Natural Oscillation Frequency Research Articles

IMPROVING THE EFFICIENCY INTO THE IMPACT FLUID FRACTURING BY ADAPTING IT TO THE PARAMETERS OF THE ENCLOSING ENVIRONMENT

The principle of formation of the oriented crack by displacement of a plastic substance from the well in the mode providing coincidence of frequency of influence on a plastic substance and natural frequency of oscillations of the host medium is discussed. The technical solution of adaptation of the mode of injection of a plastic substance into the formed crack to the changing parameters of the host medium is given. The means of implementation of this technical solution and the results of engineering calculations of their main components are presented.

Experimental determination of dynamic characteristics and analysis of acceleration of vibrations of pedestrian bridges

This article discusses the design of pedestrian bridges. When designing pedestrian bridges, engineers are guided mainly by the static characteristics of the types of spans under consideration. If you want to build a load-bearing beam structure of a large span, you cannot lose sight of their relatively large mass and low stiffness due to the length of the bridge. These factors lead to a low natural frequency close to the frequency of pedestrian load, in the form of people passing through this structure, which, in turn, act as recipients of vibrations. The structure is a metal span restructure with two I-beam main beams with a solid sloping wall, an orthotropic plate of the passer-by part below, a calculated width of 44.0 m, a total length of 44.6 m and a pedestrian dimension of 3.25 m. In the course of dynamic tests of the pedestrian bridge span, experimental values of the natural vertical vibration frequencies were determined, followed by the determination of the attenuation decrement. The natural oscillation frequency was 2.0 Hz, which corresponds to a period of 0.5 s oscillation.

Badania eksperymentalne zjawiska unoszenia częstotliwości w przypadku przepływomierza z oscylatorem mechanicznym

Oscillatory flowmeters are susceptible to pulsatile flow and mechanical oscillator flowmeters are no exception. The experimental study was conducted to determine possible measurement errors for specific pulsation amplitude thresholds. The study verified that no frequency lock-in takes place for pulsation frequencies which are subharmonics of the natural oscillation frequency, nor for harmonics higher than the 2nd.

Research of resonance vibrations of the system «Telescopic screw — bulk medium» caused by torsional vibrations

The article outlines the relevance of using the principle of telescopy in the process of creation screw conveyors, which nowadays are folded to obtain significant lengths, which makes their designs expensive and structurally unreasonably complicated. It has been shown an experimental equipment, which provides measurement results of the research process in a wide range with high accuracy in an automated control mode with the necessary data capture. Based on the constructed mathematical model, the dependences of the angular perturbation velocity on the physicomechanical and geometric parameters of the «telescopic screw — bulk medium» system have been obtained. Because of analytical relations describing the laws of variation of characteristic parameters for its oscillation resonance case have been received. It has been proved that for resonant oscillations, when there are significant angular velocities of rotation, the natural frequency of the bending oscillations is smaller and at the same time the amplitude of the transition through the resonance is smaller. The results of the amplitude of the transverse oscillations of the system for different values of the angular velocity of rotation in time during the transition through the internal resonance, which largely depends on the physicomechanical and geometric characteristics of the motion of the medium, have been presented.

Determining the features of loading the improved bearing structure of a platform wagon for the transportation of military equipment

