Natural Frequency Of System Research Articles

Optimization based Feedforward mitigation of Elastic Flexure of Distributed Parameter System due to Reference Tracking

If a large scale structure performs a rigid body motion, this motion is superposed by an elastic flexure due to its inherent elasticity. In order to mitigate the elastic motion feedforward and feedback laws can be applied. By minimizing the L2-norm of the elastic flexure subject to a reference trajectory and the elastic system description we derive a feedforward signal that attenuates elastic motions of the structure. A comparison to simplified solution approaches shows a major improvement for reference signals in the range of the system's natural frequencies.

Vibration control of submerged floating tunnel in waves and earthquakes through tuned mass damper

In this study, a passive tuned mass damper (TMD) is investigated to dampen resonant motions of a submerged floating tunnel (SFT) in waves and earthquakes. TMD is adopted to control resonant lateral motion. A time-domain dynamics simulation model that considers the elasticity of the tunnel and mooring lines is first established, which is based on the lumped mass method and Morison equation, and the SFT-TMD interaction is considered through springs and dampers. Next, by using the harmony search (HS) algorithm, TMD's spring and damping coefficients are optimized; the dynamics simulations under white noise seismic excitations are continuously carried out with updated spring and damping coefficients produced by HS rules until the designed maximum iteration number. The influence of TMD's mass is individually investigated through a parametric study. After the optimization process is completed, the global performances of SFT with and without TMD are systematically evaluated in both waves and earthquakes. It is found that TMD plays a crucial role in controlling SFT vibrations when environmental loads are close to the system's fundamental lateral natural frequency under both wave and seismic excitations. TMD also enhances the comfort of passengers and reduces static and dynamic mooring tensions. • A time-domain dynamics simulation model is built for the interaction of a submerged floating tunnel and a tuned mass damper. • The harmony search algorithm shows good optimization performance for the tuning mass damper parameters. • A tuned mass damper effectively reduces resonant motions and mooring tensions under wave and seismic excitations.

DEVELOPMENT OF A METHOD FOR CALCULATING THE PROTECTION OF PERSONAL DATA FROM THE CENTRALITY OF THE NETWORK

A mathematical model has been developed and a study of the model of personal data protection from network clustering coefficient and data transfer intensity in social networks has been carried out. Dependencies of protection of the system from the size of the system (and from the amount of personal data); information security threats from the network clustering factor. A system of linear equations is obtained, which consists of the equation: rate of change of information flow from social network security and coefficients that reflect the impact of security measures, amount of personal data, leakage rate, change of information protection from network clustering factor, its size, personal data protection. As a result of solving the system of differential equations, mathematical and graphical dependences of the indicator of personal data protection in the social network from different components are obtained. Considering three options for solving the equation near the steady state of the system, we can conclude that, based on the conditions of the ratio of dissipation and natural frequency, the attenuation of the latter to a certain value is carried out periodically, with decaying amplitude, or by exponentially decaying law. A more visual analysis of the system behavior is performed, moving from the differential form of equations to the discrete one and modeling some interval of the system existence.Mathematical and graphical dependences of the system natural frequency, oscillation period, attenuation coefficient are presented. Simulation modeling for values with deviation from the stationary position of the system is carried out. As a result of simulation, it is proved that the social network protection system is nonlinear.

ДИНАМІЧНИЙ СИНТЕЗ МОБІЛЬНОЇ ЗЕМЛЕРИЙНОЇ МАШИНИ БЕЗПЕРЕРВНОЇ ДІЇ З ЛАНЦЮГОВО-БАЛКОВИМ РОБОЧИМ ОРГАНОМ

This article depics the mobile continuous earth-moving machine dynamic model with a chain-type trenching equipment in order to determine the effect of changes in the elastic-inertial system parameters on its own resonant frequencies. The object of the research: natural resonant transmission frequencies of the soil-working working equipment drive in the mobile earth-moving continuous action machine with a chain-beam working body. The purpose of the work: to determine the system elements, in which the elastic-inertial parameters affect the lower natural resonant frequencies. To give practical recommendations on the parameter choice of such elements in order to deviate from the resonant frequency. Creation of strong, reliable and durable machines depends on the dynamic load accuracy and ways to reduce it. Modern earthmoving machine structure formation can be realized using the modular principle, but always with taking into account the full picture of possible machine loads and their drives in the process, these load magnitude and their dynamic characteristics. In accordance with the dynamic synthesis conditions, the dynamic system machine parameters should be selected so that the external load machine change frequency in its maximum productivity mode doesn’t coincide with the dynamic system natural frequency. According to the theoretical and strain gauge research results, it is established that the frequency of the first form of earth-moving machine drive torsional oscillations is close to 9 Hz. The first frequency oscillation shape has a node between the gearbox masses, which can lead to fatigue shaft destruction, joints or gears of the base tractor transmission part destruction. The frequency of the natural oscillation system is close to the traction chain link engagement frequency with the sprocket teeth in the earth-moving machine maximum productivity mode.

