Stability of parametric vibrations of laminated composite plates
The dynamic stability of laminated composite plates subjected to arbitrary periodic loads is studied based on the first-order shear deformation plate theory. The in-plane load is taken to be a combination of periodic biaxial and bending stress. A set of second-order ordinary differential equations with periodic coefficients of Mathieu-Hill type is formed to determine the regions of dynamic instability based on Bolotin's method. Numerical results reveal that the dynamic instability is significantly affected by the modulus ratio, number of layer, static and dynamic load parameters. The effects of various important parameters on the instability region and dynamic instability index are investigated.
Chaotic dynamics of two coaxially-nested cylindrical shells reinforced by two beams
Abstract Non-linear dynamics and contact interactions of beam-shell structures composed of two closed cylindrical shells which are coaxially nested and reinforced by two beams located symmetrically on the shell external perimeter is studied. In the present work, clearances between the mentioned structural members are taken into account, two beams are subjected to harmonic loads, and the dissipation factors are neglected. 3D PDEs governing non-linear dynamics of beams and shells within the geometric theory of Novozhilov are employed, whereas the contact pressure is defined through Kantor's model. PDEs are reduced to ODEs by means of the FEM (finite element method), and the solution convergence is validated through different numbers of finite elements located along the structural members thickness and by employment of the Runge principle with respect to spatial coordinates. The Cauchy problem is solved by the explicit integration (Euler method), which allows one to carry out the computation without the need to define solutions in a few initial points. Analysis of vibrations, including contact interactions, is realized with the use of methods of non-linear dynamics and the qualitative theory of differential equations, time histories/signals, phase portraits, Poincare sections, Fourier spectra, wavelet-based analysis as well as the Lyapunov exponents.
Fragment Rotational State Distributions From The Dissociation Of NeIBr: Experimental And Theoretical Results
The IBr fragment rotational state distributions that result when the NeIBr van der Waals molecule undergoes vibrational predissociation have been measured in a pump–probe laser‐induced fluorescence experiment. Independent of initial vibrational state and the number of quanta of vibrational energy lost from the I–Br coordinate, the rotational distributions extend over the full range of energetically accessible states. From the observation of energetic constraints on the rotational distribution, the dissociation energy (D0) is calculated to be 65.5±1.2 cm−1 for the A electronic state, v=16. For the X electronic state, v=0, D0=71.8±1.2 cm−1. Quantum mechanical bound state calculations carried out on a model A electronic state potential energy surface are in quantitative agreement with this result. The rotational distributions are broader than that predicted by either a Franck–Condon or classical impulsive model for the dissociation. The distributions are qualitatively in accord with classical trajectory calc...