Complex dynamics and targeted energy transfer in linear oscillators coupled to multi-degree-of-freedom essentially nonlinear attachments

We study the dynamics of a system of coupled linear oscillators with a multi-DOF end attachment with essential (nonlinearizable) stiffness nonlinearities. We show numerically that the multi-DOF attachment can passively absorb broadband energy from the linear system in a one-way, irreversible fashion, acting in essence as nonlinear energy sink (NES). Strong passive targeted energy transfer from the linear to the nonlinear subsystem is possible over wide frequency and energy ranges. In an effort to study the dynamics of the coupled system of oscillators, we study numerically and analytically the periodic orbits of the corresponding undamped and unforced hamiltonian system with asymptotics and reduction. We prove the existence of a family of countable infinity of periodic orbits that result from combined parametric and external resonance interactions of the masses of the NES. We numerically demonstrate that the topological structure of the periodic orbits in the frequency–energy plane of the hamiltonian system greatly influences the strength of targeted energy transfer in the damped system and, to a great extent, governs the overall transient damped dynamics. This work may be regarded as a contribution towards proving the efficacy the utilizing essentially nonlinear attachments as passive broadband boundary controllers. PACS numbers: 05.45.Xt, 02.30.Hq     

Classification of periodic orbits of two-dimensional homogeneous granular crystals with no pre-compression

In the present study we classify the periodic orbits of a squarely packed, uncompressed and undamped, homogeneous granular crystal, assuming that all elastic granules oscillate with the same frequency (i.e., under condition of 1:1 resonance); this type of Hamiltonian periodic orbits have been labeled as nonlinear normal modes. To this end we formulate an auxiliary system which consists of a two-dimensional, vibro-impact lattice composed of non-uniform “effective particles” oscillating in an anti-phase fashion. The analysis is based on the idea of balancing linear momentum in both horizontal and vertical directions for separate, groups of particles, whereby each such a group is represented by the single effective particle of the auxiliary system. It is important to emphasize that the auxiliary model can be defined for general finite, squarely packed granular crystals composed of n rows and m columns. The auxiliary model is successful in predicting the total number of such periodic orbits, as well as the amplitude ratios for different periodic regimes including strongly localized ones. In fact this methodology enables one to systematically study the generation of mode localization in these strongly nonlinear, highly degenerate dynamical systems. Good correspondence between the results of the theoretical model and direct numerical simulations is observed. The results presented herein can be further extended to study the intrinsic dynamics of the more complex granular materials, such as heterogeneous two-dimensional and three-dimensional granular crystals and multi-layered structures.     

Green synthesis and antioxidant activity of new PEGylated ferulic acids

PEGylation of ferulic acid is described through a green esterification process involving poly(ethylene glycol) (PEG) with three different average molecular weights (200, 400 and 1000 g/mol) as both reactive and solvent. Esterification with PEG400 and PEG1000 leads to original compounds soluble in all proportions in water. These new compounds display an antioxidant activity similar to that of ferulic acid.     

Structure elucidation by synthesis of four metabolites of the antitumor drug ENMD-1198 detected in human plasma samples

ENMD-1198 is a biologically active analogue of the antitumor drug 2-methoxyestradiol. Four human metabolites of ENMD-1198 were identified through synthesis and liquid chromatography/mass spectrometry comparisons of the metabolites with the synthetic standards. Two metabolites (3 and 4) are epimers resulting from benzylic hydroxylation at C-6. Two additional metabolites (5 and 6) are formed by epimeric hydroxylation at C-6 and α-epoxidation of the 16,17-alkene. The syntheses provided sufficient quantities of the metabolites for cytotoxicity studies to proceed. The 6-β-ol 4 was moderately less cytotoxic than the parent drug, while the remaining three metabolites (3, 5, and 6) were significantly less cytotoxic.     

Generation of Accurate Finite Element Models of Nonlinear Systems – Application to an Aeroplane-Like Structure

Model updating and validation is currently a central issue in the fields of computational structural mechanics and dynamics. The vast majority of applications however concerns linear structures. On the other hand, updating nonlinear models is something the structural dynamicist prefers to avoid mainly because tools such as modal analysis are no longer available. The objective of the present study is to propose a two-step methodology for dealing with nonlinear systems. Its most appealing feature is that it decouples the estimation of the linear and nonlinear parameters. A numerical application consisting of an aeroplane-like structure is used to assess the efficiency of the procedure.     