Smooth and robust multi-mode shaped commands

Smooth robust shaped commands with general polynomial and waveform profiles are proposed for eliminating residual vibrations in multi-mode damped systems. The command time length of the proposed commands is selectable which helps in designing an optimum command that results of a desired reduction in the induced transient vibration, utilizes the maximum input capability of the actuator, and enhances the command robustness to the uncertainties in the system parameters. The commands are generated using the system natural frequencies and damping ratios. This is attractive for complicated multi-mode damped systems where mathematical models are difficult to derive. The continuous-time profiles of the proposed commands that are based on the monomial and Fourier bases render the possibility of enhancing the robustness and smoothness in order to eliminate jerks, i.e., inrush current, and inaccurate timing and delay of the actuator. The efficacy of their performance in eliminating residual vibrations is validated using numerical simulations and experiment. Their sensitivity to system modeling uncertainties is further reduced using three different approaches; relaxing the command length, flattening the sensitivity curve at and adjacent to the modeling frequencies, and introducing virtual frequencies adjacent to the design frequencies to enhance the bandwidth of the reduced sensitivity region.

Force measurements near a natural frequency of a measurement system using inverse filters

Accurate time-resolved force measurements for complex experimental systems are important for minimizing erroneous and misleading data. These measurements become difficult when a natural frequency of the system is in or near the expected frequency domain of the time-varying force being applied. In the cases where it is not possible to avoid this occurrence, the experimenter typically abandons the setup. This work presents an inverse filter method to compensate for the dynamic response of the measurement system. A two degree-of-freedom measurement system is used to obtain force measurements with dominant forcing frequencies above and below the first natural frequency of the system. The results show that inverse filtering can be used along with digital low pass filters to correct amplification and phase shift due to the dynamic response of the measurement system to within ±4.0 of total forcing amplitude and ±5.0∘. A simple cam follower mechanism is proposed as a method of low-frequency dynamic testing.

Horizontal cyclic response of bucket caisson for offshore wind turbines in over-consolidated clay

Compared with pile foundations, bucket caisson has the advantages of convenient installation and recyclability, and is more suitable as foundation for offshore wind turbines. Horizontal cyclic response is very important for the stability analysis of bucket caisson as it suffers long-term wave loadings in service period. This study presents the results of a series of 1 g model tests under horizontal cyclic loadings in over-consolidated clay. The cumulative deformation, stiffness changes and rotation centre variation of caisson model were discussed in detail. Test results indicated that the horizontal displacement of caisson model in over-consolidated clay accumulated with the increase of cyclic number and horizontal loadings. However, the increase of horizontal displacement gradually decreases for each cycle. Based on this, an empirical equation between Tb and ζb was proposed to predict the accumulated rotation of bucket caisson in over-consolidated clay. The position of rotation centre for caisson model in this study had the tendency to move up gradually. When the caisson model was under fatigue limit state (ζb=0.4), the type of rotation changes from deep to shallow certre. Under the state of ULS/1.35 (ζb=0.6), the type of rotation is always shallow centre during the whole cyclic loadings. The unloading stiffness of caisson model decreases logarithmically and tends to be stable with the increase of loading cycles. Due to the change of unloading stiffness, the system natural frequency of bucket caisson is reduced by about 37%. This study can provide theoretical basis for the design of bucket caisson as offshore wind power foundation in over-consolidated clay.

Numerical Analysis of Picking Mechanism of Power Loom with use of Lagranges’s Method

The vibration analysis of Picking mechanism of Power loom carried numerically employing Lagranges’s Equation with treating forced vibration with multi-degree of freedom. From Lagranges’s Equation provides equation motion. The equation of motion is used to determine the natural frequency of system.

