We consider axially symmetric shear waves propagating in an incompressible hyperelastic thick-walled cylindrical shell, whose strain energy function is expressible as a truncated power series in terms of the basic strain invariants. A continuous pulse is initiated at the interior boundary of the cylinder by surface tractions of finite duration. The pulse propagates away from the interior boundary, then reflects from the outer boundary, and subsequently reflects back and forth between the two boundaries of the cylinder. We analyze shock development of the first incident and first reflected wave. The incident pulse can break before it reaches the outer boundary. Using Whitham's nonlinearization technique, we determine conditions under which the incident wave breaks and which shock waves can subsequently occur. Similar calculations are carried out for the first reflection. The formulas obtained for the incident pulse provide accurate estimates of the breaking distance and time, and the location of the shock paths, for any incident shock waves that occur. Results obtained for the reflected wave cannot be used to make similar estimates, but they do reveal that once the pulse has completely left the outer boundary, the possible shock that can occur is the same as for the incident wave. Our analysis is carried out for axial shear waves. A similar analysis can be done for torsional shear waves, but not for combined axial and torsional shear wave propagation. We illustrate the conclusions of our shock analysis with numerical solutions obtained using a relaxation scheme for systems of conservation laws. Numerical results are obtained for axial shear and for combined axial and torsional shear. These results indicate that the shock behavior indicated by our analysis of axial shear is also valid for combined axial and torsional shear wave propagation.

A wavefront analysis is employed to study the propagation of axial shear waves in an incompressible hyperelastic solid, whose strain energy function is expressible as a truncated power series in terms of the basic invariants of the left Cauchy-Green tensor. Waves are generated by the application of an axial shear stress at the surface of a cylindrical cavity in an unbounded medium. Depending on the nature of the boundary condition, an acceleration front or a shock front propagates from the boundary of the cavity. For an acceleration front, the coefficients in the wavefront expansion satisfy a sequence of transport equations which can be solved analytically. For a shock front, a wavefront analysis gives approximate formulas for the wave speed, shock front and intensity of the various field variables at the front. As well, our shock front analysis is used to devise a method of estimating the breaking distance of a shock front. In order to test the validity of the results of our wavefront analysis, numerical solutions are obtained for waves initiated by a step function or by a finite duration pulse at the boundary. Our numerical solutions are found by using a recently proposed relaxation scheme for systems of conservation laws.

Methods of constructing asymptotic wavefront expansions for non-linear waves in continuous dissipative media are presented. We consider those cases where the dissipation mechanisms are provided through relaxation (rate dependence) and/or stratification (inhomogeneity) of the medium. Apart from the first non-constant one, the coefficients in these expansions are shown to be governed by linear transport equations. Numerical results, based on a Padé-extended version of these expansions, are presented for waves in fluid filled compliant tubes. Comparisons with results derived by the method of characteristics are made and presented graphically.

Asymptotic wavefront expansions are here employed in the study of nonlinear hyperbolic waves. Numerical results based upon these methods are obtained for a particular case of interest and both these results and those obtained by the method of characteristics are presented graphically. The wavefront-based method is accurate, requires an order of magnitude less computer time, and offers a clearer understanding of the underlying wave process.

Isochromatic curve patterns are calculated for the dynamic stress field in a semi-infinite thin elastic plate whose edge is subject to a point load.

Diagrams of the developing isochromatic curve patterns associated with the dynamic stress field arising when a circular cavity is subjected to a spatially nonuniform dynamic load are computed. These diagrams show for the first time the detailed wave fronts and zones of stress for this technically interesting problem. Since isochromatic lines correspond to the fringe patterns of photoelasticity, the results presented here suggest the possibility of direct experimental confirmation of the theory upon which the computations are based.

A procedure for solving elastodynamic problems involving moving, spatially nonuniform loads applied to the surface of a circular cavity is developed and employed to study some general problems of technical interest. Detailed numerical results are presented in graphical form.

The concept of characteristic impedance together with an experimentally tested model of wave propagation in fluid filled tubes is employed to model the interaction between a transient pressure pulse and either a stenosis or an aneurysm.

Here we employ an experimentally tested theory of wave propagation in liquid filled distensible tubes to study the interaction of periodic pressure waves with a finite segment of tubing whose characteristic impedance differs from those of the adjoining tubes. Such a tube system occurs when surgical bypass techniques are employed in the arterial system. In this case the source of the pressure pulse (the heart) is periodic and reflections from the insert could reinforce subsequent pulses arriving from the heart causing abnormally high pressures in the adjoining artery. This paper sheds some light on this phenomenon.

Previous attempts at analysing tube propagation in a viscoelastic tube containing a viscous liquid have concentrated on examining sinusoidal wave trains of infinite length. This paper takes viscosity into account in the formulation of initial and boundary value problems which mimic experimental configurations.

Diagrams of the developing isochromatic curve patterns associated with the dynamic stress field of a normally impacted isotropic plate under uniaxial tension are computed to show the accompanying wave fronts and zones of stress when plugging occurs.

Isochromatic curves are calculated for the stress field round a nonuniformly loaded circular cavity in an elastic plate.

A two dimensional initial boundary value problem for the dynamic response of liquid filled viscoelastic tube systems is formulated and solved. Integral transform techniques are employed and numerical results presented graphically.

In a previous paper the present authors developed a model describing wave propagation in liquid filled distensible tubes and tested it against impulse experiments involving water filled latex rubber tubes. This model incorporates both dissipative and dispersive mechanism which are absent from the commonly employed linear long wave-length (LLW) theory of haemodynamics. This higher order theory is here employed to study propagation of an impulse in a semi infinite tube, reflection of an impulse from the distal end of a finite length tube, and reflection and transmission of impulses impinging on a function connecting dissimilar liquid filled tubes. Both open and closed type reflections are treated and numerical results presented graphically. To the best of our knowledge this is the first time that such a higher order theory has been employed to treat reflection and transmission of waves in tube systems.

Bergman-type series solutions involving iterated complementary error integrals are constructed for nonlinear boundary-value problems associated with heat conduction in a region bounded internally by a cylindrical or spherical surface. In particular, a small-time solution is developed when the nonlinear boundary condition is of the Stefan-Boltzmann type. This solution is extended via Padé approximants.

A theory of wave propagation in liquid filled distensible tubes, which extends the region of validity of the linear long wavelength theory commonly employed in haemodynamics, is presented and tested against experiments on water filled latex tubes. The theory which is linear and involves but a single free parameter provides excellent agreement with the impulse experiments.

Employing a previously established theory for wave propagation in liquid-filled distensible tubes [1] we analyse the propagation and subsequent reflection of a transient pulse from the distal end of a finite length tube. Conditions pertaining to pulse generation at the proximal end of the tube are specified so as to approximate the conditions of experiments carried out on water-filled latex tubes [1]. Laplace transforms are employed and numerical results presented graphically.