Natural Oscillation Frequency Research Articles

Monoreactive multimass oscillator of non-fixed frequency

Introduction. The work relates to the field of mechanical engineering, namely to oscillating mechanical systems. The relevance of the study is determined by the fact that vibrations of inertial masses occur everywhere.Target. Development of a mathematical model of a monoreactive multimass oscillator of non-fixed frequency.Research methods. It is proved that the points that are the coordinates of the end of an arbitrary vector in the coordinate system are the vertices of a regular polygon. The shape and dimensions of the polygon are not related to the coordinates of the vector, i.e. unchangeable. The center of a regular polygon in all cases coincides with the middle of the vector. In the considered (idealized) case, the polygon, at the vertices of which oscillating loads of masses m are located, lies in the Z plane. In technical applications, the loads should not interfere with each others movements, therefore, each load should have its own plane, and all planes should be parallel (like multi-piston mechanism).Results. The condition for the occurrence of free harmonic oscillations is the equality to zero of the total energy of the system, which in the case under consideration is exclusively kinetic, which determines the monoreactive nature of the oscillator. In the considered multidimensional flat monoreactive oscillator, free harmonic linear oscillations of weights can occur.Conclusion. Only kinetic energy is involved in energy exchange. There is no need for elastic elements. The oscillator does not have a fixed natural frequency of oscillation. The frequency depends on the initial speeds and positions of the weights. A regular polygon undergoes a double rotation - around point 0 and around point r. At the same time, the loads carry out linear harmonic oscillations with amplitude . The use of a crank-slider or crank-rod mechanism will allow for parallel movement of loads.

Mathematical Model of Vibration-Centrifugal Processing of Parts Using Loose Abrasive

The article presents some new theoretical and experimental solution of a scientific and applied problem of technological support for vibratory centrifugal processing of complex-profiled parts in a bulk abrasive environment. This solution aims to increase productivity while ensuring the desired quality of the processed surfaces. The authors have developed a mathematical model that describes the action of abrasive particles on the surface of the parts, taking into account the parameters of the granular abrasive medium based on Voigt’s law. This allows the description of dynamic processes in the processing environment for a wide range of material types. The natural frequencies of oscillations of the processed medium layer have been determined, which depend on the amplitude of its vibrations for different densities of soft and hard materials of the processed medium and the medium with linear-elastic properties. The methodology includes the use of test equipment to conduct experimental research on the process, which involves determining changes in specific metal removal rates and surface roughness using the frequency converter Altivar 71 with the PowerSuite v.2.5.0 software.

Relationship between natural muscle oscillation frequency and lower limb muscle performance during instrumented sit-to-stand and stand-to-sit movements on a novel device in sedentary subjects

BackgroundDespite the significance of muscle oscillation frequency, previous research has not established a correlation with muscle performance due to the challenges of applying resistance without altering natural motion during functional tests. Research questionWhat is the correlation between muscle oscillation frequency and lower limb muscle strength, power, and work during an instrumented sit-to-stand and stand-to- sit (iSTS-TS) task among sedentary subjects? MethodsIn a cross-sectional study, the oscillation frequency of the gastrocnemius medialis (GM), biceps femoralis (BF), and vastus medialis (VM) muscles in both the dominant (D) and non-dominant (ND) legs was assessed with a handheld myotonometer in 34 sedentary individuals before performing the iSTS-TS task. ResultsIn the isokinetic mode, no significant correlations were found. In the isotonic mode, the BF muscle oscillation frequency in the D and ND legs exhibited significant positive correlations with peak force, peak power, and work during sitting down, as well as peak power and work during standing up. Positive correlations were observed in both legs between the GM oscillation frequency and sitting down peak force and work. Additionally, significant positive correlation was found with standing up work in the D leg. Muscle oscillation frequency of the VM exhibited a positive correlation with sitting down peak force in the ND leg. SignificanceDue to a greater number of correlations found, it is advisable to use the isotonic mode when assessing muscle oscillation frequency in relation to muscle performance during functional iSTS-TS tasks in sedentary subjects.