The paper reports the improvement in the bearing structure of a platform wagon that transports military equipment and is involved in artillery fire. A special feature of the platform wagon is the presence of rotary sectors made from a composite material with viscous or elastic-viscous links, which makes it possible to absorb the kinetic energy that is transmitted to the frame when firing from the wagon, as well as enables the loading/unloading of military equipment from its side. We have investigated the dynamic loading of the bearing structure of a platform wagon for military equipment transportation and combat operations. A mathematical model has been constructed, which takes into consideration the movement of the bearing structure of a platform wagon when firing from it. It has been considered that the platform wagon is loaded with two anti-aircraft guns. The mathematical model was solved in the Mathcad programming environment. The study was conducted in a flat coordinate system. We have determined the accelerations that act on the bearing structure of a platform wagon. The maximum acceleration rate, in this case, is about 3.6 m/s 2 at bouncing oscillations and 4.0 m/s 2 at galloping oscillations. In other words, considering the proposed technical solutions, the dynamic loading of the bearing structure of a platform wagon in the vertical plane at firing decreases by almost 30 %. The magnitude of the acceleration is almost independent of the firing angle in this case. The derived acceleration values have been taken into consideration in determining the strength indicators for the bearing structure of a platform wagon. Calculation was carried out by the method of finite elements in the CosmosWorks programming environment. The maximum equivalent stresses in the bearing structure of a platform wagon amounted to about 285 MPa; they are concentrated in the region where the bearing structure rests on the trolley. Consequently, the durability of the bearing structure of a platform wagon is ensured. Modal analysis of the bearing structure of a platform wagon has been conducted. The values of the natural oscillation frequencies are within allowable limits. Our research would contribute to designing innovative structures for platform wagons

Dipole scattering of a short radiation pulse on hydrogen-like atoms

Our theoretical model of forced dipole oscillation demonstrates that when the amplitude of the forcing field is changing fast, the oscillations of the bound electron in the atom or molecule initially proceed at two frequencies: the frequency of the natural electron oscillations and the frequency of the forcing field. Particularly, applied to the science of scattering, this model of transient forced atomic and molecular oscillations suggests that accurate interpretation of the laser scattering experiments using short laser pulses must include both the conventionally known scattering at the laser frequency (Rayleigh) and the predicted by our theoretical spectral emission that corresponds to the natural frequency of the electronic oscillations. This article presents the results of numerical simulations using our model performed for the hydrogen atom. The characteristics of the components of scattered radiation, their polarization, and Doppler thermal broadening are discussed.

Influence of dissipative properties on the magnetoelectric coefficient in bilayer films

The theory of the direct magnetoelectric effect in a bilayer ferromagnetic—piezoelectric structure is presented with the exact consideration for electric fields, inhomogeneous over the thickness of the piezoelectric layer. The solution of the motion equations for a piezoelectric and ferromagnetic medium made it possible to numerically-analytically calculate the dependence of the natural frequency of mechanical oscillations on structure parameters and frequency dependence of the magnetoelectric coupling coefficient. Consideration of the structure dissipative properties makes it possible to estimate the maximum value of the magnetoelectric coupling coefficient.

Research on piezoelectric energy harvester based on coupled oscillator model for vehicle vibration utilizing a L-shaped cantilever beam

Piezoelectric energy harvester can replace the battery and provide energy for most kinds of micro devices. And due to its advantages of considerable output power and high output voltage, it has bright prospects. This paper presents a piezoelectric energy harvester based on coupled oscillator model utilizing a L-shaped cantilever beam to collect the vibration energy of the vehicle with the frequency band from 5 Hz to 25 Hz. The finite element analysis of the designed piezoelectric energy harvester is carried out by running ANSYS simulation software, including modal analysis, transient response analysis and harmonic response analysis. The results shows that under the coupling, the amplitude-frequency characteristic curve of each oscillator has two peak points, which widens the working frequency band of the energy harvester. Meanwhile, experimental research is carried out on the collector prototype. By analyzing the experimental results, the natural frequency of oscillator 1 is about 17.1 Hz, and the natural frequency of oscillator 2 is about 21.1 Hz. Therefore, these natural frequencies meet the need to collect vibration energy of 5 Hz to 25 Hz. In addition, by comparing the frequency response curves of the open circuit output voltage of the energy collectors working independently and under coupling, the results show that the operating frequency band of the energy collector is broadened under coupling.