The Method of Proper Orthogonal Decomposition for Dynamical Characterization and Order Reduction of Mechanical Systems: An Overview

Modal analysis is used extensively for understanding the dynamic behavior of structures. However, a major concern for structural dynamicists is that its validity is limited to linear structures. New developments have been proposed in order to examine nonlinear systems, among which the theory based on nonlinear normal modes is indubitably the most appealing. In this paper, a different approach is adopted, and proper orthogonal decomposition is considered. The modes extracted from the decomposition may serve two purposes, namely order reduction by projecting high-dimensional data into a lower-dimensional space and feature extraction by revealing relevant but unexpected structure hidden in the data. The utility of the method for dynamic characterization and order reduction of linear and nonlinear mechanical systems is demonstrated in this study.     

Theoretical and Experimental Study of Multimodal Targeted Energy Transfer in a System of Coupled Oscillators

The purpose of this study is the theoretical and experimental investigation of targeted energy transfers from a two-degree-of-freedom primary structure to a nonlinear energy sink (NES). It is demonstrated that an NES can resonate with and extract energy from both modes of the primary structure. By facilitating these energy transfers, notably through excitation of appropriate periodic and quasi-periodic orbits, one can promote dissipation of a major portion of externally induced energy in the nonlinear attachment.     

Smoothing Sample Extremes with Dynamic Models

The study of extreme values is of crucial interest in many contexts. The concentration of pollutants, the sea-level and the closing prices of stock indexes are only a few examples in which the occurrence of extreme values may lead to important consequences. In the present paper we are interested in detecting trend in sample extremes. A common statistical approach used to identify trend in extremes is based on the generalized extreme value distribution, which constitutes a building block for parametric models. However, semiparametric procedures imply several advantages when exploring data and checking the model. This paper outlines a semiparametric approach for smoothing sample extremes, based on nonlinear dynamic modelling of the generalized extreme value distribution. The relative merits of this approach are illustrated through two real examples.AMS 2000 Subject Classification. Primary—62G32, 62G05, 62M10     

A Spectroscopic and Molecular Modelling Study of the Nature of the Association Complexes of Nile Red with Cyclodextrins

The polarity-sensitive fluorescent dye Nile Red forms association complexes with various cyclodextrins in aqueous solution. The formation of such association complexes has a significant effect on the Nile Red fluorescence, with the largest effect being observed in -cyclodextrin solution. When -cyclodextrin is used to increase the Nile Red concentration in solution, the absorption spectrum shows a large blue shift indicating the formation of an inclusion complex, but surprisingly the Nile Red fluorescence is strongly suppressed. A proposed explanation for this observation involves the formation of 1:2 host:guest complexes, in which the Nile Red guests are included as relatively non-fluorescent dimers. When the solutions were prepared by adding -cyclodextrinto a near-saturated aqueous solution of Nile Red (so that 1:1 or 2:1 complexation shouldbe favoured), significant fluorescence enhancement was observed. Analysis of thefluorescence enhancement as a function of host concentration indicated the formationof 2:1 host:guest complexes in these solutions. However, electrospray mass spectroscopic studies show no evidence for the formation of any such inclusion complexes. Furthermore, molecular modelling shows that the formation of a complex involving full insertion of Nile Red in the -cyclodextrin cavity is not stable, and will quickly eject the Nile Red guest molecule. These modelling results suggest that an association complex involving capping (via the association of Nile Red parallel to the cavity opening, or by partial insertion into the cavity) of the -cyclodextrin cavity by one or two Nile Red molecules is much more likely.     

Optimized liquid chromatography-mass spectrometry approach for the isolation of minor stress biomarkers in plant extracts and their identification by capillary nuclear magnetic resonance

A LC-MS approach is presented for the isolation of minor key plant biomarkers, in view of their characterization by NMR at the microgram scale. Due to the complexity of plant extracts, the purification of metabolites present in low concentrations is critical. The strategy used relies on the optimization of the chromatographic analysis using ultra-performance liquid chromatography-time-of-flight mass spectrometry (UPLC-TOF-MS), thanks to modelling software. The optimized method is then transferred to semi-preparative LC conditions with MS detection. The approach is illustrated by the isolation of wound-induced jasmonate derivatives revealed by a metabolomic study in Arabidopsis thaliana leaves and their subsequent characterization by capillary NMR (CapNMR).