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Papers by Graham Rogerson

Journal of Mechanics of Materials and Structures, 2008

A two-dimensional model describing the equilibrium state of a cracked inhomogeneous body with a r... more A two-dimensional model describing the equilibrium state of a cracked inhomogeneous body with a rigid circular inclusion is investigated. The body is assumed to have a crack that reaches the boundary of the rigid inclusion. We assume that the Signorini condition, ensuring non-penetration of the crack faces, is satisfied. We analyze the dependence of solutions on the radius of rigid inclusion. The existence of a solution of the optimal control problem is proven. For this problem, a cost functional is defined by an arbitrary continuous functional, with the radius of inclusion chosen as the control parameter.

The phononic band structure of waves, which travel though composites, results from the geometric ... more The phononic band structure of waves, which travel though composites, results from the geometric and mechanical properties of the materials and from the interaction of the different constituents. In this article, we study two different models to simulate imperfect bonding and their impact on the phononic bands: (a) imperfect bonding is simulated by introducing an artificial interphase constituent with properties which define the bonding quality; (b) imperfect bonding is described by conjugate conditions in the interface, in which the difference in the displacement is proportional to the interfacial stress. Viscoelastic behavior of the constituents has a crucial influence on the traveling signal, and the wave attenuates with increasing viscosity. We study the interaction of the different bonding conditions and the viscoelastic behavior as well as the impact of such interplay on the wave attenuation and dispersion characteristics of the material.

It is well known that an elastic material subject to N (0 ⩽ N ⩽ 3), internal constraints upon the... more It is well known that an elastic material subject to N (0 ⩽ N ⩽ 3), internal constraints upon the deformation gradient admits the propagation of 3 — N distinct plane waves in most directions. Those directions in which more than 3 — N waves may propagate are termed exceptional . Here we investigate wave propagation in a material subject to two constraints by slightly relaxing both constraints and asymptotically expanding the wave speeds and the polarizations in inverse powers of the large elastic moduli associated with the slightly relaxed constraints. The limits in which (1) both constraints operate exactly, and (2) one constraint is exact and one slightly relaxed are both discussed and shown to confirm previous results. The theory and graphical illustrations of the slowness surface are presented for two examples of a practical nature: (1) an incompressible material reinforced by a set of parallel inextensible fibres; (2) a material reinforced by two sets of mutually orthogonal inex...

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

We aim to study how the interplay between the effects of nonlinearity and heterogeneity can influ... more We aim to study how the interplay between the effects of nonlinearity and heterogeneity can influence on the distribution and localization of energy in discrete lattice-type structures. As the classical example, vibrations of a cubically nonlinear elastic lattice are considered. In contrast with many other authors, who dealt with infinite and periodic lattices, we examine a finite-size model. Supposing the length of the lattice to be much larger than the distance between the particles, continuous macroscopic equations suitable to describe both low- and high-frequency motions are derived. Acoustic and optical vibrations are studied asymptotically by the method of multiple time scales. For numerical simulations, the Runge–Kutta fourth-order method is employed. Internal resonances and energy exchange between the vibrating modes are predicted and analysed. It is shown that the decrease in the number of particles restricts energy transfers to higher-order modes and prevents the equiparti...

International Journal of Engineering Science

Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences

Propagation of anti-plane waves through a discrete square lattice and through a continuous fibrou... more Propagation of anti-plane waves through a discrete square lattice and through a continuous fibrous medium is studied. In the long-wave limit, for periodically heterogeneous structures the solution can be periodic or anti-periodic across the unit cell. It is shown that combining periodicity and anti-periodicity conditions in different directions of the translational symmetry allows one to detect different types of modes that do not arise in the purely periodic case. Such modes may be interpreted as counterparts of non-classical waves appearing in phenomenological theories. Dispersion diagrams of the discrete square lattice are evaluated in a closed analytical from. Dispersion properties of the fibrous medium are determined using Floquet–Bloch theory and Fourier series approximations. Influence of a viscous damping is taken into account.

Journal of Sound and Vibration

Zeitschrift für angewandte Mathematik und Physik

ABSTRACT An investigation of harmonic wave propagation in an idealised bre-reinforced layer is ca... more ABSTRACT An investigation of harmonic wave propagation in an idealised bre-reinforced layer is carried out in respect of the most general appropriate strain energy function and for propaga- tion along a non-principal direction. The dispersion relation, giving phase speed as an implicit function of wave number, associated with incremental traction free boundary conditions is derived and decomposed into flexural and extensional motions. Some conditions for the existence of sur- face waves are derived, such a wave speed being the high wave number limit of both fundamental modes. As regards the harmonics, two distinct cases are observed numerically. For both cases asymptotic high wave number expansions are derived which oer an excellent approximation to the numerical solution in the moderate and high wave number region.

International Journal of Solids and Structures

International Journal of Non-Linear Mechanics