Vladislav Sorokin

Effects of corrugation shape on frequency band-gaps for longitudinal wave motion in a periodic elastic layer

The paper concerns determining frequency band-gaps for longitudinal wave motion in a periodic waveguide. The waveguide may be considered either as an elastic layer with variable thickness or as a rod with variable cross section. As a result, widths and locations of all frequency band-gaps are determined by means of the method of varying amplitudes. For the general symmetric corrugation shape, the width of each odd band-gap is controlled only by one harmonic in the corrugation series with its number being equal to the number of the band-gap. Widths of even band-gaps, however, are influenced by all the harmonics involved in the corrugation series, so that the lower frequency band-gaps can emerge. These are band-gaps located below the frequency corresponding to the lowest harmonic in the corrugation series. For the general non-symmetric corrugation shape, the mth band-gap is controlled only by one, the mth, harmonic in the corrugation series. The revealed insights into the mechanism of band-gap formation can be used to predict locations and widths of all frequency band-gaps featured by any corrugation shape. These insights are general and can be valid also for other types of wave motion in periodic structures, e.g., transverse or torsional vibration.

Effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli–Euler beam

The paper deals with analytically predicting the effects of weak nonlinearity on the dispersion relation and frequency band-gaps of a periodic Bernoulli–Euler beam performing bending oscillations. Two cases are considered: (i) large transverse deflections, where nonlinear (true) curvature, nonlinear material and nonlinear inertia owing to longitudinal motions of the beam are taken into account, and (ii) mid-plane stretching nonlinearity. A novel approach is employed, the method of varying amplitudes. As a result, the isolated as well as combined effects of the considered sources of nonlinearities are revealed. It is shown that nonlinear inertia has the most substantial impact on the dispersion relation of a non-uniform beam by removing all frequency band-gaps. Explanations of the revealed effects are suggested, and validated by experiments and numerical simulation.

Surface and volumetric effects in a fluid subjected to high-frequency vibration

In this article, the results of experimental study of surface and volumetric effects arising in a fluid under the action of high-frequency vibration are considered. Some elements in the theory of the surface effects are analyzed with regard to their origin and interrelations with other similar phenomena. The height of splashing fountains on the fluid surface is assessed based on the analogy with particle bounce over a vibrating plane. It is found that the influence of vibration on the average velocity of fluid flow is more pronounced at such excitation parameters that enhance the surface effects under study, namely, the formation of cellular structures (Faraday ripple), the creation of turbulence in the fluid surface layer and splashing. The analytical study of motion of a bubble in an oscillating volume of a fluid, saturated with gas at a certain depth, is provided, with compressibility of both the bubble and surrounding gas-saturated fluid layer being taken into account. The condition of bubble sinking in such a compressible medium and the condition of vibrational instability of the separate state of the gas–fluid system are determined.

FREQUENCY DETUNING EFFECTS FOR PARAMETRICALLY AND DIRECTLY EXCITED ELASTIC STRUCTURES

This study investigates the frequency detuning effects of parametric and direct excitation for near-resonant nonlinear structural vibrations. Specifically, the detuning effects of a two-to-one frequency ratio between the parametric and direct excitation, and of a drift in natural frequency, are studied. These effects are investigated theoretically using a DuffingMathieu equation as the model system, and experimentally using a cantilever beam as the model object. The approximate analytical responses are derived using the method of varying amplitudes, and compared with results of direct numerical integration and experiments showing good agreement. For frequency detuned superthreshold parametric excitation some of the theoretical frequency-amplitude solution branches appear to merge. For some ranges of parametric excitation frequency a drop in experimental steady-state vibration amplitude was found, indicating performance degradation whereas for other frequency ranges, frequency detuning may yield an increased steady-state vibration amplitude. This makes frequency detuning a feature which can purposefully be avoided or utilized, dependent on the application.