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THE steady increase in speed and use of thin aerofoils compels a deeper consideration of the problem of oscillation. In recent years there has been a tendency to the building of large aeroplanes. This is closely connected with the problem of oscillation. The author in a first approximation tries to solve, from a proportionality point of view, the question of influence of kind of material and size of aeroplane on wing flexural and torsional natural frequencies. Following the idea of solving this problem from a qualitative and not from a quantitative point of view, the conception of proportionality instead of equality is introduced. The idea of “wing torsional rigidity” is created, being inversely proportional to the angle of twist at the end of wing. Applying Newton's Law, at first the flexural and torsional natural frequency of an oscillating rod is found. Afterwards the method is used in the case of an oscillating tubular member. The results are checked by Rayleigh's Method. Lastly, the influence of size of wings having similar shape is taken into consideration.

VIOLENT oscillations of particular parts of an aeroplane structure have been observed and studied since early days. The theory of wing oscillations is, however, rather more modern and was initiated, it is believed, by A. G. von Baumhauer and C. Koning, who presented a paper at the International Air Congress in 1923. Since that year the subject has been much developed both abroad and in this country. The literature has grown rapidly, and a detailed notice of the papers cannot here be attempted.

The Concept of Stability and Types of Instability THE term stable or unstable is applied to a body or system in accordance with the nature of the ultimate consequence of applying a disturbance. If the body or system is at rest and in equilibrium in a certain configuration, that configuration is said to be completely stable if the system ultimately comes to rest in the same configuration after the imposition of any disturbance. Frequently interest is confined to small disturbances; the term small is vague but must be interpreted as meaning that the motions of disturbance (or deviations) are so bounded that they can be described by linear differential equations. When this is so, the investigation of the stability becomes relatively easy and the actual magnitudes of the initial disturbances are not required in the discussion of the stability. The same concept of stability for small disturbances can obviously be applied to any steady motion and indeed to any regular motion. The criterion for stability is that the deviations from the basic motion consequent upon a small disturbance shall ultimately become vanishingly small.

Subsynchronous resonance (SSR) problem is often created in generator rotor systems with long shafts (non‐rigid shaft) and large inertias constituting a weakly damped mechanical system. When the electrical network resonance frequency (in which the transmission line is compensated by series capacitors) approaches shaft natural frequencies, the electrical system increases torsional torques amplitude on the shaft. The purpose of this paper is to propose a self‐tuning proportional, integral, derivative (PID) controller to damp the SSR oscillations in the power system with series compensated transmission lines.

To accommodate the PID controller in all power system loading conditions, the gradient descent (GD) method and a wavelet neural network (WNN) are used to update the PID gains on‐line. All parameters of the WNN are trained by the gradient descent method using adaptive learning rates (ALRs). The ALRs are derived from discrete Lyapunov stability theorem, which are applied to guarantee the convergence of the proposed control system. Also, the suggested controller is designed based on a non‐linear model.

The proposed self‐tuning PID controller is applied to a power system non‐linear model. Simulation results are used to demonstrate the effectiveness and performance of the proposed controller. It has been shown that self‐tuning PID is able to damp the SSR under any circumstances, because the WNN ensures the robustness of the controller. Simplicity and practicality of the proposed controller with its excellent performance make it ideal to be implemented in real excitation systems.

The proposed self‐tuning PID approach is interesting for the design of an intelligent control scheme based on non‐linear model to damp the torsional oscillations. In this suggested controller, the system conditions and requirements adjust on‐line the PID gains. On other words, to damp the SSR, PID gains are intelligently computed by the controlled system. The main contributions of this paper are: the overall control system is globally stable and hence, the SSR is controlled; the control error can be reduced to zero by appropriate chosen parameters and learning rates; and the self‐tuning PID can achieve favorable controlling performance.

THE aim of this paper is to calculate the natural frequencies and to consider the influence of the damping parameter on a wing's natural flexural and torsional vibration. The author took into account only the elastic hysteresis of the material because the structural damping, depending on the type of the aeroplane, cannot be taken into account in a general consideration.

A NUMBER of attempts have already been made to present a simple and easily understood account of wing flutter 1,2,3,4,5,6, but it appears that the subject is still obscure and difficult to many. Accordingly another elementary presentation of the subject is given in this paper, and the problem is approached in a new way. Emphasis is placed on explaining how flutter can happen; that is, on the physical mechanism by which an aeroplane wing can become a species of air engine and extract energy from the passing air. This explanation is greatly helped by experiments with a mechanism which has been called the “flutter engine”, consisting of a rigid aerofoil so arranged that when placed in an airstream it can oscillate and drive a flywheel.

This paper describes the development of a torsional vibration computer for the determination of the natural frequencies of torsional oscillations. Although a five mass system is used as an example of the proposed method the technique can be used with systems having any number of masses. Experimental results showed that the accuracy obtained with the computer was good.

THE subject of flutter is universally recognised as a difficult one, and I think it will be agreed that much work remains to be done before our knowledge is sufficient for the everyday needs of the designer. It is not that our scientists and mathematicians have been found wanting, however, for the literature on the subject is extensive and the present rate of production of papers bearing on flutter is higher than ever. But, from the point of view of the man who wishes to have a broad grasp of essential principles, the sheer quantity of theoretical material alone is bewildering.

MUCH reference is made in the aeronautical field to the flutter problem and the subject is receiving the attention of many persons engaged in research, testing, and design. Many aeronautical engineers are well acquainted with some aspect of the problem, and although only a few are concerned with its several phases it is safe to say that all aeronautical men regard it with some degree of interest. It is fitting, therefore, that although it has been adequately treated by many authors from other points of view, a statement be here made summarizing the flutter problem as one of the aeroplane designer. In order that the exact nature of this problem be appreciated it is first necessary that a few of the fundamentals be reviewed.

The drill string vibrations can create harmful effects on drilling performance because they generate the stick-slip phenomenon which reduces the quality of drilling and decreases the penetration rate and may affect the robustness of the designed controller. For this reason, it is necessary to carefully test the different rock-bit contact models and analyze their influences on system stability in order to mitigate the vibrations. The purpose of this paper is to investigate the effects of rock-bit interaction on high-frequency stick-slip vibration severity in rotary drilling systems.

The main objective of this study is an overview of the influence of the rock-bit interaction models on the bit dynamics. A total of three models have been considered, and the drilling parameters have been varied in order to study the reliability of the models. Moreover, a comparison between these models has allowed the determination of the most reliable function for stick-slip phenomenon.

The torsional model with three degrees of freedom has been considered in order to highlight the effectiveness of the comparative study. Based on the obtained results, it has been concluded that the rock-bit interaction model has big influences on the response of the rotary drilling system. Therefore, it is recommended to consider the results of this study in order to design and implement a robust control system to mitigate harmful vibrations; the practical implementation of this model can be advantageous in designing a smart rotary drilling system.

Many rock-bit functions have been proposed in the literature, but no study has been dedicated to compare them; this is the main contribution of this study. Moreover, a case study of harmonic torsional vibrations analysis has been carried out in well-A, which is located in an Algerian hydrocarbons field, the indices of vibrations detection are given with their preventions.