Balanced realisations of all-pass systems using exact arithmetic with application to the approximation of delay systems

Numerically well-conditioned state-space realisations for all-pass systems, such as Padé approximations to exp(-s), are derived that can be computed using exact integer arithmetic. This is then applied to the a series of functions of exp(-s). It is also shown that the H-infinity norm of the transfer function from the input to the state of a balanced realisation of the Padé approximation of exp(-s) is unity. © 2012 IEEE.

Normal shock interactions in rectangular channels

Experiments have been conducted to examine the mechanisms behind the coupling between corner separation and centreline separation when holding a normal shock in a rectangular channel. The study has focused on a M ∞ = 1.5 normal shock held in a wind tunnel with a parallel rectangular cross-section. The primary mechanism explaining the link between the corner separation size and the centreline separation appears to be the generation of compression waves which act to smear the adverse pressure gradient imposed upon other parts of the flow. In addition, the origin of the λ-foot leading leg appears to be depended upon the size of the corner separations. Experimental results indicate that the alteration of the λ-region, which occurs in the supersonic portion of the SBLI, is more important than the generation of any blockage in the subsonic region downstream of the shock wave. Copyright © 2012 by H. Babinsky, D.M.F. Burton.

Shock dynamics of random structures.

Predicting the response of a structure following an impact is of interest in situations where parts of a complex assembly may come into contact. Standard approaches are based on the knowledge of the impulse response function, requiring the knowledge of the modes and the natural frequencies of the structure. In real engineering structures the statistics of higher natural frequencies follows those of the Gaussian Orthogonal Ensemble, this allows the application of random point process theory to get a mean impulse response function by the knowledge of the modal density of the structure. An ensemble averaged time history for both the response and the impact force can be predicted. Once the impact characteristics are known in the time domain, a simple Fourier Transform allows the frequency range of the impact excitation to be calculated. Experimental and numerical results for beams, plates, and cylinders are presented to confirm the validity of the method.

Shock transmission in a coupled beam system

This paper investigates the circumstances under which high peak acceleration can occur in the internal parts of a system when subjected to impulsive driving on the outside. Motivating examples include the design of packaging for transportation of fragile items. The system is modelled in an idealised form using two beams coupled with point connections. A Rayleigh-Ritz model of such coupled beams was validated against measurements on a particular beam system, then the model was used to explore the acceleration response to impulsive driving in the time, frequency and spatial domains. This study is restricted to linear vibration response and additional mechanisms for high internal acceleration due to nonlinear effects such as internal impacts are not considered. Using Monte Carlo simulation in which the indirectly driven beam was perturbed by randomly placed point masses a wide range of system behaviour was explored. This facilitates identification of vulnerable configurations that can lead to high internal acceleration. The results from the study indicate the possibility of curve veering influencing the peak acceleration amplification. The possibility of veering within an ensemble was found to be dependent on the relative coupling strength of the modes. Understanding of the mechanism may help to avoid vulnerable cases, either by design or by preparatory vibration testing. © 2013 Elsevier Ltd.

Autoignition of alcohols and ethers in a rapid compression machine

The autoignition characteristics of methanol, ethanol and MTBE (methyl tert-butyl ether) have been investigated in a rapid compression machine at pressures in the range 20-40 atm and temperatures within 750-1000 K. All three oxygenated fuels tested show higher autoignition temperatures than paraffins, a trend consistent with the high octane number of these fuels. The autoignition delay time for methanol was slightly lower than predicted values using reported reaction mechanisms. However, the experimental and measured values for the activation energy are in very good agreement around 44 kcal/mol. The measured activation energy for ethanol autoignition is in good agreement with previous shock tube results (31 kcal/mol), although ignition times predicted by the shock tube correlation are a factor of three lower than the measured values. The measured activation energy for MTBE, 41.4 kcal/mol, was significantly higher than the value previously observed in shock tubes (28.1 kcal/mol). The onset of preignition, characterized by a slow energy release prior to early ignition was observed in some instances. Possible reasons for these ocurrences are discussed. © Copyright 1993 Society of Automotive engineers, Inc.