Chaotic dynamics of flexible rectangular panels in white noise field
Автор: Krylova E.Y., Yakovleva T.V., Bazhenov V.G.
Статья в выпуске: 1, 2016 года.
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The paper studies the impact of a flexible rectangular panel intensity of the external white noise field (which is normal to the panel surface) on the nature of oscillations. A mathematical model of panel oscillations is based on Kirchhoff hypotheses with dissipation. The geometric nonlinearity is taken into account in the form of Karman. We consider a rectangular panel with an aspect ratio in plan, by an external longitudinal load. Equations of motion are joined by inhomogeneous boundary conditions of bearing on flexible incompressible (inextensible) edges and zero initial conditions. The resulting system of nonlinear differential equations in private derivatives is reduced to a nonlinear system of ordinary differential equations by the method of finite differences in spatial variables. As for the time, the system is solved by the Runge-Kutta fourth-order accuracy. The number of degrees of freedom of the mechanical system in the experiment equals to 196. In order to analyze the results obtained in the work, in addition to the Fourier analysis, the authors applied the wavelet transformation unit, which allows a more detailed study of the local time signal features. The experiment has revealed a range of amplitudes outer longitudinal load, where the behavior of the dynamical system is not sustainable. For this range of amplitudes of longitudinal load we studied the influence of the white noise field with varying intensity on the nature of the panel vibrations. The numerical experiments show that the white noise field is capable of reducing the amplitude of the oscillation panel, reducing the number of frequencies in the vibration spectrum of the system and transfering to the asymmetric waveform symmetry. So, it is possible to state that effecting the dynamic system with noise field can lead to safer vibrational modes. That is, using the white noise can be controlled by the nature of vibrations of the mechanical system.
Nonlinear dynamics, parametric oscillations, dissipative systems, panels, chaotic oscillations, white noise, wavelet analysis, fourier analysis, control of oscillations
Короткий адрес: https://sciup.org/146211604
IDR: 146211604 | DOI: 10.15593/perm.mech/2016.1.06