Oscillatory Systems Research Articles

METHODS FOR CALCULATING FREE OSCILLATIONS OF BEAM SYSTEMS

Some methods for calculating free oscillations of mechanical systems with distributed parameters are described with the implementation of these methods on a concrete example. Systems may include point masses and springs. Methods of direct integration of the free oscillation equation, the method of initial parameters and the finite element method are considered. Recommendations to algorithm and calculations of natural frequencies and modes are given. For the finite element method, the influence of the number of elements on the accuracy of determining the spectrum of natural oscillations is investigated.

Low Frequency Oscillation Suppression Strategy in New Power System Based on Virtual Synchronous Generator

With the blend of massive new energy into power network systems, the inertia and damping features of new power systems are reduced, which is prone to cause low-frequency oscillations (LFO) in the power systems. Virtual synchronous generators (VSG) have received widespread attention by simulating the external characteristics of synchronous generators (SG) to enhance the inertia of new power systems and help suppress low-frequency oscillations. By analyzing the mathematical model of VSG, the control links of each part of VSG are established, the traditional reactive power-voltage (Q-V) of VSG is improved, and the formulas of active voltage control and reactive power control droop coefficient are deduced.Finally, a simulation model of VSG is created by MATLAB/Simulink platform, and new methods for suppressing LFO in power systems are compared and analyzed. The correctness of the formula and the improvement effect of reactive power and voltage control are verified.

The linear response of stellar systems does not diverge at marginal stability

ABSTRACT The linear response of a stellar system’s gravitational potential to a perturbing mass comprises two distinct contributions. Most famously, the system will respond by forming a polarization ‘wake’ around the perturber. At the same time, the perturber may also excite one or more ‘Landau modes’, i.e. coherent oscillations of the entire stellar system which are either stable or unstable depending on the system parameters. The amplitude of the first (wake) contribution is known to diverge as a system approaches marginal stability. In this paper, we consider the linear response of a homogeneous stellar system to a point mass moving on a straight line orbit. We prove analytically that the divergence of the wake response is in fact cancelled by a corresponding divergence in the Landau mode response, rendering the total response finite. We demonstrate this cancellation explicitly for a box of stars with Maxwellian velocity distribution. Our results imply that polarization wakes may be much less efficient drivers of secular evolution than previously thought. More generally, any prior calculation that accounted for wakes but ignored modes – such as those based on the Balescu-Lenard equation – may need to be revised.

Применение пьезокерамических преобразователей для ультразвуковой сварки синтетических тканей

The paper considers high-quality acoustic systems for ultrasonic welding of the synthetic fabrics. Materials, from which they are manufactured, are presented. Work was performed aimed at reducing acoustic power introduced into the welded products at ultrasonic welding of the synthetic fabrics. It was established that introduction of the small-sized piezo-ceramic transducers in welding the synthetic fabrics made it possible to increase efficiency and quality factors of the oscillatory system with low intrinsic losses. It is shown that to increase the ultrasonic welding productivity and reduce the acoustic power, it is necessary to design ultrasonic generators with the auto-tuning to a given oscillation amplitude. Technological opportunities are being considered of seam ultrasonic welding using the highly efficient piezo-ceramic transducers to estimate weldability of lavsan, nylon and polypropylene fabrics. Comparative productivity analysis was performed in ultrasonic welding of the synthetic fabrics using the piezo-ceramic and nickel transducers. Main parameters of modes in the ultrasonic welding of fabrics for the piezo-ceramic transducers were determined. It is shown that parameters of the mode in ultrasonic welding of the synthetic fabrics significantly affect the rate of reaching maximum temperatures in the welded joint zone and determine the heating intensity and, consequently, the welding productivity.

Parametric analysis of a two-body floating-point absorber wave energy converter

In the evolution of floating-point absorber wave energy conversion systems, multiple-body systems are gaining more attention than single-body systems. Meanwhile, the design and operation factors affecting the performance of multiple-body systems are much greater than those of single-body systems. However, no systematic study has yet been presented. In this article, a theoretical model is proposed by using a coupled oscillator system consisting of a damper-spring system to represent a two-body system (the floating body and the reacting body). Dimensionless expressions for the motion response and wave power absorption efficiency are derived. With the newly developed model, we prove that an appropriately tuned two-body system can obtain a limiting power absorption width of L/2π (L is the incident wavelength) as much as a single-body system. The generic case of a two-body system is presented with numerical simulations as an example. The results show that increasing the damping coefficient can reduce the wave frequency at which the peak of power absorption efficiency occurs. Increasing stiffness can make the wave frequencies for high power absorption efficiency move to a higher frequency region and can also make the spectrum bandwidth for high power absorption efficiency become narrower. Further, we show that the two-body system can absorb more wave energy at low wave frequencies than the single-body system.

