Two separate problems are to be investigated in this thesis. The first problem
is the propagation of waves through a short rod (or slug) of viscoelastic
material. The second problem is the study of impact of a short viscoelastic
rod (or slug) on a stationary semi-infinite viscoelastic. rod. The viscoelastic
materials are modelled as standard linear solids which involve 3 material
parameters and the motion is treated. as one-dimensional.
For the first study, a viscoelastic slug is placed between two semi-infinite
elastic rods and a wave initiated in the first rod is transmitted through the
slug into the second rod. The objective is to relate the transmitted signal
to the material parameters of the slug. We solve the governing system of
partial differential equations using the Laplace transform and we examine the
propagating velocity discontinuity using discontinuity analysis and the limit
theorem of the Laplace transform. We then approximate the solution of the
propagating disturbance using the regular perturbation method. We invert
the Laplace transformed solution numerically to obtain the transmitted signal
for several viscosity time constants and ratios of acoustic impedances. We
compare the results obtained using the above techniques. In the second problem, we first model the impact and solve the governing
system of partial differential equations in the Laplace transform domain.
Then we examine the propagating stress and velocity discontinuities
using discontinuity analysis. We approximate the solutions of the propagating
stress and velocity using the regular and multiple scales perturbation
methods. In this problem, we first consider the slug is elastic and the rod is
viscoelastic. Secondly, we consider the slug is viscoelastic and the rod is elastic
and thirdly, we consider both materials are viscoelastic. Numerically we
invert the Laplace transformed solutions for the interface stress and interface
velocity for several viscosity time constants and ratios of acoustic impedances
to determine whether the slug and the rod part company or remain in contact.
Then we compare the results obtained using the discontinuity analysis,
regular and multiple scales perturbation methods.
A Doctoral Thesis. Submitted in partial fulfilment of the requirements for the award of Doctor of Philosophy of Loughborough University.