A non-linear model for the dynamics of open cross-section thin-walled beams—Part I: formulation

A non-linear one-dimensional model of inextensional, shear undeformable, thin-walled beam with an open cross-section is developed. Non-linear in-plane and out-of-plane warping and torsional elongation effects are included in the model. By using the Vlasov kinematical hypotheses, together with the assumption that the cross-section is undeformable in its own plane, the non-linear warping is described in terms of the flexural and torsional curvatures. Due to the internal constraints, the displacement field depends on three components only, two transversal translations of the shear center and the torsional rotation. Three non-linear differential equations of motion up to the third order are derived using the Hamilton principle. Taking into account the order of magnitude of the various terms, the equations are simplified and the importance of each contribution is discussed. The effect of symmetry properties is also outlined. Finally, a discrete form of the equations is given, which is used in Part II to study dynamic coupling phenomena in conditions of internal resonance.     

Resonant non-linear normal modes. Part II: activation/orthogonality conditions for shallow structural systems

The general conditions, obtained in Lacarbonara and Rega (Int. J. Non-linear Mech. (2002)), for orthogonality of the non-linear normal modes in the cases of two-to-one, three-to-one, and one-to-one internal resonances in undamped unforced one-dimensional systems with arbitrary linear, quadratic and cubic non-linearities are here investigated for a class of shallow symmetric structural systems. Non-linear orthogonality of the modes and activation of the associated interactions are clearly dual problems. It is known that an appropriate integer ratio between the frequencies of the modes of a spatially continuous system is a necessary but not sufficient condition for these modes to be non-linearly coupled. Actual activation/orthogonality of the modes requires the additional condition that the governing effective non-linear interaction coefficients in the normal forms be different/equal to zero. Herein, a detailed picture of activation/orthogonality of bimodal interactions in buckled beams, shallow arches, and suspended cables is presented.     

Multiple Internal Resonance in Suspended Cables under Random In-Plane Loading

The random excitation of a suspended cable with simultaneous internal resonances is considered. The internal resonances can take place among the first in-plane and the first two out-of-plane modes. The external loading is represented by a wide-band random process. The response statistics are estimated using the Fokker-Planck-Kolmogorov (FPK) equation, together with Gaussian and non-Gaussian closures. Monte Carlo simulation is also used for numerical verification. The unimodal in-plane motion exists in regions away from the internal resonance condition. The mixed mode interaction is manifested within a limited range of internal detuning parameters, depending on the excitation power spectrum density and damping ratios. The Gaussian closure scheme failed to predict bounded solutions of mixed mode interaction. The non-Gaussian closure results are in good agreement with the Monte Carlo simulation. The on-off intermittency of the autoparametrically excited modes is observed in the Monte Carlo simulation over a small range of excitation levels. The influence of the cable parameters, such as damping ratios, sag-to-span ratio, internal detuning parameters, and excitation level on the autoparametric interaction, is studied. It is found that the internal detuning and excitation level are the two main parameters which affect the autoparametric interaction among the three modes. Due to the system's nonlinearity, the response of the three modes is strongly non-Gaussian and the coupled modes experience irregular modulation.     

Nonlinear interactions and chaotic dynamics of suspended cables with three-to-one internal resonances

Nonlinear planar oscillations of suspended cables subjected to external excitations with three-to-one internal resonances are investigated. At first, the Galerkin method is used to discretize the governing nonlinear integral–partial-differential equation. Then, the method of multiple scales is applied to obtain the modulation equations in the case of primary resonance. The equilibrium solutions, the periodic solutions and chaotic solutions of the modulation equations are also investigated. The Newton–Raphson method and the pseudo-arclength path-following algorithm are used to obtain the frequency/force–response curves. The supercritical Hopf bifurcations are found in these curves. Choosing these bifurcations as the initial points and applying the shooting method and the pseudo-arclength path-following algorithm, the periodic solution branches are obtained. At the same time, the Floquet theory is used to determine the stability of the periodic solutions. Numerical simulations are used to illustrate the cascades of period-doubling bifurcations leading to chaos. At last, the nonlinear responses of the two-degree-of-freedom model are investigated.     

