Ship control in storm conditions

Приведены выражения для определения периодов собственных поперечных и продольных колебаний судна, как точные, так и приближённые, но в тоже время достаточные для их практического использования на судне. Представлены формулы для расчёта поперечной метацентрической высоты после принятия груза судном перед выходом в море. Выведены формулы для определения критических зон резонансной качки по крену и дифференту, как по скорости судна, так и по курсовому углу по отношению к направлению распространения штормового волнения моря. Представлены формулы для определения кажущегося периода встречи судна с волной, которые являются основой для расчёта резонансных зон. Выведенные соотношения для определения зоны резонанса по скорости судна при заданном курсовом угле и по курсовому углу при заданной скорости судна представлены при условии известного периода штормового волнения моря и курсового угла судна по отношению к направлению распространения волнения моря. Приведены формулы для определения амплитуды качки в условиях резонанса, если отношение периода собственных колебаний судна к кажущемуся периоду волны находится в пределах 0,7 – 1,3. Представлены выражения для определения амплитуд качки по крену и дифференту, вызывающие морскую болезнь у персонала, а также критические значения боковых перегрузок, влияющих на правильность его действия. Expressions for determining the periods of the natural transverse and longitudinal vibrations of the vessel, both exact and approximate, are given, but at the same time sufficient for their practical use on the vessel. The formulas for calculating the transverse metacentric height after the cargo has been accepted by the vessel before going to sea are presented. Formulas are derived for determining the critical zones of resonant pitching in terms of roll and trim, both in terms of the ship's speed and in the heading angle in relation to the direction of propagation of storm waves of the sea. The formulas for determining the apparent period of the ship's meeting with the wave are presented, which are the basis for calculating the resonance zones. The derived relations for determining the resonance zone by the speed of the vessel at a given heading angle and by the heading angle at a given speed of the vessel are presented under the condition of a known period of stormy sea waves and the heading angle of the vessel in relation to the direction of propagation of sea waves. Formulas are given for determining the amplitude of pitching under resonance conditions if the ratio of the period of natural oscillations of the vessel to the apparent period of the wave is within 0.7 - 1.3. Expressions for determining the amplitudes of roll and pitch that cause motion sickness in personnel, as well as the critical values of lateral g-forces that affect the correctness of its action, are presented.

RELATIONSHIP OF MAXIMUM DEFLECTIONS AND NATURAL FREQUENCIES VIBRATIONS OF ISOTROPIC CIRCULAR PLATES WITH INHOMOGENEOUS RESISTANCE CONDITIONS ON THE OUTER AND INNER CONTOUR

The relationship between the maximum deflections from a static uniformly distributed load W0 and the fundamental frequency of natural transverse vibrations of a round isotropic plate of linearly variable thickness with thickening to the edge under homogeneous conditions of support along the outer contour, depending on the ratio of the thickness of the plate in the center to the thickness along the edge, is considered. According to the results of the study, graphs of the dependence of the maximum deflection and the frequency of natural vibrations of the plate on the ratio t1 / t2 are constructed. It is shown that for round plates of linearly variable thickness at t1/t2<1.1 coefficient K with an accuracy of 5.9% coincides with the analytical coefficient for round plates of constant thickness. Numerical studies shows that when the ratio of the thicknesses on the contour and in the center is equal to two, the difference in the coefficient K, which depends on the relationship between the static and dynamic characteristics of the platinum, is about 25% for hinged support along the contour and up to 37% for rigid support. This indicates a more significant effect of uneven mass distribution for such boundary conditions.

Time period of transverse vibration of skew plate with parabolic temperature variation

Time period of natural transverse vibration of a nonhomogeneous skew (parallelogram) plate with variable thickness and temperature field has been investigated on clamped CCCC and combination of clamped and simply supported CSCS edge conditions. The thickness variation on the plate is assumed to be linear in two dimensions, and the temperature variation on the plate is considered to be parabolic in two dimensions. For nonhomogeneity, authors considered circular variation in density. The Rayleigh–Ritz technique is applied to solve the differential equation of motion. A comparative analysis of frequency modes of the present study with the available published result is also given to support the present findings. The convergence study of obtained results is also presented with the help of figures.

Specifics of determining the tension forces of the cable-stayed bridge elements

Objective: to improve the method of determining the force in the cable stays by frequencies of natural transverse oscillations. Methods: synthesis and analysis of theoretical and experimental data, experimental methods for studying the structures. Results: in the paper, the problems of determining the tension forces of the cable stays by the frequencies of their natural oscillations are considered taking into account various factors (the design of anchor fastenings, the angle of inclination and sagging of the cable stay, the change of temperature). The estimation of possible errors in calculations is given. The degree of coincidence of the actual and design stress-strain state of the cable stays depends on the correctness of accounting the influence of the factors considered. The effect of the temperature change and the anchor fastening structure on the frequency of the natural oscillations of the cable stays has been experimentally tested. The recommendations on the determination of the forces in the cable stays by dynamic parameters are given. A method for controlling the tension forces of the cable stays and specialized software “Vant” (“Cable”) for automation of the measurement process are developed. The method has been tested on several bridge structures that have cable-stayed elements. Practical significance: the ability to use the developed method for controlling the tension forces of cable-stayed elements during the operation of artificial structures.

Natural transverse vibrations of helical springs in sections covered with elastic coatings

It has been demonstrated in previous studies that local elastomer coatings covering the end coils of helical springs can efficiently reduce the amplitudes of circum-resonant vibrations in such springs. The analysis of the influence that elastic coatings have on the frequencies and modes of natural transverse vibrations of springs is presented in this paper. The concept of the equivalent beam of the Timoshenko type is utilized in calculations of the frequencies and modes of transverse vibrations. The model developed allows users to determine the frequencies and modes of symmetric as well as antisymmetric vibrations of axially loaded springs with elastic coatings of arbitrary length. A comparison of the results obtained using FEM analysis, in which the model represented the actual spring geometry, with the results obtained by means of the presented model indicates its high accuracy.

Determining the velocity of a moving three-layered plate and the thickness of its filler using natural frequencies of flexural vibrations

Research has been performed on natural transverse vibrations of a portion of a constant length in a straight threelayered plate with a filler moving along the neutral line of a non-deformed state. The movement takes place between two rigidly fixed coaxial guides (clamps), the distance between them equalling the length of the vibrating portion. The longitudinal force is assumed to constantly act along the neutral line. It has been found that an increase in the natural frequencies of flexural vibrations of the plate occurs with an increase in the thickness of the filler. Using two frequencies of flexural vibrations, we can determine the velocity of the moving three-layered plate and the thickness of its filler. The results of the research work can find technological use in the problems on dynamics and strength of machines and mechanisms in manufacturing three-layered plate with fillers and can be used to determine the velocity of a plate and the thickness of its filler using two frequencies of flexural vibrations.