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

DETC2005-84756 ON NUMERICAL SIMULATIONS OF A NONLINEAR SELF-EXCITED SYSTEM WITH TWO NON-IDEAL SOURCES

ABSTRACT In this work, the dynamic behavior of self-synchronization and synchronization through mechanical interactions between the nonlinear self-excited oscillating system and two non-ideal sources are examined by numerical simulations. The physical model of the system vibrating consists of a non-linear spring of Duffing type and a nonlinear damping described by Rayleigh's term. This system is additional forced by two unbalanced identical direct current motors with limited power (non-ideal excitations). The present work mathematically implements the parametric excitation described by two periodically changing stiffness of Mathieu type that are switched on/off

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

Analytical and experimental investigations of an autoparametric beam structure

This paper discusses theoretical and experimental investigations of vibrations of an autoparametric system composed of two beams with rectangular cross sections. Different flexibilities in the two orthogonal directions are the specific features of the structure. Differential equations of motion and associated boundary conditions, up to third-order approximation, are derived by application of the Hamilton principle of least action. Experimental response of the system, tuned for the 1:4 internal resonance condition, are performed for random and harmonic excitations. The most important vibration modes are extracted from a real mechanical system. It is shown that certain modes in the stiff and flexible directions of both beams may interact, and, intuitively unexpected out-of-plane motion may appear. Preliminary numerical calculations, based on the mathematical model, are also presented

Nonlinear dynamics of bistable composite cantilever shells: An experimental and modelling study

The nonlinear dynamics of cantilever bistable shells with asymmetric stable configurations is investigated. The possibility of maximizing the kinetic energy associated with snap-through motion offered by the considered cantilevered shells is pursued to enhance the sought-after energy harvesting capabilities. Through an experimental campaign under harmonic forcing the resonance scenarios around the stable configurations are analysed. The resulting nonlinear behaviour observed for high amplitude excitation is adopted to guide a reduced order model derivation. By combining the experimental response with two double-well oscillators derived from FE simulations, a double-well quintic oscillator capturing the observed softening behaviour is proposed. It involves a parameter identification phase in which a nonlinear damping model is introduced. A numerical continuation approach is adopted to discuss the local periodic solutions around each stable configuration in terms of resonance curves, bifurcation diagrams and basins of attraction. The global dynamics involving regular and chaotic dynamic regimes as well as snap-through motion is eventually described