Natural Oscillation Frequency Research Articles

Spectral Distribution of Fano Interferences in Classical Damped Oscillation

We present the classical analogy of Fano interferences in helpful view to understand Fano behavior of phonons excitation as the interaction of two harmonic oscillators in damped oscillation system. In order to obtain more informative explanation, we demonstrate the coupled oscillator motions in javascript using numerical integration method of 4th Order Runga Kutta. A detailed discussion of Fano spectral distribution is shown by considering some varied oscillation parameters including natural oscillation frequency, damping factor, coupling constant, as well as applied external force. It is further shown that the oscillation phase-shift differs in those varied oscillation parameters. The range of allowed values of parameters to get the appropriate results will be listed in this article.

Calculation of the natural frequencies of the transverse of cable oscillations at the area of application of insulation

Researches the transverse vibrations of the cable in the area where the insulation is applied to it. The considered mathematical model takes into account a wide range of factors affecting the oscillations: longitudinal motion, variable bending stiffness, environmental resistance, cable tension. The object belongs to a wide range of one-dimensional objects with moving boundaries. Moving boundaries complicate the description of such objects. The article introduces new variables that stop the boundaries. In this paper, using the Galerkin method, a fourth-order algebraic equation is obtained, which makes it possible to obtain two first natural frequencies of cable oscillations. The considered methods of statement and solution of the problem allow to solve the problems arising in the study of oscillations of objects with moving boundaries. Results can be used to ensure reliable operation of the technological installation for the manufacture of cables.

Pacemaker network properties determine intestinal motor pattern behaviour.

Pacemaker network properties determine intestinal motor pattern behaviour.

Flexural vibrations of the pipeline on elastic supports with moving fluid

In the work investigated the flexural vibrations of the pipeline. Parts of the pipeline on both sides of the sagging section have elastic supports. It is assumed that a constant longitudinal force acts along the neutral line. An incompressible fluid flows through the pipe at a constant average speed. The influence of internal pressure in the pipe on these oscillations is taken into account. The direct problem of determining the eigenfrequencies of flexural vibrations of the pipeline by the Kirchhoff model using Ferrari formulas is solved. The frequency spectrum is determined depending on the fluid pressure, the elasticity of the supports, the velocity of the fluid through the pipe. Particular and limiting cases are considered, for example, when the stiffness of the supports is very large and when they are very small. Graphs of the dependence of the first and second eigenfrequencies on the velocity of the transported liquid at different values of the liquid density parameter are constructed. It is shown that with the growth of the velocity parameter there is a decrease in the natural frequencies of flexural vibrations of the pipeline, and the faster the higher the density parameter of the liquid. It is determined that with an increase in the mass of the liquid per unit length of the pipeline there is a decrease in the natural frequencies of bending vibrations of the pipe. It is found that with the increase in the mass flow through the pipe, the natural frequencies of bending oscillations also decrease. It is confirmed that the frequencies of flexural vibrations of the pipeline are the same for the cases of pipe fastening “rigid fixing — rigid fixing” and “free end — free end”. The results of the study will contribute to the development of methods of acoustic diagnostics and non-destructive testing and can find technical application for monitoring and diagnostics of pipeline systems.

Review of studies on the computational diagnosis of local defects of structural elements

Rods, beams, shafts, pipelines, round plates. membranes are parts of structures in which local defects such as cracks, dents, cavities, local corrosion can be formed. Provides an overview of the research A. G. Khakimov for the diagnosis of local defects. It is received: 1. The two eigenfrequencies of the longitudinal oscillations can determine the location and the notch parameter characterizing its size. 2. The three lower eigenfrequencies of the longitudinal oscillations can determine the initial coordinate and the value of the attached distributed mass to the stepped rod, as well as the ratio of the areas. 3. The solution of the inverse problem for extended rods allows us to determine the coordinate of the incision and the parameter containing its depth and length, according to the incident and reflected waves at the observation site. 4. The reflection from the air cavity and the passage of a longitudinal damped traveling wave in a pipeline immersed in a viscous liquid are determined, and the solution of the inverse problem allows to determine the coordinate of the air cavity and its length according to the reflected wave at the observation site. 5. The initial coordinate and the length of the longitudinal through radial section of the hollow shaft are determined by the two eigenfrequencies of torsional vibrations. 6. The coordinate, length and parameter of the drill string notch are determined by the three eigenfrequencies of the torsional vibrations. 7. The reflection from the distributed mass attached to the pipeline and the passage of the flexural traveling wave are considered. The dependence of the solution on the initial coordinate of the distributed mass and its magnitude is obtained, and the inverse problem of determining the initial coordinate of the distributed mass and its magnitude from the data of the reflected wave at the observation point is solved. 8. The radius and thickness of the thin central region of the membrane are determined by the two eigenfrequencies of the transverse vibrations. 9. The radius, thickness of the thinned central area of the plate and the value of the attached distributed mass are determined by the three natural frequencies of the bending oscillations. 10. By three frequencies of bending vibrations it is possible to determine the velocity parameter, the relative mass of the product per unit length of the pipeline and the relative mass of sediments on the walls of the pipeline and, as a consequence, the mass flow of liquid through the pipeline.

