SOME PROBLEMS OF OPTIMIZATION AND CONTROL OF THE NATURAL FREQUENCIES OF AN ELASTICALLY SUPPORTED RIGID BODY

The article analytically investigates the behavior of the frequencies and modes of natural vibrations of a rigid body, based on point elastic supports, when the position of the supports changes. It is assumed that the body is in plane motion and has two degrees of freedom. A linear description of body vibrations is accepted. The problems of determining such optimal positions of elastic supports at which the fundamental frequency of the structure reaches its maximum value are considered. Two groups of problems were studied. The first group concerns a body supported by only two supports. It was found that in the absence of restrictions on the position of the supports to maximize the fundamental natural frequency, these supports should be positioned so that the basic natural vibrations of the body are translational. Simple analytical conditions are formulated that must be satisfied by the corresponding positions of the supports. In real practical situations, these positions may be unreachable due to the presence of various kinds of restrictions due to design requirements. In this paper, optimization problems are considered taking into account a number of restrictions on the position of supports, typical for practice, expressed analytically by equations and inequalities. For each of the considered types of constraints, results are obtained that determine the optimal positions of the supports and the corresponding maximum values of the main natural frequencies. The approach applied allows us to consider other types of restrictions, which are not considered in the article. In the second group of problems for a body resting on an arbitrary number of supports, the optimal position of an additional elastic support introduced in order to maximize the fundamental frequency in fixed positions and the stiffness coefficients of the remaining supports was sought. It was found that this position depends on the value of the stiffness coefficient of the introduced support. Results are obtained that qualitatively and quantitatively characterize this position and the corresponding frequencies and modes of natural oscillations, including taking into account practically established limitations. The research method uses a qualitative approach, systematically based on the well-known Rayleigh theorem on the effect of imposing constraints on the free vibrations of an elastic structure.

Features of assessing the condition and behavior of low-water bridges

The article describes features of operation and monitoring of low-water bridges, which are found on highways of regional, intermunicipal and local importance. Vibrations of the bridge span are considered in detail, taking into account its interaction with other structural elements and the environment. As a characteristic, the change of which takes into account the change in the state of the bridge structure, it is proposed to use the frequency of natural vibrations. To simulate the dynamic effects of transport and the dynamic behavior of individual elements and the entire structure as a whole, it is proposed to use viscoelastic elements of the Kelvin–Voigt type. When solving the problem, an approach has been implemented that makes it possible to take into account the anisotropic properties of the superstructure associated with various reinforcement along and across the roadway of the bridge, and to present the design scheme of the span not in the form of a beam supported at the edges with the help of hinges or viscoelastic dampers, but in the form of a plate, which can have different fxing conditions along the entire contour. The use of the proposed model and approach will make it possible to obtain the necessary data on the state of low-water bridges, for which there is often no possibility of visual inspection or instrumental inspection from the lower side of the bearing part of the superstructure. By the values of the frequency of natural vibrations, it is possible to estimate the water level above the low-water period and predict food situations, during which the roadway of the low-water bridge may be fooded.

AIMED CONTROL OF THE FREQUENCY SPECTRUM OF EIGENVIBRATIONS OF ELASTIC PLATES WITH A FINITE NUMBER OF DEGREES OF MASS FREEDOM BY INTRODUCING ADDITIONAL GENERALIZED KINEMATIC DEVICES

As is known, targeted regulation of the frequency spectrum of natural vibrations of elastic systems with a finite number of degrees of mass freedom can be performed by introducing additional generalized constraints and generalized kinematic devices. Each targeted generalized constraint increases, and each generalized kinematic device reduces the value of only one selected natural frequency to a predetermined value, without changing the remaining natural frequencies and all forms of natural vibrations (natural modes). To date, for some elastic systems with a finite number of degrees of freedom of masses, in which the directions of mass movement are parallel and lie in the same plane, special methods have been already developed for creating additional constraints and generalized kinematic devices that change the frequency spectrum of natural vibrations in a targeted manner. In particular, a theory and an algorithm for the creation of targeted generalized constraints and generalized kinematic devices have been developed for rods. It was previously proved that the method of forming a matrix of additional stiffness coefficients, specifying targeted generalized constraint, in the problem of natural vibrations of rods can also be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which the directions of mass movement are parallel, but do not lie in the same plane. In particular, such systems include plates. The distinctive paper shows that the method of forming a matrix for taking into account the action of additional inertial forces, specifying targeted kinematic devices in the problem of natural vibrations of rods can also be applied to solving a similar problem for elastic systems with a finite number of degrees of freedom, in which the directions of mass movement are parallel, but do not lie in the same plane. However, the algorithms for the creation of targeted generalized kinematic devices developed for rods based on the properties of rope polygons cannot be used without significant changes in a similar problem for plates. The method of creation of computational schemes of kinematic devices that precisely change the frequency spectrum of natural vibrations of elastic plates with a finite number of degrees of mass freedom is a separate problem and will be considered in a subsequent paper.

