  We construct families of supersymmetric solutions of type IIB and D=11
supergravity that are invariant under the non-relativistic conformal algebra
for various values of dynamical exponent z greater than or equal to 4 and 3,
respectively. The solutions are based on five- and seven-dimensional
Sasaki-Einstein manifolds and generalise the known solutions with dynamical
exponent z=4 for the type IIB case and z=3 for the D=11 case, respectively.