METHODS OF CALCTULATING THE PARAMETERS OF VIBRATIONAL ASCILLATIONS OF THE SUPPORTS OF OFFSHORE STATIONARY PLATFORMS IN THE PRESENCE OF VARIABLE EDDY FORMATION

In the world, marine stationary platforms are actively used, which are subjected to various hydrodynamic effects. To date, the process of the emergence on the supports of the platform of non-stationary forces causing vibration of the supports along or across the sea current caused by the non-stationary pressure distribution has not been sufficiently studied. The body oscillations arising in this case begin to affect the tears of the vortices so that under certain conditions, when the amplitude of the oscillations reaches a certain flow rate at the considered flow rate, the frequency of the detachment of the vortices is compared with the frequency of the body oscillations leading to resonance. The study examines the conditions under which resonance occurs in the frequencies of natural oscillations of the supports and frequencies of variable hydrodynamic forces, and also gives a method for obtaining their numerical values and concludes that it is necessary to take into account the phenomenon of variable vortex formation when assessing the strength and life of offshore fixed platforms.

Analysis of the natural frequencies of oscillations of a planar truss with an arbitrary number of panels

Introduction. Analytical solutions for problems of structural mechanics are not only an alternative approach to solving problems of strength, reliability and dynamics of structures, but also the possibility for simple performance evaluations and optimization of structures. Frequency analysis of planar trusses, most often used in construction and engineering, is an important part of the study of structures. Objectives - development of a three-parameter induction algorithm for deriving the analytical dependence of the natural oscillation frequencies of the truss on the number of panels. Materials and methods. A flat, statically definable truss with one additional external link and double braces has been considered. The inertia properties of the truss are modeled by point masses located in the nodes of the lower straight truss belt. Each mass is assumed to have only one vertical degree of freedom. The stiffness of all truss rods is assumed to be the same. The task is to obtain analytical dependences of the oscillation frequencies of the proposed truss model on the number of panels. The derivation of the desired formulas is performed by the method of induction in three stages - according to the numbers of rows and columns of the compliance matrix, calculated using the Maxwell - Mohr formula and the number of panels. To find common members of the obtained sequences of coefficients, an apparatus was used to compile and solve the recurrent equations of the Maple computer mathematics system. The task of determining frequencies has been reduced to the eigenvalue problem of a bisymmetric matrix. Results. For the elements of the compliance matrix, general formulas have been found, according to which the frequency equations are compiled and solved. It is shown that in the frequency spectra of trusses with different numbers of panels there is always one common frequency (middle frequency) located in the middle of the spectrum. An expression is found for the maximum value of the average oscillation frequency as a function of the height of the truss. Conclusions. The proposed truss scheme, despite its external static indeterminacy and the lattice, which does not allow for the calculation of forces by such methods as the method of cutting nodes and the cross section method, allows analytical solutions for the natural frequencies of loads in the nodes. The obtained formulas have a rather simple form, and some general properties, such as frequency coincidences for different numbers of panels and the presence of an analytically calculated maximum of the average frequency function of the truss height, make this solution convenient for practical structural evaluations.

INVESTIGATIONS OF VIBRO-OSCILLATORY PROVESSES OF THE SUPPORTS OF OFFSHORE STATIONARY PLATFORMS UNDER CONDITIONS OF ALTERNATING VORTEX FORMATION CAUSED BY THE INFLUENCE OF SEA CURRENTS

Offshore platforms are exposed to hydrodynamic forces of a non-stationary nature and a wide range of frequencies. At present, hydrodynamic forces arising under conditions of alternating vortex formation have been poorly studied. These vortices are caused by the sea currents flowing around the supports of the platform, and due to their periodic occurrence and disruption, they lead to oscillations of the supports of the offshore platforms. Of particular danger are the cases of resonance of the characteristic frequency spectrum of hydrodynamic forces from the "occurrence-stalling" of vortices and natural frequencies of elements of the platform supports, which can cause fatigue damages in the platform supports. The article developed a method for determining the natural oscillation frequencies of marine supports and described the conditions under which the occurrence of alternating vortex formation is possible.