Suppression of super-harmonic resonance response using a linear vibration absorber

Super-harmonic resonances may appear in the forced response of a weakly nonlinear oscillator having cubic nonlinearity, when the forcing frequency is approximately equal to one-third of the linearized natural frequency. Under super-harmonic resonance conditions, the frequency-response curve of the amplitude of the free-oscillation terms may exhibit saddle-node bifurcations, jump and hysteresis phenomena. A linear vibration absorber is used to suppress the super-harmonic resonance response of a cubically nonlinear oscillator with external excitation. The absorber can be considered as a small mass-spring-damper oscillator and thus does not adversely affect the dynamic performance of the nonlinear primary oscillator. It is shown that such a vibration absorber is effective in suppressing the super-harmonic resonance response and eliminating saddle-node bifurcations and jump phenomena of the nonlinear oscillator. Numerical examples are given to illustrate the effectiveness of the absorber in attenuating the super-harmonic resonance response.     

Picosecond time-resolved nonresonant ionization detected IR spectroscopy on 7-azaindole dimer

The picosecond time-resolved IR spectrum of the 7-azaindole dimer has been measured by picosecond time-resolved nonresonant ionization detected IR spectroscopy. This new time-resolved technique was developed by combining nonresonant ionization detected IR (NID-IR) spectroscopy with tunable picosecond IR and UV lasers. The time-resolved NID-IR spectrum from 2 600 cm^-1 to 3 800 cm^-1 shows a drastic change from 1.5 ps to 11 ps time evolution. A mode-specific vibrational redistribution has been suggested. Received 14 May 2002 / Received in final form 11 June 2002 Published online 13 September 2002     

Non-leptonic weak charmed baryon decays in theSU(4) semidynamical scheme

We study here the Cabibbo enhanced charmed baryon decays in theSU(4) semidynamical model. The weak Hamiltonian 20″ + 15 + 45 + 45* can have the parity violating amplitude for charmed baryon decays. Decay width and α for some modes are also calculated.     

High spin states and evidence for octupole correlations in 117Xe

High-spin states of ¹¹⁷Xe were investigated by means of in-beam γ-ray spectroscopic techniques via the reaction of ²⁸Si bombarding a ⁹²Mo target at beam energies of 100-120 MeV. A positive-parity rotational band decaying into the yrast negative-parity band by a series of enhanced E1 transitions was observed for the first time, implying the existence of octupole correlations in ¹¹⁷Xe. The B(E1) values increase with spin. The νd_5/2 band was firmly established up to 27/2⁺ and the B(M1)/B(E2) ratios were extracted from the relative intensities of γ-rays in this band. The previously known νh_11/2 and νg_7/2 [413]5/2⁺α=−1/2 bands were confirmed and extended up to high spins and two bandcrossings are observed in the latter at ħω=0.33 and 0.44 MeV, respectively. The bandcrossings and configurations of these bands are discussed by TRS and CSM calculations. In a γ–γ–t measurement, the 11/2⁻ and 7/2⁻ levels were identified as two isomers with half-lives of 59.4±20 ns and 16.5±8.0 ns, respectively. Received: 17 June 1997 / Revised version: 29 September 1997     

Electron resonances in VLEED from Cu(111)

The sensitivity of the VLEED I–V curves to the shape and the position of the barrier is shown for the image- type surface barriers. For demonstration and comparison with experimental data the intensities of specularly reflected electron beams from Cu(111) are computed by dynamical theory of electron diffraction. Image plane position changes and modifications of the saturation shape of the surface barrier induce pronounced changes in the I–V curves calculated with the image-type barrier. Presented at the X-th Symposium on Suface Physics, Prague, Czech Republic, July 11–15, 2005.