Some properties of multi-degree-of-freedom potential systems and application to statistical equivalent non-linearization

This paper presents some properties of two restricted classes of multi-degree-of-freedom potential systems subjected to Gaussian white-noise excitations. Specifically, potential systems which exhibit damping terms with energy-dependent polynomial form are referred to. In this context, first systems with coupled stiffness terms and damping terms depending on the total energy are investigated. Then, systems with uncoupled stiffness terms and damping terms depending on the total energy in each degree-of-freedom are considered. For these two classes, it is found that algebraic relations among the stationary statistical moments of the energy functions can be derived by applying standard tools of Itô calculus. Further, it is noted that these relations are very useful within the framework of an equivalent statistical non-linearization technique to build approximate solutions for arbitrary non-linear systems.     

Influence of two grinding methods on the uncertainty of determinations of heavy metals in atomic absorption spectrometry/electrothermal atomisation of plant samples

 Chemical analyses of trace elements are affected by relatively high analytical errors due to the different steps of the laboratory procedures: samples grinding, mineralisation and instrumental measurements. In the present communication, the influence of the grinding phase on the global uncertainty of Pb, Cd, Ni and Cr determinations in plant samples by the classical method of atomic absorption spectrometry/electrothermal atomisation (AAS-ETA) after dry ashing is quantified. Two grinding machines, a planetary mill with balls and jars of agate versus a stainless steel grinder were compared by analysing leaf samples of cucumber, strawberry, kiwivines, apple trees and grapevines from agricultural experimental plots under controlled conditions. Variance components due to the difference between grinding methods and experimental plots were estimated. Further, the simultaneous effects of the grinding methods on all considered metals have been evaluated by analysis of variance. With the stainless steel grinder, on average, higher levels of the considered heavy metals were obtained (up to 67% of the mean values). On average, the increments were similar for metals contained in steel (Ni and Cr) and those not contained (Pb and Cd). The true causes of these differences need further investigation to determine whether the higher metal detection is due to possible contamination, to a different grinding quality or to other reasons. Finally, the grinding methods did not seem to affect the combined uncertainty of the analyses. Received: 3 November 1997 · Accepted: 29 November 1997     

SYNTHESIS AND NMR SPECTROSCOPIC STUDY OF NEW 5-METHYLFURYL-CONTAINING SCHIFF BASES AND RELATED BIS(AMINOPHOSPHONATES)

The synthesis of three novel 5-methylfuryl-containing Schiff bases: N,N′-bis(5-methylfurfurylidene)-4,4′-diaminodiphenylmethane, N,N′-bis(5-methylfurfurylidene)-1,4-phenylenediamine, and N,N′-bis(5methylfurfurylidene)benzidine and the corresponding bis(aminophosphonates) derived from them, 4,4′-bis{N-methyl(diethoxyphosphonyl)-1-[(5-methyl)-2-furyl]} diaminodiphenylmethane, 1,4-bis { N-methyl(diethoxyphosphonyl)-1-[(5-methyl)-2-furyl]} diaminobenzene, and bis{N-methyl(diethoxyphosphonyl)-1-[(5-methyl)-2-furyl]}- benzidine, is reported. The compounds have been characterized by elemental analysis, TLC, IR, and NMR ( ¹ H, ¹³ C, and ³¹ P) spectra. For comparison, new ¹³ C and ³¹ P NMR data of three furyl-containing analogues of the above bis(aminophosphonates) are also regarded. The NMR studies of the two series of bis(aminophosphonates) reveal the presence of one diastereomer (meso or racemic form).     

The effect of post-irradiation annealing on the crosslinking of high-density polyethylene induced by gamma-radiation

Samples of two high-density polyethylenes having different crystallinity levels were gamma irradiated under vacuum at doses ranging from 20 to 300 kGy. Subsequently, the vials containing the irradiated samples were exposed to different post-irradiation treatments. Parts of the specimens were annealed while still under vacuum. The annealing time was 4 h and the annealing temperatures 110 °C or 150 °C. Others were exposed directly to air opening the vials without any thermal treatment. It was verified that in all cases the dosage to produce an incipient gel increases with the crystallinity of the initial sample. The amount of gel produced after exposing specimens of the same polymer to a given dose increases with the annealing temperature. The largest increment in the amount of gel produced at the completion of the post-irradiation treatment was found on the samples with the highest initial crystallinity level.Evidence of oxidation was found in all irradiated samples. The extent of oxidation depends on the initial crystallinity of the sample, the irradiation dose and the type of post-irradiation treatment. The heat of fusion measured in the annealed samples decreases with the gel content while the fusion temperature was slightly affected. Ductile or brittle behaviors were observed after testing specimens under tensile stress. The yield stress increases proportionally to the crystallinity level that, in turn, depends on the total dosage applied to the samples. The extensibility of ductile samples is determined by the amount of gel produced regardless of the degree of initial crystallinity and the type of annealing process applied to each sample.     

A Galerkin Approach for Power Spectrum Determination of Nonlinear Oscillators

A numerical method to estimate spectral properties of nonlinear oscillators with random input is presented. The stationary system response is expanded into a trigonometric Fourier series. A set of nonlinear algebraic equations, solved by Newtons method, leads to the determination of the unknown Fourier series coefficients of single samples of the response process. For cubic polynomial nonlinearities, closed-form expressions are used to find the nonlinear terms at each step of the solution scheme. Further, a simple procedure yields an approximation of an arbitrary nonlinearity by a cubic polynomial. Power spectral density estimates for the response process are constructed by averaging the square modulus of the computed Fourier coefficients over various samples or by means of well-established smoothing techniques of spectral analysis. Two applications are presented illustrating the effectiveness of the method as compared to statistical linearization and digital Monte-Carlo simulation.