Describing function of two masses with backlash

This paper analyzes the dynamical properties of systems with backlash and impact phenomena based on the describing function method. It is shown that this type of nonlinearity can be analyzed in the perspective of the fractional calculus theory. The fractional dynamics is compared with that of standard models.

Analysis of polycyclic aromatic hydrocarbons in fish: evaluation of a quick, easy, cheap, effective, rugged, and safe extraction method

QuEChERS method was evaluated for extraction of 16 PAHs from fish samples. For a selective measurement of the compounds, extracts were analysed by LC with fluorescence detection. The overall analytical procedure was validated by systematic recovery experiments at three levels and by using the standard reference material SRM 2977 (mussel tissue). The targeted contaminants, except naphthalene and acenaphthene, were successfully extracted from SRM 2977 with recoveries ranging from 63.5–110.0% with variation coefficients not exceeding 8%. The optimum QuEChERS conditions were the following: 5 g of homogenised fish sample, 10 mL of ACN, agitation performed by vortex during 3 min. Quantification limits ranging from 0.12– 1.90 ng/g wet weight (0.30–4.70 µg/L) were obtained. The optimized methodology was applied to assess the safety concerning PAHs contents of horse mackerel (Trachurus trachurus), chub mackerel (Scomber japonicus), sardine (Sardina pilchardus) and farmed seabass (Dicentrarchus labrax). Although benzo(a)pyrene, the marker used for evaluating the carcinogenic risk of PAHs in food, was not detected in the analysed samples (89 individuals corresponding to 27 homogenized samples), the overall mean concentration ranged from 2.52 l 1.20 ng/g in horse mackerel to 14.6 ± 2.8 ng/ g in farmed seabass. Significant differences were found between the mean PAHs concentrations of the four groups.

A straightforward method to obtain the cohesive laws of bonded joints under mode I loading

A simple procedure to measure the cohesive laws of bonded joints under mode I loading using the double cantilever beam test is proposed. The method only requires recording the applied load–displacement data and measuring the crack opening displacement at its tip in the course of the experimental test. The strain energy release rate is obtained by a procedure involving the Timoshenko beam theory, the specimen’s compliance and the crack equivalent concept. Following the proposed approach the influence of the fracture process zone is taken into account which is fundamental for an accurate estimation of the failure process details. The cohesive law is obtained by differentiation of the strain energy release rate as a function of the crack opening displacement. The model was validated numerically considering three representative cohesive laws. Numerical simulations using finite element analysis including cohesive zone modeling were performed. The good agreement between the inputted and resulting laws for all the cases considered validates the model. An experimental confirmation was also performed by comparing the numerical and experimental load–displacement curves. The numerical load–displacement curves were obtained by adjusting typical cohesive laws to the ones measured experimentally following the proposed approach and using finite element analysis including cohesive zone modeling. Once again, good agreement was obtained in the comparisons thus demonstrating the good performance of the proposed methodology.

Filters method in direct search optimization, new measures to admissibility

Constrained nonlinear optimization problems are usually solved using penalty or barrier methods combined with unconstrained optimization methods. Another alternative used to solve constrained nonlinear optimization problems is the lters method. Filters method, introduced by Fletcher and Ley er in 2002, have been widely used in several areas of constrained nonlinear optimization. These methods treat optimization problem as bi-objective attempts to minimize the objective function and a continuous function that aggregates the constraint violation functions. Audet and Dennis have presented the rst lters method for derivative-free nonlinear programming, based on pattern search methods. Motivated by this work we have de- veloped a new direct search method, based on simplex methods, for general constrained optimization, that combines the features of the simplex method and lters method. This work presents a new variant of these methods which combines the lters method with other direct search methods and are proposed some alternatives to aggregate the constraint violation functions.

Fractional describing function of systems with Coulomb friction

This paper studies the describing function (DF) of systems constituted by a mass subjected to nonlinear friction. The friction force is decomposed into two components, namely, the viscous and the Coulomb friction. The system dynamics is analyzed in the DF perspective revealing a fractional-order behavior. The reliability of the DF method is evaluated through the signal harmonic contents.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.

On the numerical computation of the Mittag-Leffler function

Recently simple limiting functions establishing upper and lower bounds on the Mittag-Leffler function were found. This paper follows those expressions to design an efficient algorithm for the approximate calculation of expressions usual in fractional-order control systems. The numerical experiments demonstrate the superior efficiency of the proposed method.