sin(d0Pm))+SM2); |
| CM3=(cm2cos(d0Pm)cosh(d0Tm)+sm2sin(d0Pm)sinh(d0Tm)); |
| CM4=(-cm2cos(d0Pm)sinh(d0Tm)-sm2sin(d0Pm)cosh(d0Tm)); |
| SM3=(cm2sin(d0Pm)cosh(d0Tm)-sm2cos(d0Pm)sinh(d0Tm)); |
| SM4=(sm2cos(d0Pm)cosh(d0Tm)-cm2sin(d0Pm)sinh(d0Tm)); |
| O=abs(x-vt); |
| gm1=((cosh(OTm))(CM3cos(OPm)+SM3sin(OPm))); |
| gm2=((sinh(OTm))(CM4cos(OPm)+SM4sin(OPm))); |
| gm=(gm1+gm2); |
| wm=((4q0sin(amb0)(sin(amy1)+sin(amy2)))/(mpi(K+Dam∧4))); |
| %case 1 when O-d0>a0 |
| wm1=(wm(exp(-OTm))(CM1cos(OPm)+SM1sin(OPm))); |
| %case 2 when |O-d0|<a0 |
| wm2=(wm(1+(exp(-OTm))(CM2cos(OPm)+SM2sin(OPm))+gm)); |
| %case 3 when (O-d0<-a0) |
| wm3=(wm(2CM2cos(OPm)cosh(OTm)-2SM2sin(OPm)sinh(OTm))); |
| C0=(e33-(1/(S11+S12))2d31∧2)lpbp/hp; |
| syms m |
| WM1=(symsum(wm1sin(amy), m, 1, N)); |
| WM2=(symsum(wm2sin(amy), m, 1, N)); |
| WM3=(symsum(wm3sin(amy), m, 1, N)); |
| WM=WM1+WM2+WM3; |
| WM=vpa(WM,3); |
| gx=gradient(WM,x); |
| gx=vpa(gx,3) |
| gy1=gradient(gy); |
| gy1=vpa(gy1,3);%deba2w(x,y,t)wrt y |
| fun=vpa((gx1+gy1),3); |
| term=vpa(int(fun,x),3); %first integral |
| initial=subs(term,x,xp1); %limits |
| final=subs(term,x,xp2); |
| term=vpa((final-initial),3); |
| TERM=vpa(int(term,y),3); |
| initial1=subs(TERM,y,yp1); %limits |
| final1=subs(TERM,y,yp2); |
| TERM=vpa((final1-initial1),3); |
| Q=-((d31hc)/(S11+S12))TERM; %fill up the two integrals |
| ex=-hcgx1; |
| ex=vpa(ex,3); |
| ey=-hcgy1; |
| ey=vpa(ey,3); |
| e31=d31/(S11+S12); |
| V= e31lpbp(ex+ey)/C0; |
| % for y=8 t=8/30 |
| V=subs(V,y,8); |
| V=subs(V,t,8/30); |
| V=subs(V,x,1); |
| V=vpa(V,2) |
| AA=int((Qexp(t/RC0)),t); |
| Vt=(Q/C0)-((1/RC0∧2)(exp(-t/(RC0)))(AA)); |
| Vt1=vpa(Vt,2) |
| Vt1=subs(Vt1,t,8/30) |