Increasing of elevation angles in vibratory conveyor with electromagnetic drive

The design of conveyor intended for automation of inter-operational movement and supply of details and materials on the mechanized military enterprises and warehouses is considered. It is based on two-mass vibratory conveyor with independent electromagnetic drives of longitudinal and normal oscillations of conveying track and with horizontally mounted flat latticed springs. Electromagnetic drive allows implementing the optimal by velocity biharmonic normal oscillations of conveyor’s working body with a certain value of natural frequency, which depends on the inclination angle of conveyor’s track. The latticed springs are mounted between the working body and reactive frame of conveyor with the possibility to change the working length of springs and as a result the natural frequency of normal oscillations. The presented vibratory conveyor allows increasing the conveying velocity and the elevation angles, when the loads are moving up, without design’s complication.

Estimation of fatigue margins for composite parts of aircraft engine on the base of vibration tests

During the modernization of the low-pressure compressor of the regional aircraft engine, a flow separator made of polymer composite material was developed, which has less weight, is easier and cheaper to manufacture. However, the separator must undergo a series of tests before being installed on the engine, in particular the endurance tests, necessary to assess the fatigue strength margin. A method for determining the endurance limit of a large part of an aircraft engine is developed in the presented work and consists in replacing the tests of the entire separator with tests of individual structural elements cut from the part. The shape, dimensions and fixation of the elements have been chosen in such a way that their own test frequency was close to the natural frequency of the flow separator on the engine. The natural oscillation frequencies and places of maximum dynamic stresses have been determined before testing on three-dimensional models of the flow separator and elements cut from it. As a result, the structural elements have been tested until appearance of fatigue cracks which allowed to assess the endurance limit and evaluate fatigue strength margin of the separator.

APPLICATION OF LOCAL SPECTRUM OF NATURAL OSCILLATIONS FOR MONITORING OF STRESS STATE IN NON-METALLIC ELEMENTS OF STRUCTURES

This work offers a method based on extraction of specially selected localized forms of oscillations from the general spectrum of frequencies of natural oscillations of a part by means of which non-destructive monitoring of stress state in various points of non-metallic parts is performed. Frequency spectrum is localized by use of special oscillation transducers with adjustable mechanic filter at the inlet before piezoelectric plate. Such filter allows both to extract localized frequency spectrum and to ensure adjustment of frequencies of natural oscillations of transducer rod wrt frequencies of natural oscillations of the part being monitored. The transducers operated as a part of acoustic impedance flaw detector «ДАМИ-С09». Stress variations at the points of the part were captured on the screen of the flaw detector by energy redistribution between the forms of natural oscillations of transducer rod. Captured energy redistribution between the forms of oscillations took place due to shift of frequencies of natural oscillations of the part during stress variation wrt to frequencies of natural oscillations of transducer rod and summing up of their amplitudes. Here, the amplitudes of some oscillations intensified and some subsided. The results which were experimentally gained during monitoring demonstrate variations of local stress state at the point on the perimeter of the square plate made of sphere plastic under effect of compressive stresses on the perimeter of the plate and in the centre. In the first case at the point of measurement “conditional compression” took place and in the second case it was “conditional tension”.

Двухмассовая газовая гирочастица как инструмент анализа сверхзвуковой аэроупругости

When a flying vehicle reaches a high supersonic speed, plasma occurs in the flow, hampering the application of the traditional piston theory and its modifications to solve the aeroelasticity problem. This work considers flow modelling using a system of two-mass gas gyro-particles capable of dividing into two charges and ionizing the flow. The two-mass gas gyro-particle has two elements and two pairs of multiple frequencies. As the gyro-particle interacts with the surface of an elastic body, it starts to rotate and pulsate, and the multiple frequencies split. As the pulsation frequency of the gas gyro-particle reaches the natural oscillation frequency of the elastic structure, resonance occurs and the structure flutters. It is assumed that the supersonic character of the flow is determined not by the velocity of the flying vehicle, but by the rotational frequency of the gas gyro-particle. The higher the particle’s rotational frequency, the higher the aerodynamic drag. If the rotational frequency is high enough, then the screening effect takes place: the vehicle decelerates and turns upside down. This is called divergence, and the plasma is not taken into account. In this work, a 2D model is used to interpret the flutter and the divergence effects.