Modeling of External Dynamics of Frictional Interaction Using the Elastic System Stability Theory

This work is focused on investigation into the surface structure of tribological pairs. The parametric identification is used to determine the main characteristics of the external dynamics of frictional interaction, namely, the damping coefficient, the natural oscillation frequency, and the dynamic friction coefficient. This method provides an opportunity to study in the real-time mode the evolution of friction processes of tribological pairs, which are accompanied by a change in the dynamic parameters. In turn, taking into account the influence of bifurcation processes associated with the loss of stability of individual elements of microcontacts, it is possible to match the dynamic characteristics of friction interactions with the measure of surface roughness of tribopair specimens.

Development of a method for obtaining a section of reduced stiffness on the elastic characteristic of a vehicle tire

This article is devoted to the development of a method for obtaining a section of reduced stiffness on the elastic characteristic of a pneumatic tire of a wheeled vehicle. A way is proposed to reduce the radial stiffness of a tire by obtaining a section with reduced stiffness on the elastic characteristic of pneumatic tires, which, unlike the known ways, can significantly reduce the radial stiffness of a pneumatic tire with-out increasing its static radial deformation and rolling losses. The essence of the method for obtaining a section with reduced stiffness is to reduce the air pressure in the pneumatic tire while increasing its radial deformation using original internal devices located inside the tire. An algorithm has been developed that includes four stages; the elastic characteristic of the pneumatic tire 8.40-15 with a section with reduced rigidity by 4 times is obtained. This ensures a decrease in the natural frequency of vertical oscillations of the sprung mass on the bus by almost 2 times from 3,5 to 1,8 Hz. On the basis of the developed method, the dependences of the length of the reduced stiffness section and the force change in this section on the natural frequency of the sprung masses on the tire realized in this section are determined. For the tire 8.40-15, the dependence of the change in force in the section with a given reduced stiffness on its length was determined, which showed that with increasing length of this section there is a progressive change in the load on the tire in the same section. In addition, the dependences of the pressure change in the tire on its radial deformation in areas of reduced stiffness were obtained for various given frequencies of natural oscillations of the mass of the load on the tire. Structural diagrams of vehicle wheels are presented, in which the tire contains internal structural elements that implement the proposed method for reducing the radial stiffness of a vehicle tire and, in addition, possessing internal hydraulic or air damping of the vertical vibrations of the wheel.

Justification of the bridge span vertical stiffness on high-speed railways

When designing bridges on high-speed railways, special attention should be paid to ensuring the safety of train traffic and the comfort of passengers. Excessive structure deformations (both elastic and non-elastic) result in unfavorable irregularities in the train movement pattern on the bridge and so can lead to violation of the traffic safety requirements as well as to vibration and acceleration of the train body, which is inadmissible due to its effect on the human body or the transported goods. In this paper, based on numerical simulation, the results of the study of the motion of a high-speed train along bridge structures of the dynamic bridgetrain interaction was performed with respect to various models of high-speed trains running along the bridges. The obtained dependences help to provide a practical assessment of high-speed passenger car dynamics and passenger comfort under the most unfavorable conditions, when the train is running along a multi-span bridge. For these purposes, the dependences of the admissible value of the relative vertical deflection are presented, based on the envelope curves that show the typical dynamic passenger car parameters (natural frequency of car oscillations) and Corresponding with their oscillations on the multi-span girder bridges with various lengths

Determination of the speed and density of the fluid inside the pipeline on elastic supports

The natural frequencies of the bending vibrations of the pipeline are investigated. The pipe sags over the obstacle and is under the action of tensile force. Outside the sagging area, the pipe rests on elastic supports. The fluid transported through the pipeline is under pressure. The direct problem was solved earlier, in this article, the inverse problem of identifying the speed and density of the transported fluid by the known natural frequencies of bending vibrations is solved. The equation of bending vibrations of a pipeline is described by the Kirchhoff model. The characteristic equation is solved using Ferrari formulas. The general decision is determined. We substitute the general solution into the boundary conditions and obtain a system of equations. This system gives a frequency equation, which is solved numerically on a developed program in the Maple package. The method of successive approximations is applied, after the third iteration, the accuracy of calculating the parameters of the velocity and density of the liquid is approximately 10−3. Thus, it was found that with an increase in the oscillation frequency, the density of the liquid inside the pipe decreases. It is determined that with increasing natural frequencies of pipe bending vibrations, the fluid velocity parameter increases. It is shown that the two lower frequencies of bending vibrations of the pipeline can be used to determine the parameters of the velocity and density of the liquid. The dependence of the mass flow rate of the liquid on the first natural frequency of the pipe oscillations is given. It is shown that with increasing frequency, the mass flow rate decreases. The research results will help the development of acoustic diagnostic methods and non-destructive testing methods and will find technical application for monitoring and diagnosing the state of pipeline systems.

