Thermal ignition for a reactive viscous flow between two symmetrically heated walls is investigated. The second order nonlinear boundary value problem governing the problem is obtained and solved analytically using a special type of Hermite-Padé approximation technique. We obtained very accurately the critical conditions for thermal ignition together with the two solution branches. It has been observed that an increase in viscous heating due to viscous dissipation can cause a rapid decrease in the magnitude of thermal ignition critical conditions.

©. Segµa, C.M. Kalker-Kalkman. Optimization of torsional systems with self-regulated pneumatic clutches. CAMES 2005 (12)

In this paper possibilities of optimization of two torsional mechanical systems with one and two differential pneumatic clutches with self-regulation are shown. The systems are excited by harmonic components of the periodic moment caused by an engine. The advantage of the differential pneumatic clutch lies in the fact that its torsional stiffness can be controlled by the pressure of a gas medium in it. Optimization of such systems enables not only minimization of vibrations and dynamic effects but also avoiding resonance regimes in relatively wide frequency intervals (speeds of rotation of the system). As objective function the mean total amplitude of relative vibration is used. The constraints on the amplitudes of dynamic moments and also anti-resonance constraints are considered.
*Keywords:* mechanical system, torsional vibration, optimization, pneumatic clutch.

P. Koutmos, S. Dimopoulos. A reduced multi-step integrated oxidation scheme for methane suitable for use into complex reactive flow calculations. CAMES 2005 (12)

In Direct or Semi-Direct Numerical Simulations of turbulent reacting flows the exploitation of complex, realistic and detailed chemistry and transport models often results in prohibitive memory and CPU requirements when flows of practical relevance are treated.
The integrated Combustion Chemistry approach has recently been put forward as a methodology suitable for the integration of complex chemical kinetic and chemistry effects into large scale computational procedures for the calculation of complex and practical reacting flow configurations. Through this procedure a reduced chemical kinetic scheme involving only a limited number of species and reactions is derived from a detailed chemical mechanism so as to include major species and pollutants of interest in the main flow calculation. The chemical parameters employed in this integrated scheme i.e. rates, constants, exponents are then calibrated on the basis of a number of constraints and by comparing computations over a range of carefully selected laminar flames so as to match a number of prespecified flame properties such as adiabatic temperatures, selected target species profiles, flame speeds, extinction characteristics. The present work describes such an effort for a commonly used fuel of both fundamental and practical importance, methane. The proposed nine-step scheme involves nine major stable species and in addition to the basic methane oxidation model also includes NO_{X} production and soot formation submodels.
*Keywords:* integrated combustion chemistry, reduced chemistry mechanisms, laminar flames, chemical reaction schemes.

S. P. Harsha, P. K. Kankar, R. K. Purohit. Nonlinear dynamic dnalysis of high speed rolling element bearings due to cage run-out. CAMES 2005 (12)

The paper presents an analytical model to investigate the nonlinear dynamic behavior of rotor bearing system due to cage run-out. Due to run-out of the cage, the rolling elements no longer stay equally spaced. The mathematical model takes into account the sources of nonlinearity such as Hertzian contact force and cage run-out, resulting transition from no contact-to-contact state between rolling elements and races. The contact between the rolling elements and races is treated as nonlinear springs. The nonlinear stiffness is obtained by application of Hertzian contact deformation theory. The implicit type numerical integration technique Newmark-β with Newton Raphson method is used to solve the nonlinear differential equations iteratively. The results are presented in the form of Fast Fourier Transformations (FFT) and contact force-time responses. It is implied from the obtained FFT that due to the cage run-out, the ball passage frequency is modulated with the cage frequency.
*Keywords:* nonlinear dynamic response, chaotic vibration, Newmark-β, ball passage frequency.

T. Ebinger, H. Steeb, S. Diebels. Modeling and homogenization of foams. CAMES 2005 (12)

The mechanical modeling of foams is discussed on a microscopic, mesoscopic and macroscopic scale. A homogenization procedure is proposed to relate the models and to give detailed insight into the deformation behavior of foams. The mesoscopic model of open-cell foams is based on beam elements and evaluated for regular hexagonal structures considering small deformations. This approach gives rise to a Cosserat continuum on the macroscopic scale. Especially the misfit in the parameters governing the standard macroscopic model can be explained by the proposed homogenization procedure. This misfit results from the neglect of the rotations of the cell walls, see Diebels and Steeb [6, 7].

R. Walentyński. Refined least squares approach to the initial-value problems unstable in the Lyapunov sense. CAMES 2005 (12)

The paper presents application of the Refined Least Squares method to the initial value problems that are instable in the Lyapunov sense. There is shown that the method is not sensitive to this kind of instability. The method is especially useful in search of particular integral of the considered problem. The method has an additional tool to evaluate quality of approximation. The approach is based on minimization of the functional, which square root can is generalized norm L_{2} and can be used to estimate global error of approximation. The expected value of the functional is equal to zero. The approximation is satisfactory if both results converge and functional reaches value close to zero. The consideration is illustrated with examples. There are shown initial-value problems which have physical sense and are applicable in mechanics. Whereas numerical approach may fail for these tasks, Refined Least Squares approach returns reliable approximation. The last example presents application of the special feature of the method, which allows neglecting influence of general integral on the solution. The method may be used in sensitivity analysis, search of the problem parameters, verification of numerical methods and an antonymous method in computational physics and mechanics.