VIBRATONAL MECHANICS AND STOCHASTIC QUASI-RESONANCES

The concept of vibrational mechanics was pioneered in the works by Professor I.I. Blekhman and developed by his numerous disciples and coleagues. It is a powerful tool for the study of such systems with fast excitations, in which slow motion is of primary interest. One important application of this approach is the stochastic resonance, the phenomenon of resonance-like response of slow variables to intensity of stochastic excitation. This phenomenon is considered within the framework of vibrational mechanics as forced lowfrequency oscillations near the natural frequency, which evolves under the influence of changing high-frequency stochastic excitation. We propose a generalization of this approach to the case when the evolution of low-frequency properties of the system leads not to the equality of the natural frequency and the frequency of the external slow force, but to the loss of stability in a certain interval of the stochastic excitation intensity. Since in this case, as for stochastic resonance, the external manifestation of the process is the resonance-like response of the system, the considered effect can be called stochastic quasi-resonance, As an example, we consider a rotor with anisotropy of bending stiffness under the action of stochastic angular velocity oscillations.

Effect of Perforations on Resonant Modes of Flat Circular Plates

The vibration of perforated plates is central to certain engineering applications, such asdroplet-on-demand, inject printing and aerosol generation. To the author’s knowledge, there is limitedpublished literature outlining the effect of perforations on the natural frequency of a flat circular plate.This paper aims to further the understanding in this field research, by determining analytically theeffect of perforations on the natural frequency of boundary clamped flat circular plate. The methodology of this paper outlines the development of a dynamic finite element (FE) model which accurately embodies the effect of perforations on the natural frequency of a boundary clamped flat circular plate using modal analysis. This dynamic FE model aids in optimising the vibrational mechanics of perforated plates for specific engineering applications. The finding from this analysis demonstrates that the published literature is less conservative when compared to the FE method in predicting the effect of perforations on the natural frequency of a boundary clamped flat circular plate. Published literature uses a numerical analysis which underestimates the effect of perforations on the natural frequency of a boundary clamped flat circular plate when compared to the FE analysis reported in this study.