Porous Gas Journal Bearings: An Exact Solution Revisited and Force Coefficients for Stable Rotordynamic Performance

Having come of age, gas film bearings enable high-speed oil-free (micro) rotating machinery with gains in efficiency and reliability, longer maintenance intervals, and a reduction in contaminants released to the atmosphere. Among gas bearing types, porous surface gas bearings (PGBs) have proven successful for 50+ years and presently are off-the-shelf mechanical elements. This paper reviews the literature on PGBs since the 1970s and reproduces an exact solution for the performance of cylindrical PGBs. Both the analytical model and an accompanying finite-element (FE) model predict the performance for two PGBs, a commercially available 76 mm diameter bearing and a smaller 25 mm diameter laboratory unit whose experimental performance is available. As expected, the FE model results reproduce the analytical predictions obtained in a minuscule computing time. For a set external supply pressure, as the radial clearance increases, the flow rate through the bearing grows until reaching a peak magnitude. The PGB load capacity is a fraction of the product of the set pressure difference (pS − pa) and the bearing projected area with a significantly large centering static stiffness evolving over a narrow region of clearances. Operation with shaft speed enhances the bearing load capacity; however, at sufficiently high speeds, significant magnitude cross-coupled forces limit the stable operation of a PGB. At constant operating shaft speed, as the whirl frequency grows, the bearing effective stiffness (Keff) increases, while the effective damping (Ceff) becomes positive for whirl frequencies greater than 50% shaft speed. Similar to a plain hydrodynamic journal bearing, the PGB is prone to a half-frequency whirl, albeit the system natural frequency can be high, mainly depending on the external supply pressure. In essence, for the cases considered, PGBs are linear mechanical elements whose load capacity is proportional to the journal eccentricity.

Defect and damage detection in filament wound carbon composite cylinders: A new numerical-experimental methodology based on vibrational analyses

Due to its high efficiency, carbon fibre reinforced composite materials are used in many applications, including aeronautical, automotive, and civil structures. A wide range of manufacturing processes are used in composites production and each of these processes is marked by many processing parameters. However, because of the variations that are inherent to the manufacturing method, the final properties of the structure can be strongly affected, mainly the strength values. On the other hand, Vibration-Based Methods (VBM) has the advantage of simplicity and low cost, although it is very sensitive to variations in geometry and material properties. Therefore, it is strategic to deepen the research in this line to generalize the method, allowing its use in the industry as a solution to complicated real-life problems. Thus, this work presents a new numerical-experimental methodology to evaluate the effect of design parameter variations on the dynamic response of laminated composite cylinders. Numerical dynamic analyses are run via a Finite Element code, which is complemented with subroutines written in Python. A Design of Experiments (DoE) strategy is developed to reduce the number of experiments and to evaluate the effect of the design parameter variations. Three sets of nominally different composite cylinders are investigated [(90/60/-60)2/90]s, [(90/30/-30)2/90]s and [90/30/-60/60/-60/30/-30]s. System natural frequencies as taken as the primary response quantities. Frequency Response Functions (FRF) enrich the data set for more elaborate analysis. A DoE strategy is set up to deal with the range of design parameters and process parameters, a full factorial design is selected. Afterward, the results are discussed with proper attention for the potential and limitations of the proposed methodology from the perspective of usage to detect defects in real laminated composite cylinders. Finally, damage indices are calculated using the experimental FRFs magnitudes to quantify the influence of the undamaged and impact damage structure. The general conclusion is that the new methodology provides the foundations for the next generation of software systems for detecting defects from the manufacturing process and damage caused in-service of real composite structures.

A multibody dynamic model for predicting operational load spectra of dual clutch transmissions

In this paper, a generalized nonlinear time-varying multibody dynamic model of dual clutch transmissions (DCT) is presented. The model consists of clutches, shafts, gears and synchronizers, and can be used to model any DCT architecture. A nonlinear clutch model is used to determine the transmitted power to the transmission at any speed and clutch temperature. The clutch can be a single- or multi-plate clutch and can operate in a wet or dry-clutch configuration. A combined kinematic and powerflow simulation enables calculation of gear, shaft, bearing and clutch quasi-static loads as well as gear mesh frequencies following a duty cycle as the input. For the corresponding Linear-Time-Invariant (LTI) system model, natural frequencies and mode shapes are obtained by solving the eigenvalue problem. The modal summation technique is used to determine the steady state forced vibration response of the system. For the corresponding NTV system, Newmark's time-step marching based integration is used to determine both the steady state and transient forced vibration response of the system. The DCT model is exercised using a common transmission architecture operating at several different operating conditions. The resulting impact of changing operational conditions on gear and bearing loads as well as dynamic transmission error spectra are demonstrated.

