The large deformation of nonlinearly elastic rings in a two-dimensional compressible flow

The nonlinear nonlocal system of the equilibrium equations ofan elastic ring under the action of an external two-dimensionaluniformly subsonic potential barotropic steady-state gas flowis considered. The configurations of the elastic ring are identifiedby a pair of functions (, ). The simple curve represents theshape of the ring and the real-valued function identifies theorientation of the material sections of the ring. The pressurefield on the ring depends nonlocally on , and on two parametersU and P which represent the pressure and the velocity at infinity.The system is shown to be equivalent to a fixed-point problem,which is then treated with continuation methods. It is shownthat the solution branch ensuing from certain equilibrium states((₀, ₀), 0, P₀) in the solution-parameter space of ((₀, ₀),0, P₀) either approaches the boundary of the admissible ((,), U,p)'s in a well-defined sense, or is unbounded, or is homotopicallynontrivial in the sense that there exists a continuous map from the branch to a two-dimensional sphere which is not homotopicin the sphere to a constant, while restricted to the branchminus ((₀, ₀), 0, P₀) is homotopic to a constant in the sphere.Furthermore, by fixing the pressure parameter at P₀ and by consideringthe one-parameter problem in ((, ), U), the following holds.Every hyperplane in the solution-parameter space of the ((,), U)'s which contains the equilibrium state ((₀, ₀), 0) anddoes not include a welldetermined one-dimensional subspace intersectsthe solution branch above at a point different from ((₀, ₀),0).     

THE INFLUENCE OF CYLINDER LUBRICATION ON PISTON SLAP

A model has been developed for determining the time history of piston slap impact force. This model takes into account the influence of the oil film on the impact behaviour, which was found to be an important factor. However, it was also found that entrapped gas bubbles in the oil are equally significant. Three test rigs were designed and built to study these effects on the impact phenomenon and extensive tests were carried out. The impact force time history has been determined using Reynolds' theory. Results have shown that Reynolds' theory for fluid film squeezing can be applied for oil film damping determination. However, the experimental results have also shown that when gas is entrapped during the impact, this theory considerably overpredicts the magnitude of the impact. An eight-degree-of-freedom lumped parameter model was developed through the dynamic analysis of each component of an internal combustion engine's reciprocating system. The effective damping factor derived from this model was found to be inversely proportional to the oil film thickness cubed, as expected from Reynolds' theory. A dynamic model has been proposed, where the oil film mixed with bubbles is considered to be analogous to a serial spring and damping system. By incorporating a spring in series with this damper, the effect of the bubbles can also be predicted.