Determining the influence of higher harmonics of nonlinear technological load in dynamic action systems

This paper considers the influence of higher harmonics in dynamic action systems due to their complex movement in the process of interaction with the technological load. The object of research is the process of propagation of oscillations in complex dynamic systems. One of the problems in the application of oscillatory processes is the consideration of higher harmonics in the overall movement of systems. To solve the problem, the idea of using a hybrid model that takes into account both discrete and distributed parameters was proposed. The resulting mathematical discrete model in the analytical equations of motion of the dynamic system preserves continuous properties in the form of wave coefficients. These coefficients in their analytical form take into account the contribution of higher harmonics of both the reactive (elastic-inertial) and active (dissipative) components of the resistance force. The studies were carried out on a model of a plant with a multimode spectrum of oscillations and a nonlinear dynamic system, which is a system with piecewise linear characteristics.A series of experimental studies with a wide variation of the change in the frequency of oscillations was carried out on the installation with a multimode spectrum of oscillations. Zones of manifestation of higher harmonics along the vertical axis of force action were revealed. The given spectrum at the exciter frequency of 35 Hz showed the manifestation of the spectrum component (around 70 Hz) along the X axis, which is an important result for practical application. For a system with piecewise linear characteristics, the manifestation of multimode, which manifests itself in the form of subharmonic and superharmonic oscillations, was determined. The contribution of each harmonic is determined by applying the obtained dependences. The results were used in the development of algorithms and calculation methods of a new class of dynamic action systems taking into account the contribution of higher harmonics

Numerical simulation along with the experimental work for an underdamped oscillator using fourth order Runge–Kutta method. An undergraduate experiment

Experiments based on oscillatory motion are an essential part of the curricula for students of physics and engineering in their undergraduate studies, such as the determination of spring constant for a well-known classical oscillator i.e., spring-mass system. Moreover, it is important for students to understand the physics of damped oscillators because, in real-world scenarios, a system involving oscillations cannot be completely analysed without understanding conditions of damped oscillations i.e., underdamped, overdamped, and critical damped. In this work, we design a computational physics lab for the simulation of the underdamped oscillator using an Excel spreadsheet by employing 4th order Runge–Kutta method. Further, we construct a simple experimental setup to observe the damped oscillation and obtaindata for the underdamped system. Final analysis was based on comparison between the experimental data and the numerically estimated data.

An improved grasshopper-based MPPT approach to reduce tracking time and startup oscillations in photovoltaic system under partial shading conditions.

Global maximum power point (GMPP) tracking under shading conditions with low tracking time and reduced startup oscillations is one of the challenging tasks in photovoltaic (PV) systems. To cope with this challenge, an improved grasshopper optimization algorithm (IGOA) is proposed in this work to track the GMPP under partial shading conditions (PSC). The performance of the proposed approach is compared with well-known swarm intelligence techniques (SITs) such as gray wolf optimization (GWO), cuckoo search algorithm (CSA), salp swarm algorithm (SSA), improved SSA based on PSO (ISSAPSO), and GOA in terms of tracking time, settling time, failure rate, and startup oscillations. For a fair comparison, the PV system is analysed under uniform irradiance and three PSCs having four to six peaks in the power-voltage characteristic curves and using three to six search agents for each SIT. For this purpose, a PV system containing six solar panels has been built using MATLAB/SIMULINK software, and statistical analysis is performed in detail. The results show that the IGOA tracks the GMPP in 0.07 s and settles the output in 0.12 s which is 25% to 96% faster than its counterparts. Moreover, IGOA proves its consistency with a minimal tracking failure rate of 0% for four to six search agents with negligible startup oscillations. This work is expected to be helpful to PV system installers in obtaining maximum benefits from the installed system.

