Flexural-torsional bifurcations of a cantilever beam under potential and circulatory forces I: Non-linear model and stability analysis

The stability of a cantilever elastic beam with rectangular cross-section under the action of a follower tangential force and a bending conservative couple at the free end is analyzed. The beam is herein modeled as a non-linear Cosserat rod model. Non-linear, partial integro-differential equations of motion are derived expanded up to cubic terms in the transversal displacement and torsional angle of the beam. The linear stability of the trivial equilibrium is studied, revealing the existence of buckling, flutter and double-zero critical points. Interaction between conservative and non-conservative loads with respect to the stability problem is discussed. The critical spectral properties are derived and the corresponding critical eigenspace is evaluated.     

Dehydrogenation of ammonia borane aided by hydrophobic ionic liquids

The beneficial effect on the dehydrogenation of ammonia borane due to mixing with hydrophobic ionic liquids (ILs) is investigated by means of detailed combined TG–DTA and IR measurements. Desorption of several mixtures of ammonia borane with hydrophobic ILs having bis(trifluoromethanesulfonyl)-imide or trifluorosulfonyl-imide anions was studied in both isothermal and non-isothermal conditions. The addition of hydrophobic liquids lowers the dehydrogenation temperatures and allows the observation of the decomposition process without any induction time even at temperatures below 90 °C. The IR data of the products of the decomposition confirm that ILs do not react with AB but provide an highly polar medium which promotes the decomposition reaction. Furthermore, the proposed method to enhance hydrogen release from ammonia borane provides the possibility of working in air avoiding any protective atmosphere.     

Submillimeter and infrared spectroscopy on La0.85Sr0.15MnO3

The optical conductivity of La_0.85Sr_0.15MnO₃ single crystals was studied by means of submillimeter and infrared spectroscopy for frequencies cm^-1 and temperatures 10 K < T <300 K. The submillimeter conductivity follows the temperature dependence of the dc-data. The phonon spectrum of La_0.85Sr_0.15MnO₃ changes considerably below K revealing a structural phase transition induced by charge or orbital order. At T =10 K a number of phonon modes can be identified in addition to the room-temperature spectrum. The optical conductivity () in the mid-infrared reveals the characteristics of small polaron absorption. Below the magnetic ordering temperature the polaron binding energy is highly reduced, but the onset of charge order interrupts the formation of free charge carriers with a Drude-like behavior. The frequency and temperature dependence of in this regime qualitatively resembles the small polaron predictions by Millis et al. (Phys. Rev. B 54, 5405 (1996)). Received 5 November 1999     

A perturbation method for evaluating nonlinear normal modes of a piecewise linear two-degrees-of-freedom system

The classical Lindstedt–Poincaré method is adapted to analyze the nonlinear normal modes of a piecewise linear system. A simple two degrees-of-freedom, representing a beam with a breathing crack is considered. The fundamental branches of the two modes and their stability are drawn by varying the severity of the crack, i.e., the level of nonlinearity. Results furnished by the asymptotic method give insight into the mechanical behavior of the system and agree well with numerical results; the existence of superabundant modes is proven. The unstable regions and the bifurcated branches are followed by a numerical procedure based on the Poincarè map.     

Postcritical Behavior of Cables Undergoing Two Simultaneous Galloping Modes

Abstract. A nonlinear two degree-of-freedom model, describing a flexible elastic suspended cable undergoing galloping oscillations, is analyzed. By using a perturbative approach, the critical conditions occuring for different values of the aerodynamic coefficients are described. Two different type of critical conditions, corresponding to simple or double Hopf bifurcations are found. The nonlinear postcritical behavior of single taut strings in 1:1 primary internal resonance is studied through the multiple scale perturbation method. In the double Hopf bifurcation case the influence of the detuning between the critical eigenvalues on the postcritical behavior is illustrated. It is found that quasi-periodic motions, which are likely to occur in the linear field when the two critical frequencies are incommensurable, are really unstable in the nonlinear range. Therefore, the postcritical behavior of the string consists of stable periodic motions for any detuning values.Sommario. Viene analizzato un modello non lineare a due gradi di libertrappresentativo di un cavo elastico flessibile sospeso alle estremite soggetto ad oscillazioni galoppanti. Utilizzando un approccio perturbativo, vengono descritte le condizioni critiche per differenti valori dei coefficienti aerodinamici. Sono presenti due diversi tipi di condizioni critiche, corrispondenti a biforcazioni di Hopf semplici e doppie. Attraverso il metodo perturbativo delle scale multiple viene studiato il comportamento post-critico non lineare di singole stringhe tese in risonanza interna primaria 1:1. Nel caso di biforcazione doppia di Hopf viene illustrata l'influenza del detuning tra gli autovalori critici sul comportamento post-critico. Si trova che i moti quasi-periodici, presenti in campo lineare quando le due frequenze critiche sono incommensurabili, sono in realtinstabili in campo non lineare. Quindi, il comportamento post-critico della stringa risulta composto da moti periodici stabili per un qualsiasi valore del detuning.     

On inner shearing constraints for a direct beam model coarsely describing warping

We investigate inner shearing constraints for a direct one-dimensional beam model coarsely describing warping. In particular, we study how they affect the field equations for the elastic buckling of open thin-walled beams. We show that the distinction between the axes of the shear centres and of the centroids is crucial for the kinematics of the beam, and to derive expression of reactive actions, hence of buckling critical conditions. We also show how a suitable definition of the warping inertial action and properly introduced inner shearing constraints yield the field equations of the literature for the beam in a general dynamic setting.     

Point defect dynamics and evolution of chemical reactions in alanates by anelastic spectroscopy

We report the first measurements of elastic modulus and energy dissipation in Ti-doped and undoped sodium aluminum hydride. It is shown that the chemical reactions that occur by varying the sample temperatures or by aging most sensitively affect the elastic constants, such that the modulus variations allow the time and temperature evolution of decomposition to be monitored. After a well-defined thermal treatment at 436 K, a thermally activated relaxation process appears at 70 K in the kilohertz range, denoting the existence of a new species, likely involving hydrogen, having a very high mobility, that is, 10(3) jumps/s at the peak temperature corresponding to a relaxation rate of about 10(11) s(-1) at room temperature. The activation energy of the process is 0.126 eV and the preexponential factor 7 x 10(-14) s, which is typical of point defect relaxation. The peak is very broad with respect to a single Debye process, indicating strong interaction or/and multiple jumping type of the mobile entity. The present data suggest that the models aiming at interpreting the decomposition reactions and kinetics should take into account the indicated point-defect dynamics and stoichiometry defects.