Movement stability of vehicles with a rigid and free wheels mounting on wheelset axles

The article considers the actual task of improving mobile units of underground rail transport, taking into account the peculiarities of work in straight and curvilinear sections of the path of especially small curvature radius of 8–50 m, with reference to the rail track width of 600; 750 and 900 mm. The purpose of the work is to improve operational performance of rail transport of mining enterprises and improve safety of railway movements. Methods for the study of interaction processes of mobile vehicles and the rail track are presented. The study results of loading, oscillations and movement stability of vehicles with the free and rigid mounting of wheels on the axles of wheelsets are given. The resonance phenomenon due to the proximity of frequencies of forced and natural oscillations of mobile units of underground rail transport has been established. The obtained results can be applied to the development of normative documents regulating tolerances for the maintenance of rail track in the plan, profile and for the broadening of the track, taking into account the vertical, horizontal and longitudinal irregularities of the rail threads. The study results can be used to improve the design of mobile vehicles and rail track.

Electromagnetic eigenmodes of spherical thin films

Eigenmodes of the spherical and ellipsoidal dielectric thin films have been analyzed. The results of calculations of frequencies of natural electromagnetic oscillations of spherical thin films depending on their sizes and dielectric permeability of external environment are presented.

On the Natural Frequency of Oscillations of Induction Motors

For transient stability analysis, the rotor dynamics of the induction motor have to be included. These dynamics affect the system stability when severe disturbances hit it and cause frequency deviations. For large systems, frequency deviations are small. However, it may cause loss of synchronism and break the system into smaller areas. Motor loads are sensitive to system frequency deviations. Any change in the grid frequency, changes extremely the slip. This follows by changes of the motor torque and the motor speed. The demanded active and reactive powers change as well. Natural frequencies of induction motors is considered a unique property has a great effect on its behavior during different operation conditions. This work presents the performance of the induction motors through different power systems. Based on time domain simulation models study the natural frequency of induction motors, their response in normal and abnormal operation is analyzed to illustrate the dynamics associated.

Theoretical and experimental study of vibration-amplitude liquid densimeter on the basis of a high-quality tubular resonator

This paper is devoted to the current model of vibration-amplitude liquid densimeter developed by the authors. Firstly, the necessity to develop vibration-amplitude liquids densimeters with straigt-flow sensing elements (resonators) belonging to the “low cost low accuracy” category is justified. The resonator structure, developed as the result of the search using the heuristic method, is described. The proposed resonator is a tube rigidly fixed at the ends with additional weights attached symmetrically at the vertical axis at the points of the antinodes of the second fundamental oscillation mode in order to improve the resonator qualityfactor by suppressing parasitic harmonics. The structure provides the possibility to restore the resonator natural oscillation frequency (decreased with time) to the primary one. It may be achieved by sequence screwing rods with different lengths into additional masses. The choice of the operating frequency of oscillations equal to 100 Hz is proved. It ensures invariance to the presence of solid inclusions in measured liquid and simplifies the electromagnetic excitation system. There are also theoretical relations obtained as a result of solving a differential equation of natural oscillations of a rigidly fixed tube with additional point masses, which are symmetrically located relatively vertical axis. They allow determining the own resonator oscillations frequencies for given parameters. The description of the operating model of the vibration-amplitude liquids densimeter, obtained experimentally and its calibration characteristic, is given.