Discovering a pattern in the free vibrations of gently sloping shells of different geometry in the classic and refined statements

The paper reports an effective numerical procedure to solve problems on the free oscillations of isotropic gently sloping shells using a spline-approximation method of unknown functions along one of the coordinate directions. By applying the proposed procedure, we have examined the resonance frequencies of the oscillations of cylindrical shells and shells of double curvature both in a square and rectangular plan. The calculations were conducted and compared based on two theories: classic (by Kirchhoff-Love) and refined (by Timoshenko-Mindlin). We have established the dependence of natural oscillation frequencies on the ratio of shell thickness and their dimensions in the plan. It has been revealed that the frequencies of free oscillations of gently sloping shells, computed in the refined statement, have lower values than the corresponding frequencies calculated in the classic statement. With the increasing thickness of the shells, the difference in the values of corresponding frequencies increases. The calculations results were compared with the frequencies computed analytically by expanding the unknown functions into a Fourier series. The comparison has allowed us to determine the optimal scope of application of each theory. It has been established that the frequencies of free vibrations of thin gently sloping shells should be computed in a classic statement. The calculation of non-thin shell frequencies (at a ratio of the thickness to the smallest size in the plan of h/a³0.05) at any geometric parameters of the shells should be performed in the refined statement. Our results have confirmed the theoretical assumptions about the importance of considering the turning angles, first, of a rectilinear element, caused by transverse offsets, in calculating the natural oscillation frequencies of the non-thin shells. The versatility and high accuracy of the spline approximation method have been confirmed.

Numerical study on two-degree-of-freedom vortex induced vibrations suppression of a circular cylinder via synthetic jets at different excitation frequencies

In this work, a pair of synthetic jets are investigated for control of vortex induced vibration (VIV) of a circular cylinder in uniform flow in the low Reynolds number regime. In particular, the study focuses on three representative phase differences (0, π/2, and π) between the pair of synthetic jets to study the influence of synthetic jet excitation frequency ratio fsj* (fsj* = fsj/fn,water) on 2DOF VIVs control by two-dimensional numerical simulation. The Reynolds number is fixed at 150, the mass ratio m* (m* = mosc/md) of the circular cylinder is 2.0, and the natural oscillation frequencies in the in-flow and cross-flow directions are equal. The amplitude response, frequency response, hydrodynamic forces, and wake patterns are analyzed. The results show that both in-flow and cross-flow oscillations of the circular cylinder can be significantly suppressed by synthetic jets with various phase differences, and the wake becomes symmetric when fsj* ≥ 4.0. When fsj* < 4.0, many fluctuations can be observed from the changing curves of in-flow and cross-flow oscillation amplitudes, and the oscillation may be enhanced by the occurrence of lock-in between the oscillation frequencies and the synthetic jet excitation frequencies. Besides, vortex shedding modes of the controlled cases are significantly different in blowing and suction phases of the synthetic jet, when the excitation frequency is very low, such as fsj* = 0.2.

Oscillations of Pipelines Laid on Supports in the Conditions of Aerodynamic Resonance

Above-ground laying of field and main oil and gas pipelines is one of the most common methods in the conditions of the North and permafrost soils, as well as at the intersection of ravines, canals, small rivers, in rocky soils, in areas of mine workings and landslides. Under the influence of wind, above-ground pipelines can experience oscillations whose frequency is usually equal to the frequency of the fundamental tone of free oscillations. Oscillations occur not only along, but also across the wind flow. The amplitude of oscillations across the flow is greater than the amplitude of vibration along the flow. At certain values of wind speed, the amplitude of oscillations increases sharply. As a rule, when designing, in calculating the distances between the supports, in most cases this phenomenon is not taken into account and the conditions for the occurrence of aerodynamic resonance when the natural frequencies of the pipeline oscillations and the frequency of vortex formation are close are not checked. In the paper the maximum allowable distances between the supports of various above-ground pipelines are determined taking into account the detuning from wind resonance from the condition of a certain critical wind speed.