Experimental studies of the impact of fluid sloshing in the tank on the dynamic characteristics of the “wing model – fuel tank” system

Flexible response of the airframe structural elements under operational loads are one of the main sources of fatigue damage accumulation. It is known that fuel sloshing in tanks can change the dynamic (frequencies and shapes of natural oscillations) and dissipative properties (oscillation damping decrements) of an elastic system, including partially or completely fuelfilled tanks. It is specified that fuel sloshing in tanks due to the additional oscillation energy dissipation of the elastic system can have a significant impact on both the fatigue and aeroelastic characteristics of aircraft structural elements. Theoretical and experimental studies, applicably to the majority of currently operating transport aircraft, have shown that when modeling dynamic phenomena and solving aeroelasticity problems, fuel can be considered conditionally solidified, which actually does not affect the resultant effect. The advent of modern heavy transport aircraft with a high aspect ratio wing and four engines on pylons under the wing has led to a considerable change in the dynamic picture of the aircraft interaction with the environment. The main feature is that, under this arrangement, the first horizontal bending mode of the wing is embedded in the main flexible modes that determine the dynamic response to external effects. In this case, the model of solidified fuel can have a significant impact on the accuracy of predicting dynamic loads and, as a consequence, on the quantitative characteristics of durability and aeroelasticity. The article presents the results of experimental studies of the impact of fluid sloshing in the tank on the dynamic characteristics (frequencies of natural oscillations and amplitudes of forced oscillations) of the “wing model – fuel tank” system. The design of the experimental installation and the methodology of conducting experiments are described. During the experiment, the tank was partially filled with liquid or full, and horizontal bending modes of the wing model, for which considering liquid sloshing in the tank is the most relevant, were studied. The tank refueling levels are determined at which the maximum effect of the system oscillation damping is achieved due to energy dissipation under liquid sloshing. The effect of various factors (presence of a top cover, internal structural frame, perforation in the structural frame) on the amplitudes and frequencies of forced oscillations is analyzed.

Experimental studies of the influence of elastic-dissipative parameters of engine mounting units on the dynamic characteristics of the “wing model – elastic pylon – engine” system

A feature of modern heavy transport aircraft is their layout with engines on elastic pylons under the wing, with the fuel tanks located in the wing consoles. In this case, the main elastic tones of the aircraft’s own oscillations, which determine its dynamic response to external disturbing influences, include the so-called motor tones (vertical and horizontal (lateral) oscillations of engines on elastic pylons). A new type of flutter has appeared – pylon, which for some aircraft determines the critical flutter speed of the aircraft as a whole. The main reason for this phenomenon is the low oscillation damping of the engine on the pylon under the wing. Therefore, research aimed at modernizing the engine mounting points on the pylon in order to reduce the level of elastic oscillations during aircraft operation seems relevant. One of the possible ways to solve this problem is to use the concept of a freed engine, when the engine attachment points to the pylon are modernized, providing more effective damping of engine oscillations. In order to confirm the possibility of practical implementation of these solutions, corresponding experimental studies were carried out on an experimental setup developed by the authors. A design of engine mounting units has been developed that allows specified displacements of the engine relative to the pylon during forced elastic oscillations of the system, which includes a hinged suspension, installation of additional elastic elements and hydraulic dampers.The article presents the results of studies of the influence of elastic-dissipative parameters (partial frequency of natural oscillations and partial decrement of oscillations) of an engine mount on an elastic pylon on the dynamic characteristics of the dynamic system “wing model – elastic pylon – engine”. It is shown that by introducing specially designed engine suspension units on pylons, it is possible to significantly change the dynamic characteristics (frequencies and amplitudes of natural oscillations) of the elastic system as a whole. Thus, the amplitudes of oscillations of the engine’s center of mass in the region of motor tones decrease by 3...7 times during forced harmonic oscillations.

Собственные колебания упругой прямоугольной CFCF-пластинки при одноосном растяжении-сжатии ее плоскости

The influence of a uniaxial distributed load in the plane of a thin rectangular plate on the value of the first natural frequency of its oscillations has been studied. We considered a plate, two opposite faces of which are clamped, and the other two are free (CFCF-plate, C-clamped edge, F-free edge). The load is applied to the clamped edges. The main differential equation for the coordinate component of the deflection function and all the boundary conditions of the problem are fulfilled exactly using two hyperbolic-trigonometric series in two coordinates and an additional function depending on one variable x. The problem was reduced to an infinite system of linear algebraic equations with respect to one sequence of uncertain coefficients, containing as parameters the magnitude of the load and the frequency of oscillations. For a number of load values, the natural frequencies of oscillations were found by enumerating frequency values in combination with the method of successive approximations when solving a reduced system of linear algebraic equations. To ensure acceptable accuracy of calculations, the number of terms in the series (the size of the reduced system), the number of iterations and the number of significant digits in the mantissa when calculating non-trivial coefficients of the system were changed. A square plate was considered as an example. Based on the calculation results, a graph was constructed of the dependence of the first natural frequency of oscillations on the magnitude of tension-compression forces, which is a curve close to a parabola. Under Eulerian compressive load, the oscillations stop. The shapes of natural vibrations changed slightly and were similar to the shape of the curved surface of a plate under the action of a uniform transverse load. The purpose of this study is to create an effective algorithm for calculating the natural frequencies of oscillations of a CFCF-plate when the uniaxial tensile-compression load of its clamped faces changes.