Oscillation system of cyanobacterial circadian clock system revealed by an integral approach with SAXS, SANS and AUC

Oscillation system of cyanobacterial circadian clock system revealed by an integral approach with SAXS, SANS and AUC

Potential artifacts in conservation laws and invariants inferred from sequential state estimation

Abstract. In sequential estimation methods often used in oceanic and general climate calculations of the state and of forecasts, observations act mathematically and statistically as source or sink terms in conservation equations for heat, salt, mass, and momentum. These artificial terms obscure the inference of the system's variability or secular changes. Furthermore, for the purposes of calculating changes in important functions of state variables such as total mass and energy or volumetric current transports, results of both filter and smoother-based estimates are sensitive to misrepresentation of a large variety of parameters, including initial conditions, prior uncertainty covariances, and systematic and random errors in observations. Here, toy models of a coupled mass–spring oscillator system and of a barotropic Rossby wave system are used to demonstrate many of the issues that arise from such misrepresentations. Results from Kalman filter estimates and those from finite interval smoothing are analyzed. In the filter (and prediction) problem, entry of data leads to violation of conservation and other invariant rules. A finite interval smoothing method restores the conservation rules, but uncertainties in all such estimation results remain. Convincing trend and other time-dependent determinations in “reanalysis-like” estimates require a full understanding of models, observations, and underlying error structures. Application of smoother-type methods that are designed for optimal reconstruction purposes alleviate some of the issues.

Investigate the full characteristic of a centrifugal pump-as-turbine (PAT) in turbine and reverse pump modes

Large centrifugal pumps can generate electricity in reverse, reducing the power supply pressure of the power grid. However, S region may occurs during the operation and regulation of the pump as a steam turbine (PAT). The S region can cause unstable unit startup, not only causing hydraulic system oscillation, but also accompanied by strong vibration and noise. Understanding the characteristic curve of the S region is of great significance for improving unit stability and efficiency. Previously, the main research object in S area was small generator units. This article conducted unsteady numerical simulation and experimental research on a large centrifugal pump. Analysed the internal flow rate, blade load, entropy generation, and pressure pulsation under three special operating conditions: the optimal operating condition, runaway operating condition, and braking operating condition in the S region. In addition, a comparative analysis was conducted on three pairs of operating conditions: S region turbine mode and reverse pump mode, with opposite flow direction, similar flow rate, and the same speed. Research has found that in the S region of large centrifugal pumps, the flow chaos in the turbine mode mainly occurs in the impeller section, and the maximum pressure occurs in the stationary blade section. The flow chaos under reverse pump operation mainly occurs in the stationary blade section, and the maximum pressure occurs in the impeller section.

Improving power swing detection in the presence of doubly-fed induction generator wind farms based on setting adaptation

This article proposes a new approach to improve the security of transmission line protection by correctly detecting power swing when large-scale doubly-fed induction generator wind farms (DFIGWF) exist in the proximity of the relay. In the presence of large-scale DFIGWFs, following large disturbances, power swing may probably cause the distance protection to malfunction. This issue can also lead to widespread transmission line outage and cause instability in the power system. Therefore, a new approach is proposed to solve the challenge by adapting the power swing blocking (PSB) function in the distance protection relays and utilizing the dominant power system oscillation modes. Thus, related calculations are performed in a central module remotely connected to intelligent electronic devices (IEDs) for distance protection and stabilized against power swing. The calculation to adjust the PSB setting of the IEDs in the central module is based on the oscillation modes of the power system and the rate of change of impedance, which is influenced by the penetration rate of the DFIGWFs. Simulation studies have been done on two test systems and the results reveal that the proposed scheme significantly improves the security of distance protection against power swing under different DFIGWF intrusion conditions.

Nonlinear Perturbation of Random Matrix Theory.

We consider a system of linear oscillators, or quantum states, described by random matrix theory and analyze how its time evolution is affected by a nonlinear perturbation. Our numerical results show that above a certain chaos border a weak or moderate nonlinearity leads to a dynamical thermalization of a finite number of degrees of freedom with energy equipartition over linear eigenmodes as expected from the laws of classical statistical mechanics. The system temperature is shown to change in a broad range from positive to negative values, and the dependence of system characteristics on the initial injected energy is determined. Below the chaos border the dynamics is described by the Kolmogorov-Arnold-Moser integrability. Owing to universal features of random matrix theory we argue that the obtained results describe the generic properties of its nonlinear perturbation.