Impact of Geotechnical Uncertainty on the Preliminary Design of Monopiles Supporting Offshore Wind Turbines

AbstractThe growing demand for clean renewable energy sources and the lack of suitable nearshore sites are moving the offshore wind industry toward developing larger wind turbines in deeper water locations further offshore. This is adding significant uncertainty to the geotechnical design of monopiles used as foundations for these systems. Soil testing becomes more challenging, rigid monopile behavior is less certain, and design methods are being applied outside the bounds of the datasets from which they were originally derived. This paper examines the potential impact of certain elements of geotechnical uncertainty on monotonic load–displacement behavior and design system natural frequency of an example monopile-supported offshore wind turbine (OWT). Geotechnical uncertainty is considered in terms of spatial variability in soil properties derived from cone penetration tests (CPT), parameter transformation uncertainty using the rigidity index, and design choice for subgrade reaction modeling. Results suggest that spatial variability in CPT properties exhibits limited impact on design load–displacement characteristics of monopiles as vertical spatial variability tends to be averaged out in the process to develop discrete soil reaction-lateral displacement (p-y) models. This highlights a potential issue whereby localized variations in soil properties may not be captured in certain models. Spatial variability in CPT data has a noticeable effect on predicted system frequency responses of OWTs employing a subgrade reaction model approach, and the influence of subgrade reaction model choice is significant. The purpose of this paper is to investigate the effect of uncertainty in soil data, model transformation, and design model choice on resulting structural behavior for a subset of available design approaches. It should be noted that significant further uncertainty exists and a wide variety of alternative models can be used by designers, so the results should be interpreted qualitatively.

Fault line selection research of single phase grounding circuit based on improved Hilbert-Huang transform

For single-phase ground fault in resonant grounded power supply system, it is difficult to detect the fault line, while the existing methods have the shortcomings such as slow speed and large amount of computation. In our work the system natural oscillation wave contained in the zero sequence current is found to have opposite polarity and greater amplitude in fault line compared to that in non-fault line, and is proved to have a corresponding relationship with the first intrinsic mode function (IMF1) extracted from the same zero sequence current by empirical mode decomposition (EMD) of (Hilbert-Huang transform (HHT). Therefore, a new method for determining the single-phase ground fault line is proposed by finding the IMF1, extracted from the zero sequence current of each line by EMD of HHT, with the largest amplitude and opposite polarity compared to that of other lines. Meanwhile, EMD algorithm is improved to further enhance the fault detection rate based on the system natural oscillation wave's frequency and its attenuation trend in resonant grounding system. Simulation experiment and real data analysis indicate that the mentioned method is correct and fast.

Dynamic impedances and load carrying mechanism for skirted foundations

Dynamic impedances of foundations include dynamic stiffness and damping which have important effect on the internal forces in the structure. In some cases, such as offshore wind turbines, the influence of the foundation impedances on the system's natural frequency and overall damping could potentially have a significant effect on the fatigue life of the structure. The vertical, horizontal and rocking impedances of a skirted foundation (also termed bucket foundation in offshore wind industry) embedded in a fully saturated poroelastic seabed are addressed in this paper. The vertical impedance is most relevant for jacket foundations supported on three or four bucket foundations, while horizontal and rocking impedances are applicable for mono-bucket foundations. The dynamic vibration problems are solved semi-analytically with the help of dual integral equations and Green's functions. Numerical results for dynamic impedances are obtained; damping ratio are also obtained to show the importance of radiation damping for bucket foundations, even at very small excitation frequencies. The influence of length-to-radius ratio, Poisson's ratio, permeability of soil, excitation frequency and thickness-to-radius ratio on the impedances are also studied. Besides, the dynamic load sharing among the top plate, bucket shaft and bucket tip is obtained for vertical load, horizontal load and moment to shed light on the carrying mechanism of bucket foundation at dynamic working loads. It is found that for a rigid bucket foundation, even when the length-to-radius ratio is small (e.g. l/a = 1.0), most of the loads are carried by the shaft, while the top plate and tip of the bucket take only a small portion of the loads. The results of this study will be helpful for understanding the load-carrying mechanism of offshore bucket foundations for normal operation conditions.