Change of Natural Oscillation Frequencies of Buildings and Structures Depending on External Factors

Abstract —This work is devoted to the development of the engineering seismic monitoring method created in Geophysical Survey of the Russian Academy of Sciences (GS RAS). In previous years, the “method of standing waves” was created and put into practice. It helps to separate natural oscillation modes of buildings and other engineering structures. The natural oscillations of hundreds of various objects (buildings, bridges, dams, etc.) had been studied and identified. We assumed that the physical condition of studied constructions could be controlled during exploitation by measuring the changes of natural oscillation frequencies. That would help to identify the appearance of defects in constructions, to prevent the risk of their destruction. However, it turned out that not everything is that simple: changes in frequency values are logically affected by changes in the environment around the studied objects. This article provides examples of these relations, influence of changes in environmental temperature, mass of objects and precipitation on the frequencies of natural oscillations.

Study of the Dynamics and Strength of the Detachable Module for Long Cargoes under Asymmetric Loading Diagrams

This article highlights the structural features of the detachable module for the transportation of long cargoes. The choice of profiles for the detachable module was based on the resistance moments of its components. The detachable module was considered a rod structure on four supports. To determine the longitudinal loads acting on the detachable module, mathematical modeling of its longitudinal dynamics was carried out, provided they were placed on a flat car during a shunting impact. The accelerations obtained were used for the calculations of the detachable module. This article presents the results of the strength calculation of the detachable module under asymmetric loading diagrams, i.e., the action of longitudinal and lateral forces on the detachable module structure. The results of the calculations show that the maximum stresses in the structure of the detachable module when it receives longitudinal loads are 7.7% lower than the permissible ones, and when it receives lateral loads, they are 5.8% lower. Thus, the strength of the detachable module is maintained under the loading diagrams considered. This study also included a modal analysis of the detachable module structure. The first natural frequency of oscillations is found to be 20 Hz. Thus, the safety of the detachable module movement in terms of frequency analysis is ensured. This research will help to create recommendations for the design of modern modular vehicles and improve the efficiency of the transport industry.

Mechanical responses of nanoplates resting on viscoelastic foundations in multi-physical environments

This paper presents an analysis of the static bending, thermal buckling, free vibrations, and forced vibrations of nanoplates using analytical approaches. This study introduces analytical formulations for all three aforementioned difficulties concerning nanoplates, taking into account the simultaneous impact of elements such as magnetic effects, temperature, and viscoelastic basis. The research at hand is characterized by its intricate nature and captivating subject matter, as it explores the phenomenon of the flexomagnetic impact on a plate. Furthermore, the plate is exposed to both mechanical and magnetic stresses concurrently inside a temperature-controlled environment. The plate is supported by a viscoelastic foundation, with the drag coefficient of the foundation being explicitly specified. The mathematical methods used in this study are derived from classical plate theory. An explicit expression is derived for the natural oscillation frequency, critical load resulting from thermal buckling, as well as the static and dynamic displacements of the plate, taking into account the drag coefficient offered by the foundation. The study further conducts a quantitative analysis to investigate the impact of several parameters, including temperature, viscoelastic foundation, and natural frequency of external stimulation force, on the mechanical behaviors of nanoplates. The findings of this study provide a scientific foundation for addressing practical challenges in the design, production, and use of nanoplates.

Observation of fixed lines induced by a nonlinear resonance in the CERN Super Proton Synchrotron

AbstractThe motion of systems with linear restoring forces and recurring nonlinear perturbations is of central importance in physics. When a system’s natural oscillation frequencies and the frequency of the nonlinear restoring forces satisfy certain algebraic relations, the dynamics become resonant. In accelerator physics, an understanding of resonances and nonlinear dynamics is crucial for avoiding the loss of beam particles. Here we confirm the theoretical prediction of the dynamics for a single two-dimensional coupled resonance by observing so-called fixed lines. Specifically, we use the CERN Super Proton Synchrotron to measure the position of a particle beam at discrete locations around the accelerator. These measurements allow us to construct the Poincaré surface of section, which captures the main features of the dynamics in a periodic system. In our setting, any resonant particle passing through the Poincaré surface of section lies on a curve embedded in a four-dimensional phase space, the fixed line. These findings are relevant for mitigating beam degradation and thus for achieving high-intensity and high-brightness beams, as required for both current and future accelerator projects.

