Synchronous motion of two vertically excited planar elastic pendula

The dynamics of two planar elastic pendula mounted on the horizontally excited platform have been studied. We give evidence that the pendula can exhibit synchronous oscillatory and rotation motion and show that stable in-phase and anti-phase synchronous states always co-exist. The complete bifurcational scenario leading from synchronous to asynchronous motion is shown. We argue that our results are robust as they exist in the wide range of the system parameters.Comment: Submitte

Nonlinear dynamics of a spinning shaft with non-constant rotating speed

Research on spinning shafts is mostly restricted to cases of constant rotating speed without examining the dynamics during their spin-up or spin-down operation. In this article, initially the equations of motion for a spinning shaft with non-constant speed are derived, then the system is discretised, and finally a nonlinear dynamic analysis is performed using multiple scales perturbation method. The system in first-order approximation takes the form of two coupled sets of paired equations. The first pair describes the torsional and the rigid body rotation, whilst the second consists of the equations describing the two lateral bending motions. Notably, equations of the lateral bending motions of first-order approximation coincide with the system in case of constant rotating speed, and considering the amplitude modulation equations, as it is shown, there are detuning frequencies from the Campbell diagram. The nonlinear normal modes of the system have been determined analytically up to the second-order approximation. The comparison of the analytical solutions with direct numerical simulations shows good agreement up to the validity of the performed analysis. Finally, it is shown that the Campbell diagram in the case of spin-up or spin-down operation cannot describe the critical situations of the shaft. This work paves the way, for new safe operational ‘modes’ of rotating structures bypassing critical situations, and also it is essential to identify the validity of the tools for defining critical situations in rotating structures with non-constant rotating speeds, which can be applied not only in spinning shafts but in all rotating structures

Association of Tannins and Related Polyphenols with the Cyclic Peptide Gramicidin S

The association of 10 different tannins and related polyphenols with gramicidin S, a cyclic peptide having a rigid β-turn structure, has been examined using 1H-NMR spectroscopy. In the presence of pentagalloylglucose and epigallocatechin-3-O-gallate, the proton signals due to proline and the adjacent phenylalanine moieties selectively shifted to up field, suggesting a regioselective association with the β-turn structure. The association was also supported by the observation of intermolecular nuclear Overhauser effects between epigallocatechin-3-O-gallate and the peptide. In contrast, ellagitannins, biogenetically derived from pentagalloylglucose, showed small and non-selective chemical shift changes, suggesting that interaction with these tannins is relatively weak. The hydrophobicity of the tannin molecules and the steric hindrance of the interaction site are thought to be important in the association

Performance comparison between a nonlinear energy sink and a linear tuned vibration absorber for broadband control

The performance of a linear tuned vibration absorber (LTVA) and a nonlinear energy sink (NES) for the vibration mitigation of an uncertain linear primary system is investigated. An analytic tuning rule for the LTVA when the primary system contains uncertainty is derived. The behavior of the linear system coupled to the NES is analyzed theoretically. A tuning methodology for the NES in the deterministic as well as for the uncertain case is presented. © The Society for Experimental Mechanics, Inc. 2016

Fluorophosphate Nucleotide Analogs and Their Characterization as Tools for 19F NMR Studies

To broaden the scope of existing methods based on 19F nucleotide labeling, we developed a new method for the synthesis of fluorophosphate (oligo)nucleotide analogues containing an O to F substitution at the terminal position of the(oligo)phosphate moiety and evaluated them as tools for 19F NMR studies. Using three efficient and comprehensive synthetic approaches based on phosphorimidazolide chemistry and tetra-n-butylammonium fluoride, fluoromonophosphate, or fluorophosphate imidazolide as fluorine sources, we prepared over 30 fluorophosphate-containing nucleotides, varying in nucleobase type (A, G, C, U, m7G), phosphate chain length (from mono to tetra), and presence of additional phosphate modifications (thio, borano, imido, methylene). Using fluorophosphate imidazolide as fluorophosphorylating reagent for 5′-phosphorylated oligos we also synthesized oligonucleotide 5′-(2-fluorodiphosphates), which are potentially useful as 19F NMR hybridization probes. The compounds were characterized by 19F NMR and evaluated as 19F NMR molecular probes. We found that fluorophosphate nucleotide analogues can be used to monitor activity of enzymes with various specificities and metal ion requirements, including human DcpS enzyme, a therapeutic target for spinal muscular atrophy. The compounds can also serve as reporter ligands for protein binding studies, as exemplified by studying interaction of fluorophosphate mRNA cap analogues with eukaryotic translation initiation factor (eIF4E)