Multifaceted nonlinear dynamics in $$\mathcal {PT}$$-symmetric coupled Liénard oscillators

We propose a generalized parity-time ($$\mathcal {PT}$$)-symmetric Lienard oscillator with two different orders of nonlinear position-dependent dissipation. We study the stability of the stationary states by using the eigenvalues of the Jacobian and evaluate the stability threshold thereafter. In the first-order nonlinear damping model, we discover that the temporal evolution of both gain and lossy oscillators attains a complete convergence towards the stable stationary state leading to the emergence of oscillation and amplitude deaths. Also, the system displays a remarkable manifestation of transient chaos in the lossy oscillator while the gain counterpart exhibits growing oscillations for certain choice of initial conditions and control parameters. Employing an external driving force on the loss oscillator, we find that the growing temporal evolution can be controlled and a pure aperiodic state is achievable. On the other hand, the second-order nonlinear damping model yields a completely different dynamics on contrary to the first order where the former reveals a conventional quasiperiodic route to chaos upon decreasing the natural frequency of both gain and loss oscillators. An electronic circuit scheme for the experimental realization of the proposed system has also been put forward.

Increasing the smoothness of the course of the forage harvester by optimizing the mass-dimensional and inertial parameters of its body

The scientific-methodical substantiation and practical recommendations on stabilizing the movement of forage harvesters are proposed. Calculation of optimal mass and inertial parameters of the hull, as well as elastic properties of tires as the main element of the combine suspension system is theoretically grounded. The developed technique on the example of the combine prototype shows the possibility of calculating the optimal stiffness of tyres and weight of additional counterweights installed in the base of the machine to ensure the equality of natural frequencies of front and rear axle oscillations on elastic tyres. The modeling of the combine’s movement on the subsoil road and asphalt concrete highway with different speeds has been carried out on the basis of mathematical and imitation model of the combine developed by the authors earlier. In the order to evaluate the efficiency of the proposed method of improving the smoothness of running the comparison of peak and mean square values of the pitch angle of the hull, as well as the levels of vertical vibroaccelerations in the cabin on the floor under the seat of the operator of the combine in its basic design and improved version due to the use of counterweights of a given mass and optimized stiffness of tires. A simulation was used to perform an octave analysis of the workplace vibration load. It is shown that optimization of mass and inertial parameters of the body, as well as elastic properties of the combine harvester tires on the main driving modes provides improvement of comfort of the operator’s working place, especially in the most dangerous for human frequency range. The driving modes are defined, on which the best effect of rework is achieved. The stabilization process is described. The conclusions on the direction of further research are presented.