Коррекция частоты вращения шпинделя при фрезеровании по данным численного моделирования системы: приспособление-инструмент-заготовка

Abstraсt: Machining operations are unavoidably accompanied with oscillations, which, in case of their coincidence with the natural oscillations of one of the elements of the system, can cause a resonance. The latter results in the premature failure of expensive equipment, tools and tool attachment, reduces the quality characteristics of the finished product as well as leads to rejects. Therefore, the question is raised on controlling the natural oscillation frequencies of the elements of the machine-tool system, a tool and a workpiece. Based on the finite element model of the machine-tool-device-tool-workpiece system oscillations the recommendations for choosing non-resonant rotational speeds of the milling machine spindle have been developed. The studies employed experimental, analytical, and finite element modeling methods with the use of Femap automated engineering calculation system. The experiments were carried out using Polytec measuring equipment, National Instruments LabVIEW software package, Sound and Vibration module. We have obtained the finite-element models of the device-tool-workpiece system oscillations, on the basis of which recommendations are given on setting the permissible spindle rotational speeds. The approach can find application in adjusting cutting modes when milling box-type workpieces or panel-type parts, whose workpiece geometric shape and weight differ significantly from the finished part ones.

ИНЖЕНЕРНЫЙ МЕТОД РАСЧЕТА ИЗОЛЯЦИИ УДАРНОГО ШУМА МНОГОСЛОЙНЫМИ МЕЖДУЭТАЖНЫМИ ПЕРЕКРЫТИЯМИ

The proposed engineering method of calculation of sound insulation of multilayer intercommunication pen-indoor. The calculation takes into account the effect on the sound insulation of cylindrical stiffness and surface density of inertial elements, as well as the stiffness of sound-proof gasket materials, which allows for rational design of the overlap. The calculation is reduced to the calculation of the frequency response of the impact noise reduction due to the multilayer structure of the floor and to the comparison of the calculated value of the index of the reduced level of impact noise with the standard. The list of necessary initial data and the validity of the calculation are given. Formulas are given to determine the boundaries of the natural oscillation frequencies within which the value of the reduced level of shock noise is calculated. The sequence of constructing the dependence of the natural oscillation frequencies of the system and reducing the level of shock noise by multi-layer inter-floor overlap is described. It is shown that above the second resonance frequency of the eigenfrequencies of the multilayer floor, the improvement of the shock noise isolation (relative to the single-layer overlap) is 24 dB per octave in the low frequency region and 12 dB per octave in the medium and high frequency region. Comparison of the calculated and measured frequency characteristics of the impact noise reduction showed a good agreement of the results obtained by the engineering calculation method with experimental studies.

Drive systems of the drilling rigs for open pits in Ukraine: state and ways for improvement

A comparative analysis is presented of the characteristics of drilling rigs used in open-pit mining in Ukraine. The experimental studies have been conducted of the drive systems and drilling rigs influence on the dynamics of the drilling process under the mining and geological conditions of the Central Mining and Processing Plant (Kryvyi Rih city, Ukraine). The frequency characteristics have been obtained and the dynamic properties of the automated drive systems, as well as frequency characteristics of the rotation mechanism transmissions have been analyzed. The behavior of natural oscillation frequencies in closed control loops of rotational drives was studied, and it has been determined that they exceed the cutoff frequency and fall into the pass band from the attenuation band in frequency-controlled induction motors of most advanced drilling rigs with the maximum number of rods connected in the drill string. It has been established that low oscillation frequencies due to the side frequencies, generated by the drill rod oscillations, fall into the fastest internal current loop. The tasks have been formulated for further research. The purpose of research is to solve the actual scientific and applied problem of dynamic compatibility of frequency characteristics in the modern high speed drive systems with the dynamic characteristics of drilling rigs, which are multi-mass mechanisms with distributed and concentrated parameters with a change in added masses.

Static and modal analysis of the construction of the precision large-sized antenna reflector from polymer composite materials

The article presents a design of a precision large-size antenna reflector that made of polymer composite materials (PCM) based on carbon fibers. Such reflectors are used for operation in high frequency ranges, since they have a low coefficient of linear thermal expansion and a high modulus of elasticity. Therefore, the main task of this work is to design the geometric accuracy of the reflector working surface from composite materials with a diameter of more than 10 meters and a frequency range of 42.5-45.5 GHz.The developed model of the reflector includes a power frame, segments of the reflecting surface and a hub. The power frame of the reflector consists of flat trusses supplemented with rods, so that during assembly a spatial construction with axial symmetry is formed. Segments are three-layer casings of polymer composite materials with filler.The proposed model of the reflector was analyzed using the finite element method with boundary conditions: a wind load of 20 m/s in the opening of the reflector; impact of gravity on the reflector, oriented to the zenith. The wind load was modeled as a uniformly distributed pressure applied to the segments. The obtained mean square deviation (SDE) of the geometry and natural oscillation frequency of a reflector made from polymer composite materials based on carbon fibers is sufficient for operation of the satellite earth station in high radio-frequency ranges Ka, Q and V.