SERBEST DİSPLEYSIRLI BİR STİRLİNG MOTORUNUN NODAL TERMODİNAMİK VE DİNAMİK ANALİZİ

In this study, the dynamic and thermodynamic features of free displacer Stirling engines were investigated by preparing a simulation program. The dynamic component of the simulation program involves the movement equations of power piston, crankshaft and displacer. The thermodynamic component is a nodal analysis based on 24 nodal volumes. The study indicates that starting these engines requires an initial speed is required as the displacer system natural frequency. While the engine is running, the displacer exhibits some secondary vibrations (named as beatings) and causes irregularities in its work and power generation however, it can be minimized by changing some working parameters such as displacer mass, working fluid mass, external loading, spring constant etc. For each value of the working fluid charging pressure, a different spring is needed. While the spring constant is the same, the displacer mass can vary in a limited range. The thermal performance of the engine increases as the displacer mass is decreasing. For an engine working between 1000 K heater temperature, 356 K cooler temperature and 18 bar charging pressure, the effective thermal efficiency ranges between 21 and 26 %. An engine with a 3.5 liter total inner volume is capable of generating about 3.9 kW effective power and 4.7 kW indicated power. A strong relation is observed between engine performance and phase angle.

Study on electromechanical coupling torsional resonance characteristics of gear system driven by PMSM: a case on shearer semi-direct drive cutting transmission system

In this paper, the electromechanical coupling torsional resonance characteristics of the multistage gear transmission system driven by the low-speed and high-power permanent magnet synchronous motor (PMSM) are studied. Considering the PMSM electromagnetic effect and bending-torsional vibration characteristics, the mechanical-electromagnetic coupling dynamic model suitable for the speed change process is established. Then, the PMSM electromagnetic stiffness and damping characteristics are analyzed through theoretical derivation. On the basis of electromagnetic stiffness, the influence law of electromagnetic effect on the gear transmission system natural frequency and vibration characteristics is revealed systematically. By both of Campbell diagram and modal energy distribution, the potential resonance points under the influence of internal and external excitation are initially acquired. Ultimately, the potential resonance points are identified by frequency sweep analysis and time domain simulation, and the energy concentration components at resonance point are further analyzed. The results show that the electromagnetic effect reduces the first-order natural frequency and has little influence on others. Moreover, the semi-direct drive cutting transmission system in this paper has the resonance risk caused by the gear time-varying meshing stiffness when the PMSM speed is close to 330 r/min, which should be paid more attention in actual operation. This study can provide some guidance for the design and speed regulation of the gear drive system driven by high-power PMSM.

Multi-Objective Optimization Design of Natural Frequency of Two-Degree-of-Freedom Fast Steering Mirror System

In the design of two-degree-of-freedom (2-DOF) fast steering mirror (FSM) system, in order to improve the control bandwidth of the system, the low-order natural frequency in the working direction should be reduced as much as possible, and the high-order natural frequency in the non-working direction should be increased. In this paper, a deep-cut flexure hinge mirror system was studied. Firstly, the motion direction of the first to third order natural vibration mode of the system was analyzed. Next, the working stiffness in the third vibration mode direction was deduced to solve the problem that the traditional stiffness calculation method is not suitable for the third vibration mode direction. Then, the energy method and the Castigliano’s second theorem were used to analyze the working stiffness of the deep-cut flexure hinge. Next, the formula for calculating the relationship between the thickness of the mirror and the moment of inertia in the direction of the vibration mode was derived. Combined with the calculation formula of working stiffness in the vibration mode direction, the formula of the first to third order natural frequencies was derived, and the finite element verification and sensitivity analysis of structural parameters were carried out. Finally, by using NSGA-II, a multi-objective optimization design was carried out on the first to third natural frequencies of the system with hinge structure parameters and reflector thickness as independent variables, and the optimization results were analyzed by theoretical calculation and finite element simulation verification. The results show that the first and second-order natural frequencies of fast steering mirror system are reduced by 7.8% and 7.11%, and the third-order natural frequencies are increased by 139.8%. It proves that the optimized structure is much better than the original structure, and the optimal calculation can effectively increase the control bandwidth of the system

