  An abstract 2nd-order evolution equation or inclusion is discretised in time
in such a way that the energy is conserved at least in qualified cases,
typically in the cases when the governing energy is component-wise quadratic or
"slightly-perturbed" quadratic. Specific applications in continuum mechanics of
solids possibly with various internal variables cover vibrations or waves in
linear viscoelastic materials at small strains, coupled with some inelastic
processes as plasticity, damage, or phase transformations, and also some
surface variants related to contact mechanics. The applicability is illustrated
by numerical simulations of vibrations interacting with a frictional contact or
waves emitted by an adhesive contact of a 2-dimensional viscoelastic body.
