MATH920 L07: Viscoelastic elements

Elastic elements in series

m=4;
vars=Table[(Subscript[X, i])[s],{i,1,m}];Eqs=Table[(s^2) (Subscript[X, i])[s] == (ω^2)((Subscript[X, i-1])[s]-2 (Subscript[X, i])[s]+(Subscript[X, i+1])[s])+ (Subscript[x, i])[0],{i,1,m}] /. {(Subscript[X, 0])[s]->0,(Subscript[X, m+1])[s]->0}

sol=Solve[Eqs,vars][[1]]

Xsol[s_]=vars /. sol

Xsol[s][[1]]

xsol[t_,ω_]=InverseLaplaceTransform[Xsol[s][[1]],s,t]

inicnd = Table[(Subscript[x, i])[0]->0.1i,{i,1,m}]

x1[t_]=xsol[t,1.]/. inicnd

Plot[x1[t],{t,0,40}]

Maxwell elements in series