A novel methodology for a time-delayed controller to prevent nonlinear system oscillations

The paper investigates the nonlinear transversal vibrations of a cantilever beam structure in the primary resonance case. A time-delayed position-velocity control is suggested to reduce the nonlinear vibrations of the structure under consideration. A non-perturbative method (NPM) is used to get an equivalent analogous linear differential equation (DE) to the original nonlinear one. For the benefit of the readers, a comprehensive description of the NPM method is provided. The theoretical findings are validated through a numerical comparison carried out by employed the Mathematica Software. Both the numerical solutions and the theoretical outcomes showed excellent agreement. As well-known, all classic perturbation techniques use Taylor expansion, when the restoring forces are present, to expand these forces and therefore lessen the difficulty of the given problem. Under the NPM, this weakness is no longer present. Furthermore, one may examine the stability examination of the issue with the NPM something that was not possible with prior traditional techniques. The controlled linear equivalent model is examined using the multiple-scales homotopy method. The amplitude-phase modulation equations which control the dynamics of the structure at the various resonance circumstances are established. The loop-delay stability diagrams are analyzed. It is looked at how the different controller parameters impact the oscillation behaviors of the system. The obtained theoretical outcomes showed that the loop delay has an important impact on the effectiveness of the control. Therefore, the ideal loop-delay values are given and used to develop the enactment of the organized control. The completed analytical results are also numerically validated, to reveal their good correlation with the achieved theoretical new results.

Self-Vibration of a Liquid Crystal Elastomer Fiber-Cantilever System under Steady Illumination.

A new type of self-oscillating system has been developed with the potential to expand its applications in fields such as biomedical engineering, advanced robotics, rescue operations, and military industries. This system is capable of sustaining its own motion by absorbing energy from the stable external environment without the need for an additional controller. The existing self-sustained oscillatory systems are relatively complex in structure and difficult to fabricate and control, thus limited in their implementation in practical and complex scenarios. In this paper, we creatively propose a novel light-powered liquid crystal elastomer (LCE) fiber-cantilever system that can perform self-sustained oscillation under steady illumination. Considering the well-established LCE dynamic model, beam theory, and deflection formula, the control equations for the self-oscillating system are derived to theoretically study the dynamics of self-vibration. The LCE fiber-cantilever system under steady illumination is found to exhibit two motion regimes, namely, the static and self-vibration regimes. The positive work done by the tension of the light-powered LCE fiber provides some compensation against the structural resistance from cantilever and the air damping. In addition, the influences of system parameters on self-vibration amplitude and frequency are also studied. The newly constructed light-powered LCE fiber-cantilever system in this paper has a simple structure, easy assembly/disassembly, easy preparation, and strong expandability as a one-dimensional fiber-based system. It is expected to meet the application requirements of practical complex scenarios and has important application value in fields such as autonomous robots, energy harvesters, autonomous separators, sensors, mechanical logic devices, and biomimetic design.

Recurrent neural network based design of fractional order power system stabilizer for effective damping of power oscillations in multimachine system

The complexity of modern power systems has risen due to the growing demand for electricity. To mitigate this problem, the role of the electric utility in supplying safe and reliable electricity has become increasingly crucial. Low-frequency oscillations (LFOs) in a power system are an inevitable aspect. Therefore, the reliability of the system requires appropriate damping to overcome these LFOs. This paper proposes a novel design methodology for a fractional-order power system stabilizer (FO-PSS) to enhance the stability of the power system network. FO-PSS is designed to effectively dampen LFOs in both single-machine infinite bus systems (SMIB) and multi-machine power systems (MMPS). Recurrent neural network (RNN) is used to predict the parameters of proposed PSSs. To evaluate the efficacy of the proposed PSS, various test cases are considered. The results are compared to those obtained from traditional PSSs and optimization based PSSs. The effectiveness of the proposed RNN-based FO-PSS is demonstrated under diverse loading conditions.

Locomotion characteristics of a wheeled vibration-driven robot with an enhanced pantograph-type suspension.

