On the use of negative penalty parameters in aeroelastic divergence analysis of lifting surfaces

This paper shows that a numerical modelling method in which constraints are replaced with positive and negative penalty functions, which may be regarded as artificial elastic restraints of positive and negative stiffness, may be safely used to determine the critical speed associated with aeroelastic divergence. The critical speeds of a beam with restraints of positive and negative stiffness are found to converge to that of the constrained system, from below if the stiffness is positive and from above otherwise. A uniform Euler–Bernoulli beam clamped at the rear end is analysed using an artificial restraint to enforce the constraint of zero rotation at the clamp, and the results are compared with the exact critical speed of the constrained system obtained analytically. The paper shows that, contrary to common belief that the penalty parameter must be positive, the inclusion of a negative penalty parameter enables the determination of errors due to violation of the constraints.     

Holomorphic Flows on Simply Connected Regions Have No Limit Cycles

The dynamical system or flow = f(z), where f is holomorphic on C, is considered. The behavior of the flow at critical points coincides with the behavior of the linearization when the critical points are non-degenerate: there is no center-focus dichotomy. Periodic orbits about a center have the same period and form an open subset. The flow has no limit cycles in simply connected regions. The advance mapping is holomorphic where the flow is complete. The structure of the separatrices bounding the orbits surrounding a center is determined. Some examples are given including the following: if a quartic polynomial system has four distinct centers, then they are collinear.     

Decoupling and recoupling of detonation waves associated with sudden expansion

Detonation propagation behavior associated with sudden expansions has been investigated both experimentally and numerically. Different mechanisms, from sustained propagation to detonation failure and reinitiation including shock and flame front decoupling and recoupling have been observed with the schlieren technique. The shock-induced flame propagation has been modeled with two-step chemistry and structured two-dimensional CFD on arbitrary geometries. The results of the numerical simulations show good correspondence to the variety of phenomena observed in experiments. Thus the numerical simulation can be used to study detonation propagation in complex geometries. It provides a tool for the design of safety devices and aids experimental investigations. Received 4 August 1995 / Accepted 25 April 1996     

Direct initiation of detonation in cryogenic gaseous H2-O2 mixtures

Critical conditions for the direct initiation of self-sustained detonation in cryogenic hydrogen-oxygen mixtures are examined experimentally. These initial conditions are expected to depend mainly on four parameters: the equivalence ratio of the mixture, the amount of the initial energy deposition, the initial temperature and pressure of the mixture. These critical conditions are determined by fixing alternatively three of these parameters and varying the fourth one from subcritical to supercritical detonation conditions. Results are presented for initial pressuresP _o and equivalence ratios ranging from 0.3 to 1 bar and from 1 to 2 respectively, for the two initial temperaturesT _o, 123 K and 293 K. These results indicate that for the lowest values of the initial pressure, a decrease of initial temperature may favour the onset of detonation. Whatever the initial conditions, the measured detonation pressures and velocities are in reasonably good agreement with the corresponding Chapman-Jouguet values computed using the ideal-gas equation of state.     

Flutter instability and other singularity phenomena in symmetric systems via combination of mass distribution and weak damping

The local dynamic instability of autonomous conservative, lumped-mass (discrete) systems, is thoroughly discussed when negligibly small dissipative forces are included. It is shown that such small forces may change drastically the response of these systems. Hence, existing, widely accepted, findings based on the omission of damping could not be valid if damping, being always present in actual systems, is included. More specifically the conditions under which the above systems may experience dynamic bifurcations associated either with a degenerate or a generic Hopf bifurcation are examined in detail by studying the effect of the structure of the damping matrix on the Jacobian eigenvalues. The case whereby this phenomenon may occur before divergence is discussed in connection with the individual or coupling effect of non-uniform mass and stiffness distribution. Jump phenomena in the critical dynamic loading at a certain mass distribution are also assessed. Numerical results verified by a non-linear dynamic analysis using 2-DOF and 3-DOF models confirm the validity of the theoretical findings as well as the efficiency of the technique proposed herein.     

Hydrophobic terminal group of surfactant initiating micellization as revealed by 1H NMR spectroscopy

The critical aggregation concentration (CAC) of four with three kinds of conventional surfactants, namely, two cationic surfactants [hexadecyltrimethyl ammonium bromide (CTAB) and tetradecyltrimethyl ammonium bromide (TTAB)], one anionic surfactant [sodium dodecyl sulfate (SDS)], and a nonionic surfactant [Triton X-100 (TX-100)], were determined by variation of ¹H chemical shifts with surfactant concentrations. Results show that the CAC values of protons at different positions of the same molecule are different, and those of the terminal methyl protons are the lowest, respectively, which suggests that the terminal groups of the alkyl chains aggregates first during micellization. Measurement of the transverse relaxation time (T₂) of different protons in SDS also show that the terminal methyl protons start to decrease with the increase in concentration first, which supports the above mentioned tendency.     

Hamiltonicity of edge chromatic critical graphs

Vizing conjectured that every edge chromatic critical graph contains a 2-factor. Believing that stronger properties hold for this class of graphs, Luo and Zhao (2013) showed that every edge chromatic critical graph of order $n$ with maximum degree at least $\frac{6n}{7}$ is Hamiltonian. Furthermore, Luo et al. (2016) proved that every edge chromatic critical graph of order $n$ with maximum degree at least $\frac{4n}{5}$ is Hamiltonian. In this paper, we prove that every edge chromatic critical graph of order $n$ with maximum degree at least $\frac{3n}{4}$ is Hamiltonian. Our approach is inspired by the recent development of Kierstead path and Tashkinov tree techniques for multigraphs.     

Effect of Lateral Linear Stiffness on Nonlinear Characteristics of Hunting Motion of a Railway Wheelset

Railway wheelset experiences the problem of hunting above a critical speed, which is a kind of self-excited oscillation. At the critical speed, it is known that the system undergoes a subcritical Hopf bifurcation. Therefore, for clarifying the nonlinear characteristics of hunting it is very important to detect, for example, the nonlinear forces in the wheelset due to the creep forces acting between the wheels and rails, and the nonlinear component of the resorting forces by the suspensions. However, it is impossible to determine each force quantitatively. In the present paper, it is first shown, by using the center manifold theory and the method of normal form, that the nonlinear characteristics of the bifurcation in a wheelset model with two degrees of freedom are governed by a single parameter, hence each nonlinear force need not be detected when examining the nonlinear characteristics. Also, a method of determining the governing parameter from experimentally observed radiuses of the unstable limit cycle is proposed. Next, we experimentally investigate the variation of the parameter due to the presence of linear spring suspensions in the lateral direction and discuss the variation of the nonlinear characteristics of the hunting motion, which depends on the lateral stiffness. As a result, the improvement of the stability of the wheelset against the disturbance by the linear spring suspensions is clarified.