Parametric oscillations and stability of systems with large modulation coefficient

We study parametric oscillations of linear systems with one degree of freedom for large values of the modulation coefficient. We use the classical analytic Lyapunov-Poincaré perturbation methods and an original numerically-analytic method of accelerated convergence to construct periodic solutions and the corresponding eigenvalues. We find the boundaries of stability and instability domains. We use specific models to illustrate the main properties of parametric oscillations of systems with singular character of the perturbation dependence on the modulation coefficient. We consider periodic boundary value problems for the modified Mathieu equation and the Kochin equation modeling crankshaft torsional vibrations and show that there are significant differences between weakly and essentially perturbed periodicmotions both for the lowest and arbitrary oscillation modes. We also describe the unusual properties of the boundaries in the domain of the system determining parameters.     

Buckling of a stiff thin film on a compliant substrate in large deformation

A finite-deformation theory is developed to study the mechanics of thin buckled films on compliant substrates. Perturbation analysis is performed for this highly nonlinear system to obtain the analytical solution. The results agree well with experiments and finite element analysis in wavelength and amplitude. In particular, it is found that the wavelength depends on the strain. Based on the accurate wavelength and amplitude, the membrane and peak strains in thin films, and stretchability and compressibility of the system are also obtained analytically.     

Thermodynamic parameters of urethane formation reactions and concomitant processes

Thermodynamic parameters of reactions of methyl and phenyl isocyanates with a series of compounds were determined by quantum-chemical calculations. The products of these reactions model for various functional groups present in commercial polyurethanes. The thermodynamic stability series for compounds formed from aliphatic and aromatic isocyanates were constructed.     

Influence of the composition of the polymer matrix on the electrooptical properties of films with a dispersed liquid crystal

Polymer films with a dispersed liquid crystal were prepared by photopolymerization of (meth)acrylic monomers. The electrooptical properties of these films were studied. The influence exerted by the composition of the monomer mixture, cross-linking agents, and chain-transfer agent on the liquid crystal drop size and on the transmission of the polymer-liquid crystal films was examined.     

Electrohydrodynamic instability in some nematic cyanobiphenyls in an a.c. electric field

Electrohydrodynamic instability in homeotropically oriented nematic samples of 4'-n-octyl-4-cyano-biphenyl and 4'n-alkyloxy-4-cyanobiphenyl, (n = 8.9) have been studied in an a.c. electric field. The domain patterns during the instability in these compounds in a very low frequency a.c. field are very similar to those in a d.c. field. The domain patterns observed at higher frequencies have been identified as 'maltese crosses' or 'crossed isogyres'. The electro-convective 'isotropic' flows near the electrode play an important role in the observed instability.     

Numerical simulations of a filament in a flowing soap film

Experiments concerning the properties of soap films have recently been carried out and these systems have been proposed as experimental versions of theoretical two‐dimensional liquids. A silk filament introduced into a flowing soap film, was seen to demonstrate various stable modes, and these were, namely, a mode in which the filament oscillates and one in which the filament is stationary and aligns with the flow of the liquid. The system could be forced from the oscillatory mode into the non‐ oscillatory mode by varying the length of the filament. In this article we use numerical and computational techniques in order to simulate the strongly coupled behaviour of the filament and the fluid. Preliminary results are presented for the specific case in which the filament is seen to oscillate continuously for the duration of our simulation. We also find that the filament oscillations are strongly suppressed when we reduce the effective length of the filament. We believe that these results are reminiscent of the different oscillatory and non‐oscillatory modes observed in experiment. The numerical solutions show that, in contrast to experiment, vortices are created at the leading edge of the filament and are preferentially grown in the curvature of the filament and are eventually released from the trailing edge of the filament. In a similar manner to oscillating hydrofoils, it seems that the oscillating filaments are in a minimal energy state, extracting sufficient energy from the fluid to oscillate. In comparing numerical and experimental results it is possible that the soap film does have an effect on the fluid flow especially in the boundary layer where surface tension forces are large. Copyright © 2004 John Wiley & Sons, Ltd.     

Sulfonated poly(aryl ether ketone)s containing naphthalene moieties obtained by direct copolymerization as novel polymers for proton exchange membranes

A series of sulfonated poly(aryl ether ketone)s (SPAEKs) were prepared by aromatic nucleophilic polycondensation of 2,6‐dihydroxynaphthalene with 5,5′‐carbonyl‐bis(2‐fluorobenzenesulfonate) and 4,4′‐difluorobenzophenone. The structure and degree of sulfonation (DS) of the SPAEKs were characterized using ¹H NMR spectroscopy. The experimentally observed DS values were close to the expected values derived from the starting material ratios. The thermal stabilities of the SPAEKs were characterized by thermogravimetric analysis, which showed that in acid and sodium salt forms they were thermally stable in air up to about 240 and 380 °C, respectively. Transparent membranes cast from the directly polymerized SPAEKs exhibited good mechanical properties in both dry and hydrated states. The dependence of water uptake and of membrane swelling on the DS at different temperatures was studied. SPAEK membranes with a DS from 0.72 to 1.60 maintained adequate mechanical properties after immersion in water at 80 °C for 24 h. The proton conductivity of SPAEK membranes with different degrees of sulfonation was measured as a function of temperature. The proton conductivity of the SPAEK films increased with increased DS, and the highest room temperature conductivity (4.2 × 10^?2 S/cm) was recorded for a SPAEK membrane with a DS of 1.60, which further increased to 1.1 × 10^?1 S/cm at 80 °C. © 2004 Wiley Periodicals, Inc. J Polym Sci Part A: Polym Chem 42: 2866–2876, 2004