MATH920 L06: Nonlinear materials

Harmonic array of oscillators

Series[x[h]-2x[0]+x[-h],{h,0,3}]/(h^2)

Obtain wave equation

(Subscript[u, t t])=(Subscript[u, x x])

Fermi Ulam Pasta

Quadratic nonlinearity

Series[x[h]-2x[0]+x[-h]+α((((x[h]-x[0]))^2)-(((x[0]-x[-h]))^2)),{h,0,3}]/(h^2)

(Subscript[u, t t])=(Subscript[u, x x])+ν (Subscript[u, x]) (Subscript[u, x x])

Cubic nonlinearity

Series[x[h]-2x[0]+x[-h]+β((((x[h]-x[0]))^3)-(((x[0]-x[-h]))^3)),{h,0,4}]/(h^2)

(Subscript[u, t t])=(Subscript[u, x x])+ν (Subscript[(u^2), x]) (Subscript[u, x x])