Method for Tuning the Parameters of Active Force Reducing Building Vibrations—Numerical Tests

The paper formulates a method of active reduction of structure vibrations in the selected resonance zones of the tested object. The method ensures reduction of vibrations of the selected resonance zones by determining the parameters of the active force that meets the desired dynamic properties. The paper presents a method for determining the parameters of the active force by reducing the vibrations of the structure in its resonance zones to a given vibration amplitude. For this purpose, an analytical form was formulated, which will clearly define the dynamic properties of the tested object and the force reducing the vibrations in the form of a mathematical model. The formulated mathematical model is a modified object input function, which in its form takes into account the properties of the active force reducing the vibrations. In such a case, it is possible to use the methods of mechanical synthesis to decompose the modified characteristic function into the parameters of the system and the parameters of the force being sought. In the formulated method, the desired dynamic properties of the system and the vibration reducing force were defined in such a way that the determined parameters of the active force (velocity-dependent function) had an impact on all forms of natural vibrations of the tested system. Based on the formalized method, the force reducing the vibrations of the four-story frame to the desired displacement amplitude was determined. Two cases of determining the active force reducing the vibrations to the desired vibration amplitude of the system by modifying the dynamic characteristics describing the object together with the active force were considered. For both cases, the system’s responses to the oscillation generated by harmonic force of frequencies equal to the first two forms of natural vibrations of the tested system were determined. In order to verify the determined force reducing the vibrations of the object and to create a visualization of the analyzed phenomenon, the building structure dynamics were analyzed with the use of PLM Siemens NX 12 software. The determined force parameters were implemented into the numerical model, in which the tested system was modelled, and the response time waveforms were generated with regard to the considered story. The generated waveforms were compared with the waveforms obtained in the formalized mathematical model for determining the active force reducing the vibrations. The vibrations of the tested numerical model were induced by the kinematic excitation with the maximum amplitude equal to 100 mm, which corresponds to the vibration amplitude during the earthquake with a force equal to level 5 on the Richter scale.

Determination of the main elements and characteristics of a tuna vessel in the early stages of its design

В статье приведены результаты статистического анализа средних тунцеловных судов, позволившие определить диапазон изменения их основных элементов, выбрать судно «прототип» и провести ряд вариационных исследований по определению влияния основных элементов тунцеловного судна (изменении расчетной длины и ширины) на его качества. Ошибочно выбранные главные размерения на ранних стадиях проектирования приводят к финансовым и временным затратам в процессе проектирования и постройки судна. В связи с этим, важно на ранних стадиях проектирования для выбора оптимальных размерений, иметь показатели качеств, для каждого из выбранных габаритов судна. Для рассматриваемых вариантов судна построены теоретические чертежи, кривые элементов теоретического чертежа и проведено их цифрование. По результатам исследований мореходных качеств (проверка остойчивостии и оценка буксировочного сопротивления), а также анализа частот собственных колебаний корпуса по первому тону, при изменении расчетных длины и ширины судна, сделаны соответствующие выводы. The article presents the results of a statistical analysis of medium-sized tuna vessels, which made it possible to determine the range of changes in their main elements, choose a prototype vessel and conduct a series of variational studies to determine the influence of the main elements of a tuna vessel (change in the calculated length and width) on its quality. Incorrectly chosen main dimensions in the early stages of design lead to financial and time costs during the design and construction of the vessel. In this regard, it is important at the early stages of design to select the optimal dimensions, to have quality indicators for each of the selected dimensions of the vessel. For the variants of the vessel under consideration, theoretical drawings, curves of the elements of a theoretical drawing were constructed and digitized. Based on the results of studies of seaworthiness (stability check and assessment of towing resistance), as well as analysis of the frequencies of natural vibrations of the hull by the first tone, when changing the calculated length and width of the vessel, the corresponding conclusions were drawn.

A method of forming a spacecraft adapter layout to meet the requirements of dynamic compatibility by topological and parametric optimization methods

At present, the developers of launch vehicles impose a requirement for dynamic compatibility of the spacecraft with the launch vehicle, which consists in limiting the lower boundary of the first transverse and first longitudinal fundamental (primary) frequencies of the natural vibrations of the spacecraft fitted with an adapter of relatively rigid base. One of the tasks that must be solved in order to meet this requirement is the development of the spacecraft adapter layout. The traditional process of designing the adapter consists in developing its design on the basis of analogues and carrying out verification analysis with subsequent refinement of the design to meet the strength and stiffness requirements. However, this approach takes a lot of time and is not adaptable to constant changes in the input data at the initial design stage. The article presents a technique allowing the adapter layout to be quickly designed. The layout is determined to a greater extent by calculations using the topological and parametric optimization methods. The application of the developed technique is shown on the example of the development of an adapter for a promising spacecraft. It should be applied in the early stages of design. The results obtained by the method should be used as input data and recommendations for the design of the adapter.

The Influence of the Grid Density of Measurement Points on Damage Detection in an Isotropic Plate by the Use of Elastic Waves and Laser Scanning Doppler Vibrometry

Damage detection in structural components, especially in mechanical engineering, is an important element of engineering practice. There are many methods of damage detection, in which changes in various parameters caused by the presence of damage are analysed. Recently, methods based on the analysis of changes in dynamic parameters of structures, that is, frequencies or mode shapes of natural vibrations, as well as changes in propagating elastic waves, have been developed at the highest rate. Diagnostic methods based on the elastic wave propagation phenomenon are becoming more and more popular, therefore it is worth focusing on the improvement of the efficiency of these methods. Hence, a question arises about whether it is possible to shorten the required measurement time without affecting the sensitivity of the diagnostic method used. This paper discusses the results of research carried out by the authors in this regard both numerically and experimentally. The numerical analysis has been carried out by the use of the Time-domain Spectral Finite Element Method (TD-SFEM), whereas the experimental part has been based on the measurement performed by 1-D Laser Doppler Scanning Vibrometery (LDSV).