Metal wire embrittlement monitoring by the measurement of wire oscillation frequency

In the process of irradiation of materials by fluxes of heavy particles (protons, neutrons, alpha particles), damage to material structure is often observed. As a result of the accumulation of such damages, there is a subsequent change in the properties of materials, in particular, its embrittlement and hardening. Monitoring of the embrittlement process is important for nuclear reactor vessels exposed to high neutron fluxes. In this work, to observe the effect of heavy irradiation particles on the mechanical properties of metals, we propose to use vibrating wire resonators, in which the natural frequency of oscillations of the wire strongly depends on its tension. The change in the elastic characteristics of the wire alters the value of the natural frequency of wire oscillations. The natural oscillations are generated by a special circuit. Preliminary experiments to study the embrittlement effect of a stretched wire are performed by heating the wire with an electric current. In the case of short pulses, a significant increase in frequency is achieved, which is explained by the process of hardening of the material as a result of the thermal impact on the wire (rapid heating and cooling).

Vertical convection regimes in a two-dimensional rectangular cavity: Prandtl and aspect ratio dependence

Vertical convection is the fluid motion that is induced by the heating and cooling of two opposed vertical boundaries of a rectangular cavity (see e.g. Wang et al., J. Fluid Mech., vol. 917, 2021, A6). We consider the linear stability of the steady two-dimensional flow reached at Rayleigh numbers of O( $10^8$ ). As a function of the Prandtl number, $Pr$ , and the height-to-width aspect ratio of the domain, $A$ , the base flow of each case is computed numerically and linear simulations are used to obtain the properties of the leading linear instability mode. Flow regimes depend on the presence of a circulation in the entire cavity, detachment of the thermal layer from the boundary or the corner regions and on the oscillation frequency relative to the natural frequency of oscillation in the stably temperature-stratified interior, allowing for the presence of internal waves or not. Accordingly, the regime is called slow or fast, respectively. Either the global circulation or internal waves in the interior may couple the top and bottom buoyancy currents, while their absence implies asymmetry in their perturbation amplitude. Six flow regimes are found in the range of $0.1 \leq Pr \leq 4$ and $0.5 \leq A \leq 2$ . For $Pr \lessapprox 0.4$ and $A>1$ , the base flow is driven by a large circulation in the entire cavity. For $Pr \gtrapprox 0.7$ , the thermal boundary layers are thin and the instability is driven by the motion along the wall and the detached boundary layer. A transition between these regimes is marked by a dramatic change in oscillation frequency at $Pr = 0.55 \pm 0.15$ and $A <2$ .

Experimental study on the flow-induced vibrations of a circular cylinder with a rear flexibly hinged splitter plate

The flow around a circular cylinder is a canonical configuration that may be encountered in many engineering applications, as for instance, civil engineering, architecture, or marine structures. In particular, when bluff bodies are slender and feature low mass-damping characteristics, they may undergo flow-induced vibrations (FIVs), which may result in severe structural fatigue and damage. Here, we present an experimental study on the effect of flexibly hinged splitter plates in the FIV of a flexibly mounted circular cylinder (of diameter D) subject to an uniform cross-flow of velocity u∞. The dynamic response and forcing of the low mass-damping system is characterized for plates of different lengths Lp and different values of the torsional stiffness of the hinge kp. Reductions of the dynamic response of more than 90% can be generally reached at the upper branch, especially when a plate of length l*=Lp/D=2 with intermediate degree of torsional stiffness is attached, which is shown to represent the best solution as it mitigates the oscillations of the system (cylinder and plate) for the whole range investigated of reduced velocity U*=u∞/fnD=[3.9,9.8], where fn is the natural frequency of oscillation. In general, the hinged plates are able to attenuate the vortex-induced vibration system response by increasing shedding frequency, until the ratio f*=f/fn>1 is reached. At high values of U*, a general transition to galloping-like dynamics, characterized by f*<1, occurs. The tested hinged plates modify the transition between regimes, which is associated with shifts in the phase difference between the forcing and response, combining features of the dynamics of both flexible and static rigid plates already reported in the literature. The use of hinged plates has been proven to provide with a significant attenuation of the system response and its associated drag, a feature that can be considered of practical relevance in many engineering applications. In addition, the key aspects for designing these elements as the torsional stiffness and plate length have been analyzed here.