РЕШЕНИЕ ЗАДАЧИ СНИЖЕНИЯ ВЛИЯНИЯ БОКОВОЙ СИЛЫ НА УСТОЙЧИВОСТЬ ПИЛЬНОГО ПОЛОТНА

The accuracy of the thickness of lumber is one of the most important indicators of sawing. It is inextricably linked with saw stabilization in the plane of the greatest stiffness. The aim of the study is to eliminate the influence of lateral force on the saw blade and the thickness of the resulting lumber. The issue of eliminating the influence of lateral force in frame sawing and sawing on band saws belongs to the constructive decision in combination with the analytical one according to classical methods. Therefore, the most important issue in the development of a new machine is to identify the presence of a huge range of frequencies of natural and parametric oscillations of saw blades. Previously, these frequencies could not be analytically found to the full extent and, respectively, the tuning out the machine operating frequencies of the possible oscillation frequencies of saw blades could not be carried out. Due to the complexity and the science intensity of the problem solving, it is not conceivable without modern numerical methods of calculation. Among them are the fnite element method, modern software of NX and ANSYS, as well as other original programs. One of such methods, which allow to reduce the influence of lateral force, is determination of stability of the plane form of bending by the Eulerʼs method. The technical solution presented by a fundamentally new saw block with a circular translational motion of the blades reduce dramatically the impact of lateral force on the accuracy of sawing in conjunction with a number of other advantages. At the same time, the issue of ensuring the dynamic stability of the blades both when sawing and at idling speed is solved. It is necessary to point out that with circular translational motion the tooth side cutting edges are under alternating load when scraping over the cut surface. There fore, the tooth cutting element is a subject of increased strength requirements. The angles of their sharpening were adjusted in order to preserve the integrity of the corners of the teeth tips. The possibility of strengthening the teeth lateral cutting edges of saw blades made of steels of different grades was investigated. The reasons of wear and corrosion, both the elements of the saw module and its operating part (blade teeth) were studied and it was decided to supply the teeth with a hard alloy of the stellite type as the most optimal. However, this provision requires additional targeted feld tests. Preliminary calculations showed that the daily productivity of a machine with circular translational motion of the blades (model M2005) in comparison with saw frames increases by 2–4 times; in comparison with band saw equipment of any class by 3–6 times; and in comparison with the circular saw equipment (for small and medium enterprises) by 2–4 times. Analyzing the design scheme and the dynamics of the saw modules, it is possible to fnd a number of advantages of the multi-saw unit presented as part of the machine. The simplicity and reliability of the design allows us to hope for high functional characteristics. Among those we should highlight the following:increasing the accuracy of sawn products due to the rigidity of short blades, increasing the productivity, improving the quality of treated surfaces, as well as reducing the energy consumption, relatively light weight and dynamic balance of the main units with increased mobility of equipment and the absence of a massive foundation. For citation: Blokhin М.A., Podlesny D.A., Rodionov O.A. Solving the Problem of Reducing the Influence of Lateral Force on the Saw Blade Stability. Lesnoy Zhurnal [Russian Forestry Journal], 2020, no. 2, pp. 118–128. DOI: 10.37482/0536-1036-2020-2-118-128

New method for monitoring the residual life of high pressure hoses

The presented method is designed to monitoring the residual life of hydraulic drive elements. In this work, as an element of the hydraulic drive, high-pressure hoses are used, which are used in hydraulic drives of technological equipment of transport and technological machines. As a diagnostic parameter that characterizes the technical condition of the high-pressure hose, the frequency of natural oscillations of the pipeline with the liquid is adopted. Experimentally, the dependence of the natural oscillation frequency of the high-pressure hose on the dynamic loading cycles of the harmonic type was obtained, which were used to determine the probability of failure of pipelines and to find a strategy for their replacement. The probability of failure of high-pressure hoses for different periods of operation is determined on the basis of the obtained experimental dependences of the natural vibration frequency of pipelines on their operating time. Using the obtained dependences of the probability of failure of high-pressure hoses, it is possible to determine the possible residual life of pipelines and the need for their replacement. This method can be used to determine the probability of failure of other elements of the hydraulic drive, such as hydraulic cylinders, hydraulic valves, pumps, and others.

SOME ASPECTS OF INFLUENCE OF THE CONNECTING ROD DESIGN ON THE OUTPUT PARAMETERS OF HIGH-SPEED INTERNAL COMBUSTION ENGINES

A comparative analysis of the stress-strain state of the connecting rods with a traditional I-beam and H-beam rod profiles was performed in order to compare various designs of the connecting rods and identify the factors that affect the main parameters of the internal combustion engine. Using the finite element simulation, it was found that the H-beam conrod has a much greater transverse bending rigidity, but is inferior to the I-beam profile conrod in terms of its mass. The calculations also determined that the frequency of natural oscillations of the H-beam profile conrod is significantly higher as well, what was confirmed by the testing on high-speed engines. The obtained data on piston operation with the H-beam conrod concluded that a more rigid connecting rod makes it possible to exclude transverse oscillations, reduce mechanical losses and improve the characteristics of the engine.