Chaotic vibrations of a beam with non-linear boundary conditions

Forced vibrations of an elastic beam with non-linear boundary conditions are shown to exhibit chaotic behavior of the strange attractor type for a sinusoidal input force. The beam is clamped at one end, and the other end is pinned for the tip displacement less than some fixed value and is free for displacements greater than this value. The stiffness of the beam has the properties of a bi-linear spring. The results may be typical of a class of mechanical oscillators with play or amplitude constraining stops. Subharmonic oscillations are found to be characteristic of these types of motions. For certain values of forcing frequency and amplitude the periodic motion becomes unstable and nonperiodic bounded vibrations result. These chaotic motions have a narrow band spectrum of frequency components near the subharmonic frequencies. Digital simulation of a single mode mathematical model of the beam using a Runge-Kutta algorithm is shown to give results qualitatively similar to experimental observations.     

Syntheses of (−)-gabosine A, (+)-4-epi-gabosine A, (−)-gabosine E, and (+)-4-epi-gabosine E

(+)-4-epi-Gabosine A 1 and (−)-gabosine A 2 have been synthesized starting from methyl α,d-glucopyranoside and methyl α,d-mannopyranoside, respectively, by utilizing Pd(0) catalyzed Stille coupling as the key step. On the other hand, syntheses of (+)-4-epi-gabosine E 3 and (−)-gabosine E 4 have been accomplished from methyl α,d-glucopyranoside and from methyl α,d-mannopyranoside, respectively, by utilizing DMAP catalyzed Morita-Baylis-Hillman reaction as the key step. Presence of acetyl group at C-6 position of sugar derived cyclic enone prevented the aromatization of MBH adduct. A plausible mechanism is also described.     

CO2 laser-induced decomposition of ethanol

The multiple photon absorption and decomposition of ethanol irradiated by pulsed 9P18 infrared radiation (1048.7 cm^?1) from a TEA CO₂ laser has been studied in the fluence range 15 to 5 J cm^?2. The absorption cross-section is pressure-dependent due to rapid collisional rotational hole-filling. At low pressures the only important decomposition channel following absorption is molecular dehydration of ethanol to yield ethene, but at higher pressures hydrogen, methane, carbon monoxide, ethane, and ethyne are also produced. In the irradiation of pure ethanol under ‘collision-free’ conditions, thermal decomposition following collisional redistribution of energy makes only a small contribution to the overall decomposition yield at fluences above 3.5 J cm^?2 but may become more significant at lower fluences. Modelling using RRKM calculations has been employed to link measured absorbed energies to extents of decomposition of ethanol. Both these calculations and the absorption measurements indicate that at low pressures only a fraction of the irradiated ethanol molecules absorb the 9P18 radiation. © 1993 John Wiley & Sons, Inc.     

Discontinuous Galerkin finite element methods for dynamic linear solid viscoelasticity problems

We consider the usual linear elastodynamics equations augmented with evolution equations for viscoelastic internal stresses. A fully discrete approximation is defined, based on a spatially symmetric or non‐symmetric interior penalty discontinuous Galerkin finite element method, and a displacement‐velocity centred difference time discretisation. An a priori error estimate is given but only the main ideas in the proof of the error estimate are reported here due to the large number of (mostly technical) estimates that are required. The full details are referenced to a technical report. © 2007 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2007     

Post-harvest processing methods for reduction of silica and alkali metals in wheat straw

Silica and alkali metals in wheat straw limit its use for bioenergy and gasification. Slag deposits occur via the eutectic melting of SiO₂ with K₂O, trapping chlorides at surfaces and causing corrosion. A minimum melting point of 950°C is desirable, corresponding to an SiO₂:K₂O weight ratio of about 3:1. Mild chemical treatments were used to reduce Si, K, and Cl, while varying temperature, concentration, % solids, and time. Dilute acid was more effective at removing K and Cl, while dilute alkali was more effective for Si. Reduction of minerals in this manner may prove economical for increasing utilization of the straw for combustion or gasification.     

Measurement and analysis of the ν2 band of D216O

The rotational structure of the ν₂ band of D₂¹⁶O between 700 and 1550 cm^?1 has been analyzed from spectra recorded with a Fourier transform spectrometer (nominal resolution: 0.1 cm^?1). By applying Watson's reduced Hamiltonian and a least squares method to the set of observed transitions, together with microwave data and the infrared data of Williamson, 22 rotational constants for the ground state and 17 for the upper state have been obtained which predict the positions of more than 700 observed lines with a standard deviation of 0.04 cm^?1.     

Earphones in audiometry. Committee on Hearing, Bioacoustics, and Biomechanics. Commission on Behavioral and Social Sciences and Education. National Research Council Working Group

The advantages and disadvantages of three types of earphones for audiometric testing are discussed. Supraaural earphones continue to be recommended for this purpose, in preference to circumaural and insert types.     

Measurements of some reaction rates of importance in KrF lasers

A flowing afterglow method has been used to study a number of reactions of importance in KrF lasers using NF₃ as the fluorine donor. Total rate constants are reported for Kr^*(³ P ₂)+NF₃ and Kr⁺+NF₃. The thermal energy attachment coefficient has been measured for NF₃ and the cross section for the electron excitation process Kr^*(³ P ₂) +e→Kr^*(³ P ₁)+e has been estimated. The relevance of these results to discharge pumped KrF lasers is discussed.