CFD simulation of unstable fluid flows in the rotor of a high-speed precipitation centrifuge

The results of a numerical study of unstable fluid flows in the rotor of a high-speed vertical precipitation centrifuge are presented. It is shown that during the operation of a high-speed precipitation centrifuge, a qualitative change in the hydrodynamic regime is possible from conditionally laminar to conditionally turbulent, characterized by large-scale axial and radial pulsations of the liquid phase, accompanied by a significant decrease in sedimentation efficiency. It has been established that the flow pulsations are not random in nature, but the amplitude of these pulsations first increases with increasing rotation rate of the centrifuge rotor, and after passing a certain “critical” rotation rate it begins to decrease. Thus, the “critical” rotor rotation rate can be considered as a resonant rate, at which the frequency of turbulent flow pulsations (natural oscillation frequency) coincides with the rotor rotation frequency (forced oscillation frequency). The dependences of the pitch, frequency, and amplitude of liquid flow pulsations on the edge of the centrifuge overflow disk on the rotor rotation rate were obtained. It has been established that in the “subcritical” and “supercritical” operating modes, the amplitude and step of liquid pulsations on the overflow disk of the centrifuge are increasing and decreasing respectively.

The influence of anisotropic properties of the under-rail base on the track dynamic settlement

The article presents the results of a study of the anisotropy of the under-rail base on the dynamic settlement of sections of transitional stiffness reinforced with bottomless boxes. It is proposed to model the railway track by flat elements, each of which is represented by an anisotropic plate resting on a deformable base with its own deformability parameters. Three main directions of change in the mechanical and geometric characteristics of the structure are identified: horizontal directions along the rail strands, transverse directions along the sleepers, and vertical directions down from the level of the rail head. Setting boundary conditions for individual fragments of the track structure and varying the anisotropy coefficients allows to achieve a good correspondence between the real railway track structure and its mathematical model. Graphical dependencies for the vertical displacement of points on the median surface of a flat element modeling a segment of a railway track were constructed and analyzed based on the results of determining the frequencies of natural oscillations.

Використання моделі балістичного маятника в аналізі перехідних процесів кранових систем

A number of factors affecting the accuracy of experimental determination of small velocities of pendulum vibrations of the load on the rope of the crane hoisting mechanism, arising at start-up, braking or reversing of the crane system, have been analyzed. The rope is considered as an elastic thread. The influence of finite mass and bending elasticity of the viscus on the frequency of natural oscillations of the pendulum is theoretically analyzed. It is shown that the main factor influencing the natural frequency is the bending elasticity of the viscus thread, and the influence of the mass of the thread (rope) of the ballistic pendulum can be minimized. An exact analytical expression for the natural frequency of a real pendulum at arbitrary stiffness of the lightweight viscus is obtained. For small mass of cargo and speed of movement at impulse influence on the crane system (starting, braking, reversing) there are certain difficulties in taking into account the final mass and stiffness of the viscus for calculation of natural frequency of pendulum oscillations. In an ideal situation, the mass of the temple can be made too small compared to the mass of the pendulum (load and rope), but with a short length of rope increases the natural frequency of the pendulum, which reduces the sensitivity of the system to external impulsive influences, and increases the influence of the elasticity of the thread (rope) on this frequency. Therefore, in a real situation, the mass of the pendulum, its length (of the rope) and the stiffness of the temple should always be chosen and taken into account in accurate studies (and calculations) based on compromise considerations. In this study, the degree of influence of the above factors on the natural frequency of oscillation of a pendulum (i.e., essentially a weight on a rope) is theoretically evaluated in the small-parameter approximation. The results obtained in this study can be further used to refine and improve the existing engineering methods of calculation and analysis of transients (start-up, braking, reversing, etc.) of crane systems both at the stages of their design and in the modes of real operation to optimize the performance of the above systems (and mechanisms).

