Wavelet-Based Analysis of the Regular and Chaotic Dynamics of Rectangular Flexible Plates Subjected to Shear-Harmonic Loading

Abstract

We investigate non-linear dynamics of flexible rectangular plates subjected to external shear harmonic load action. We show that an application of the classical and widely used Fourier analysis does not allow to obtain real picture of the frequency vibration characteristics in each time instant. On the other hand, we show that application of the wavelets approach allows to follow frequency time evolutions. Our numerical results indicate that vibrations in different plate points occur with the same frequencies set although their power is different. Hence, the vibration characteristics can be represented by one arbitrary taken plate point. Furthermore, using wavelets scenarios of transitions from regular to chaotic dynamics are illustrated and discussed including two novel scenarios not reported so far in the existing literature.

Regular and Chaotic Dynamics of Flexible Plates

“…Vibrations are studied in the time interval ∈ [0, 286], for = / = 1, dissipation factor = 1, and the Poisson coefficient = 0.3. Results obtained for the center of the middle plate surface are generalized into the whole plate [13]. In the numerical experiment with the excitation frequency = 2.9 a new modified Feigenbaum scenario has been obtained (see Table 2).…”

“…Transitions into the system with finite (many) degrees of freedom chaotic dynamics are reported in a series of references [8][9][10][11][12]. The advantages of wavelet-oriented analysis of nonlinear vibrations of continuous mechanical systems are described in [13]. Although we aim here at numerical investigations, it should be noted that there is a possibility to apply the method of an artificial perturbation parameter to study nonlinear plate vibrations [14].…”

Application of the Lyapunov Exponents and Wavelets to Study and Control of Plates and Shells

“…The partition number of spatial coordinates is n=14 while applying FDM. Validity and reliability of the obtained results regarding the number of partitions has been discussed by Awrejcewicz et al [14].…”

Wavelet Analysis of EEG Signals in Epilepsy Patients

“…This will reveal abnormal brain activity. Morle wavelet is used for this task, which has proven itself in the study of signals of different nature: historical [20], mechanical [21], [22]. Frequency analysis of EEG signals will also be carried out.…”