Papers by Keyword: Parametric Resonance

Abstract: The problems of increasing the efficiency of water disinfection by means of nature-friendly technologies that can restore the balance between the biosphere and the technosphere disturbed by man are considered. For this purpose, it is proposed to use the aspects of thunderstorm activity as a promising technology for cleaning and disinfecting the air-water basin of the Earth. Based on the principles of similarity and analogy methods, it is proposed to implement a method of electrophysical influence on water, by means of a device for producing electromagnetic fields in the regime of vortex-wave resonance. The force action of crossed electromagnetic fields on the bacterial cell, at a certain level of field strength, will lead to its lysis. In addition, the dispersion of various inclusions, clusters and water molecules, allows the saturation of water with ions of oxygen and hydroxyl groups, and, consequently, its disinfection.

Abstract: This paper deals with two frequency parametric excitation in presence of internal resonance. The cubic nonlinearity is inserted into the equation of motion by considering the mid-line stretching of the beam. The perturbation method of multiple scales is applied directly to the governing nonlinear fourth order integro-partial differential equation of motion. This leads to a set of first order differential equations known as the reduced equations or normalized reduced equations, which are utilized to determine the additional instability zones, appeared in the trivial state stability plot, the bifurcation and stability of fixed-points, periodic, quasi-periodic, mixed mode and chaotic responses. The transition of system behaviour from stable periodic to unstable chaotic occurs through intermittency route

Abstract: Parametric resonance can lead to roll motions and endanger the ship, cargo and crew. The QR-factorization method for calculating lyapunov characteristic exponents (LCEs) was introduced. And then, parametric resonance stability of ships in longitudinal waves was analyzed by taking the fishing-entertainment rotational molding boat as an example. Simulation results show that, this method can be used to analyze ship stability and to accurately identify safe and unsafe operating conditions for a ship in longitudinal waves.

Abstract: The averaging method has been applied to calculate the critical conditions of parametric resonance instability of the first order mode shape of clamped-clamped and pinned-pinned pipes conveying fluid. The influence of gravity factor on parametric resonance of pipe conveying fluid, with different supporting forms and different flow velocity, has been studied based on the comparison results of gravity factor being considered and neglected. It is concluded that gravity factor has a greater influence on parametric resonance region of pinned-pinned pipe than the one of clamped-clamped pipe, and, at a higher flow velocity, gravity factor is more influential to both pinned-pinned pipe and clamped- clamped one.

Abstract: The electromagnetic force produced by air-gap eccentricity magnetic field includes kinds of frequencies, and excites multiform magnetism and solid coupling vibrations of stator system. In this paper, based on the improved model of double-shell system of asynchronous machine, the magnetism and solid coupling vibration equations of double-shell system are obtained. Considering the air-gap eccentricity, an improved expression of electromagnetic force is derived. Then the method of multiple scales is applied to solve the nonlinear parametric resonance. Through the numerical calculation, the influence of electromagnetic and mechanic parameters on amplitude- frequency characteristics is analyzed.

Abstract: In this paper, the dynamic stability of stepped columns under the axial resonant force is investigated, and the dynamic stability, which is also known as parametric resonance, of stepped columns with two ends simply supported and clamped ones are studied, respectively. The dynamic stability of multi-stepped columns is obtained by using Mathieu Equation deduced by Hamiliton Principle. The formula of the dynamic stability region is given and the effect of stiffness of stepped columns on the dynamic stability is analyzed. Results show that the area of dynamic instability decreases with the increase of the ratio of each section’s stiffness, and that the dynamic stability would be better when each section is of similar size.

Abstract: Bottom hole assemblies (BHA) of oil drilling engineering were simplified as simply supported beam, and parametric resonances of BHA in mud drilling and air drilling were studied. Lateral vibration of BHA, which was induced by bit/formation interaction, was described and reduced into Mathieu equation by means of separation of variables and Galerkin method. Modified strained parameter method was adopted in stability analysis. The parametric resonance zones expressed by weight on bit (WOB) are presented here. It is found that drilling method, speed of rotation (SOR), material properties, and length of compression drillstring all can influence parametric resonance zones. So unstable responses can be avoided by adjusting these parameters.

Abstract: Cable-stayed bridges frequently experience vibrations due to a variety of mechanisms, exacerbated by their very low inherent damping. A research group of the University of Bristol has focused lately on the study of cable-stayed bridges, some advances have led to the identification of vortex-induced deck vibrations occurring at the Second Severn Crossing (SSC) and improved methods of analysis of field vibration data. Based on such experience, it aims to study the autoparametric excitation which, due to very great amplitudes, can seriously damage the structure. It has been suggested that this may have been the mechanism of excitation of some large amplitude cable vibrations on real bridges, but the details of the behaviour are not very well understood and several cases of large cable vibrations on full scale bridges have not been fully explained. In this paper we examine a previously established cable-deck model and compare it to a new, more exact model in a different coordinate basis.