Introduction: The paper considers the improved design of the wheeled vibration-driven robot equipped with an inertial exciter (unbalanced rotor) and enhanced pantograph-type suspension. The primary purpose and objectives of the study are focused on mathematical modeling, computer simulation, and experimental testing of locomotion conditions of the novel robot prototype. The primary scientific novelty of the present research consists in substantiating the possibilities of implementing the enhanced pantograph-type suspension in order to improve the robot's kinematic characteristics, particularly the average translational speed. Methods: The simplified dynamic diagram of the robot's oscillatory system is developed, and the mathematical model describing its locomotion conditions is derived using the Euler-Lagrange differential equations. The numerical modeling is carried out in the Mathematica software with the help of the Runge-Kutta methods. Computer simulation of the robot motion is performed in the SolidWorks Motion software using the variable step integration method (Gear's method). The experimental investigations of the robot prototype operating conditions are conducted at the Vibroengineering Laboratory of Lviv Polytechnic National University using the WitMotion accelerometers and software. The experimental data is processed in the MathCad software. Results and discussion: The obtained results show the time dependencies of the robot body's basic kinematic parameters (accelerations, velocities, displacements) under different operating conditions, particularly the angular frequencies of the unbalanced rotor. The numerical modeling, computer simulation, and experimental investigations present almost similar results: the smallest horizontal speed of about 1mm/s is observed at the supplied voltage of 3.47V when the forced frequency is equal to 500rpm; the largest locomotion speed is approximately 40mm/s at the supplied voltage of 10V and forced frequency of 1,500rpm. The paper may be interesting for designers and researchers of similar vibration-driven robotic systems based on wheeled chassis, and the results may be used while implementing the experimental and industrial prototypes of vibration-driven robots for various purposes, particularly, for inspecting and cleaning the pipelines. Further investigation on the subject of the paper should be focused on analyzing the relations between the power consumption, average translational speed, and working efficiency of the considerer robot under various operating conditions.

An Investigation into the Primary and Subharmonic Resonances of the Swing Equation

A study is conducted to obtain a deeper insight into the primary and subharmonic resonances of the swing equation. The primary resonance, which can result in increased oscillatory responses, voltage instability, and potential system collapse, happens when the external disturbance frequency coincides with the natural frequency of the system. Subharmonic resonance occurs when the disturbance frequency is an integer fraction of the natural frequency, leading to low-frequency oscillations and possible equipment damage. The purpose of this study is to provide an extension of the existing literature of the effects of primary resonance and further provide a thorough understanding of subharmonic resonance on the stability of a certain power system paradigm. Motivated by the rich nonlinear dynamical behaviour exhibited by this evergreen model, analytical and numerical techniques are employed to examine the underlying principles, creating an efficient control solution for this resonant-related problem. The main objective of this research is to provide a comprehensive understanding of the primary and subharmonic resonances considering the dynamical and bifurcational behaviour of the underlying swing equation, whereby both analytical and numerical techniques are employed, allowing for an identification of certain precursors to chaos that may lead and cater for the safe operation of practical problems.

White Rabbit Expansion Board: Design, Architecture, and Signal Integrity Simulations

The White Rabbit protocol allows synchronization and communication via an optical link in an integrated, modular, and scalable manner. It provides a solution to those applications that have very demanding requirements in terms of synchronization. Field-programmable gate arrays are used to implement the protocol; additionally, special hardware is needed to provide the necessary clock signals used by the dual-mixer time difference for precise phase measurement. In the present work, an expansion board that allows for White Rabbit functionality is presented. The expansion board contains the oscillators required by the White Rabbit protocol, one running at 125 MHz and another at 124.922 MHZ. The architecture of this board includes two oscillator systems for tests and comparison. One is based on VCOs and another on crystal oscillators running at the desired frequencies. In addition, it incorporates a temperature sensor, from where the medium access control address is extracted, an electrically erasable programmable read-only memory, a pulse-per-second output, and a USB UART to access the White Rabbit IP core at the field-programmable gate array. Finally, to ensure the quality of the layout design and guarantee the level of synchronization desired, the results of the power and signal integrity simulations are also presented.

Pinning control for stabilization of coupled stochastic strict‐feedback nonlinear systems

AbstractThis article introduces a novel class of coupled stochastic strict‐feedback nonlinear systems (CSSFNSs) whose topology is not strongly connected. We are devoted to investigating the stabilization issue of CSSFNSs via pinning control. First, the specific form of controllers is decided through the back‐stepping method and the design of virtual controllers. Second, we find a new method to construct the global Lyapunov function of CSSFNS by employing the Lyapunov function of each stochastic strict‐feedback nonlinear system (SSFNS). Meanwhile, combining Lyapunov method with graph theory, several sufficient conditions to guarantee exponential stability in mean square of CSSFNS are obtained in the form of coefficients‐type criterion. Ultimately, our theoretical results are applied to a class of coupled oscillator systems and a predator‐prey model. Furthermore, the validity and feasibility of the theoretical results are illustrated by some numerical simulations.