Wave motion and impact effects in viscoelastic rods
thesisposted on 30.10.2012 by Abu Bakar Musa
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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.
- Mathematical Sciences