  In this paper we revisit the derivations of model equations describing long
nonlinear longitudinal bulk strain waves in elastic rods within the scope of
the Murnaghan model in order to derive a Boussinesq-type model, and extend
these derivations to include axially symmetric loading on the lateral boundary
surface, and longitudinal pre-stretch. We systematically derive two forced
Boussinesq-type models from the full equations of motion and non-zero surface
boundary conditions, utilising the presence of two small parameters
characterising the smallness of the wave amplitude and the long wavelength
compared to the radius of the waveguide. We compare the basic dynamical
properties of both models (linear dispersion curves and solitary wave
solutions). We also briefly describe the laboratory experiments on generation
of bulk strain solitary waves in the Ioffe Institute, and suggest that this
generation process can be modelled using the derived equations.