Synchronisation of the ensemble of nonidentical FitzHugh–Nagumo oscillators with memristive couplings

The aim of the study is to investigate the features of synchronization in ensembles of nonidentical neuron-like FitzHugh–Nagumo oscillators interacting via memristor-based coupling. Methods. The collective dynamics in a ring of FitzHugh–Nagumo oscillators connected via memristive coupling was studied numerically and experimentally. The nonidentity of oscillators was achieved by detuning them by the threshold parameter responsible for the excitation of oscillator, or by detuning them by the parameter characterizing the ratio of time scales, the value of which determines the natural frequency of oscillator. We investigated the synchronization of memristively coupled FitzHugh–Nagumo oscillators as a function of the magnitude of the coupling coefficient, the initial conditions of all variables, and the number of oscillators in the ensemble. As a measure of synchronization, we used a coefficient characterizing the closeness of oscillator trajectories. Results. It is shown that with memristive coupling of FitzHugh–Nagumo oscillators, their synchronization depends not only on the magnitude of the coupling coefficient, but also on the initial states of both the oscillators themselves and the variables responsible for the memristive coupling. We compared the synchronization features of nonidentical FitzHugh–Nagumo oscillators with memristive and diffusive couplings. It is shown that, in contrast to the case of diffusive coupling of oscillators, in the case of meristive coupling, with increasing coupling strength of the oscillators, the destruction of the regime of completely synchronous in-phase oscillations can be observed, instead of which a regime of out-of-phase oscillations appears. Conclusion. The obtained results can be used when solving the problems of synchronization control in ensembles of neuronlike oscillators, in particular, for achieving or destroying the regime of in-phase synchronization of oscillations in an ensemble of coupled oscillators.

Characterization and Analysis of Mechanical Vibrations in Photovoltaic Modules Transported by Road in Spain

Large deployment of photovoltaic (PV) installation worldwide demands reliability assurance of the systems to maintain the confidence in the markets. With the diversity of PV applications, it is essential the detection of circumstances that can be the root of failure mechanisms, such as transportation and installation of the modules. They are one of the main sources of induced vibrations, which, in its turn, can provoke defects and damages in the PV modules. In this work, we have measured and analyzed tri-axial accelerations and mechanical vibration that photovoltaic crystalline modules withstand during transportation by road, including loading and unloading operations. We have also analyzed the natural oscillation frequencies, the resonance phenomena and the highest impacts. It is concluded that a proper fastening of the load inside the truck is necessary and that high impacts during loading and unloading should be avoided. Packing the modules to reduce vibrations is also recommendable. Several solutions to perform this are proposed.

Features of a finite-element modeling of a tubular tower for a wind-power unit

Introduction. Being indisputably relevant, an identification of the features of modeling tower structures can simplify the work of engineers and simultaneously move the design decision-making to a qualitatively new level.Aim. To assess the effect, caused by some particular features of a computational modelling, on the resulting parameter, representing the frequency behavior of a tubular tower for wind-power units.Materials and Methods. Numerical studies were conducted using a domestic SCAD Office programming and computing suite. In computational modeling, 41st, 42nd, 44th and 50th FE types were used. During the assessment of effects, caused by the finite element type, calculations of a cylindrical tower with fixed parameters were performed, taking into account variations in the type and size of the FE. Estimating factors in calculations included: variations in stresses, as well as in the frequency of first-mode natural oscillations. During the comparison of stress values, the plate of the third from the fixed base row was taken as the design one. Turbowind T600-48 and Eviag EV 100 were considered as wind turbines.Results. A sufficient discretization value of the computational model for determining the frequency of natural oscillations equals to nR = 12, since a further increase in the value of nR will lead to variations in the frequency of natural oscillations by less than 1%. The individual frequencies of 0.275 and 0.825 Hz were determined for an Eviag EV 100 wind turbine. For a Turbowind T600-48, the range of resonant frequencies is determined due to the presence of a variable rotor speed: starting and maximum frequency ranges of 0.255–0.765 and 0.383–1.149 Hz, respectively.Conclusions. During the modeling of a tower in the SCAD Office PCS, it is feasible to use the 44th type of finite elements, taking into account the obtained sufficient discretization value. The obtained spectrum of natural and resonant frequencies allows avoiding the appearance of a resonant effect when making design decisions.

Model of influence of a rope defect on the spectrum of its free transverse vibrations

In earlier work the possibility of diagnosing a defect of a steel wire rope by spectral composition of its free transverse vibrations was substantiated. In the present work, an analytical model of transverse vibrations of a steel wire rope with local damage is proposed. The presence of the defect in the model is taken into account only in the form of a loss of bending stiffness of the corresponding section without changing the specific mass along the length. The model represents three homogeneous rope sections “stitched” together, where the middle one represents a defective section with a lower value of bending stiffness. According to the model calculations, it is shown that the character of the dependence of the natural frequencies of oscillations on their number practically does not change in the presence of a defect. However, its presence and location affects the ratio of vibration amplitudes of undamaged sections, which can be used to monitor the condition of the rope.