Behavior of linear compliant mechanism using numerical and experimental method

In today's fast-moving and competitive world, the engineering applications are evaluated based on the precise and accurate results. The intense need for precision motion is achieved with the help of deflection of beams in compliant mechanism. A special class of mechanism is referred to as compliant mechanisms that are based on the rigidity and mobility of a component, which lead to greater precision without affecting its accuracy. Major failures of compliant mechanism are due to in plane and out of plane movement of compliant beams for the repetitive use. Life of compliant mechanism needs to improve for large deflection values. Motion is created by molecular deformation with bending of beams in elastic zone. Compliant mechanism are used in modern techniques such as micro-nano processing microscopy, biomedical scanner are existing mechanisms for precision scanning. Available biomedical scanner is using ball screw mechanism to achieve X directional and Y Directional scanning range. Ball screw mechanism provides 0.5 mm displacement in single stroke which takes so much times to stabilize the image. Compliant mechanism provides displacement of 0.1 mm in step. Biomedical scanner required X and Y Direction scanning range of 6 mm which we can achieve by using compliant mechanism. In present paper Experimental and Numerical analysis of compliant mechanism is done for linear motion which is used in biomedical scanner. Static structural analysis on Compliant mechanism is performed to get linear displacement values with steel, Titanium alloy and Aluminium alloy. Modal analysis of Compliant mechanism is performed to get natural frequency of system with steel, Titanium alloy and Aluminium alloy for better stability of mechanism we can operate Compliant system below that resonance frequency. By using Compliant mechanism we will get smooth range of motion over ball screw mechanism.

Efficacy of ancillary fluid injection technique for mitigation of vortex rope in hydraulic turbines: A review

Penetration of variable renewable energy into the electric grid requires parallel employment of power generation sources that can quickly balance the fluctuation in frequency of electric grid. Hydro power, being one of the most flexible power supplies, thus takes on an instrumental role in balancing the grid. However, in hydraulic turbines such flexibility is achieved at the expense of departure from turbine operation at the best efficiency point (BEP). Turbine operation at off-design conditions like part load (PL) or high load (HL) results in significant flow instability in the draft tube. Of particular prominence is the vortex breakdown phenomenon which manifests as a precessing vortex rope in the draft tube. The vortex rope causes dynamic pressure fluctuations in the system, additive to the compromise in efficiency. If resonant with the system natural frequency, these pressure fluctuations may affect the mechanical torque delivered by the turbine and cause a phenomenon called power swing. As such it is of paramount importance to circumvent the effects of the rope. Amidst many techniques developed by various investigators for mitigation of the rope, particularly recent the ancillary fluid injection technique exhibits promise. Ancillary fluid injection involves riddance of the stagnation zone that leads to rope formation, through transfer of momentum from a fluid injected at an appropriate location and velocity. This is usually accomplished using water. Admission of air for flow aeration is another method. An experimental as well as numerical perspective of these techniques as developed by various researchers is laid, to assess the benefit obtained alongside the entailing compromise.

METHOD OF CALCULATING THE PROTECTION OF PERSONAL DATA FROM THE NETWORK CLUSTERING FACTOR

A mathematical model has been developed and a study of the model of personal data protection from network clustering coefficient and data transfer intensity in social networks has been carried out. Dependencies of protection of the system from the size of the system (and from the amount of personal data); information security threats from the network clustering factor. A system of linear equations is obtained, which consists of the equation: rate of change of information flow from social network security and coefficients that reflect the impact of security measures, amount of personal data, leakage rate, change of information protection from network clustering factor, its size, personal data protection. As a result of solving the system of differential equations, mathematical and graphical dependences of the indicator of personal data protection in the social network from different components are obtained. Considering three options for solving the equation near the steady state of the system, we can conclude that, based on the conditions of the ratio of dissipation and natural frequency, the attenuation of the latter to a certain value is carried out periodically, with decaying amplitude, or by exponentially decaying law. A more visual analysis of the system behavior is performed, moving from the differential form of equations to the discrete one and modeling some interval of the system existence. Mathematical and graphical dependences of the system natural frequency, oscillation period, attenuation coefficient are presented. Simulation modeling for values with deviation from the stationary position of the system is carried out. As a result of simulation, it is proved that the social network protection system is nonlinear.