Oscillations Of Pendulum Research Articles

Taming non-stationary chimera states in locally coupled oscillators

The imperfect traveling chimera (ITC) state is a novel non-stationary chimera pattern in which the incoherent domain of oscillators spreads into the coherent domain. We investigate the ITC state in locally coupled pendulum oscillators with heterogeneous driving forces. We introduce the heterogeneous phase value in the driving forces by two different ways, namely, the random phase from uniform distribution and random phase directions with identical amplitude. We discover two transition mechanisms from ITC to coherent state through traveling chimera-like state by taking the two different phase heterogeneity. The transition phenomena are investigated using cylindrical and polar coordinate phase spaces. In the numerical study, we propose a quantitative measurement named "spatiotemporal consistency" strength for distinguishing the ITC from the traveling one. Our research facilitates the exploration of potential applications of heterogeneous interactions in neuroscience.

Investigation of internal resonance on widening the bandwidth of energy harvester based on a cantilevered double pendulum structure

With the development of small-scale electronic elements and wireless sensor networks, energy harvesting technologies have attracted much attention because they can offer environment-friendly, long-lifetime, and no replacement requirements. However, energy harvesting techniques for collecting ultralow frequency vibrations remain a challenge because of the ultralow frequency, low excitation amplitude, and non-continuous vibrations. This study proposes an ultralow frequency broadband energy harvester based on a double-pendulum structure and cantilevered beam, which utilizes the internal resonance to widen the bandwidth of the energy harvester. The double pendulum oscillator with appropriate parameters can yield two resonance frequencies in an ultralow frequency band (from 1 to 5 Hz). The cantilevered beam can achieve 1:2 internal resonance with the double pendulum oscillator in the second resonance frequency of the double pendulum oscillator. The experiment result shows that the internal resonance vibration piezoelectric energy harvester based on a double-pendulum structure can obtain a bandwidth of 4.4 Hz under 0.4 g excitation.

On Oscillations of Connected Pendulums with Cavities Filled by Homogeneous Fluids

We consider the problem and normal oscillations (eigenoscillations) of the system of three connected (coupled to each other) pendulums with cavities filled with one or several immiscible homogeneous fluids. We study the case of partially dissipative system where the cavity of the first pendulum is completely filled with two ideal fluids, the cavity of the second one is filled with three viscous fluids, and the cavity third one is filled with one ideal fluid. We use methods of functional analysis. We prove the theorem on correct solvability of the initial-boundary value problem on any interval of time. We study the case of eigenoscillations of conservative system where all fluids in cavities of pendulums are ideal and the friction in joints (points of suspension) is not taken into account. We consider in detail three auxiliary problems on small oscillations of single pendulums with three above variants of fluids in cavities.

Decayless longitudinal oscillations of a solar filament maintained by quasi-periodic jets

Context. As a ubiquitous phenomenon, large-amplitude longitudinal filament oscillations usually decay in 1–4 periods. Recently, we observed a decayless case of such oscillations in the corona. Aims. We try to understand the physical process that maintains the decayless oscillation of the filament. Methods. Multiwavelength imaging observations and magnetograms were collected to study the dynamics of the filament oscillation and its associated phenomena. To explain the decayless oscillations, we also performed one-dimensional hydrodynamic numerical simulations using the code MPI-AMRVAC. Results. In observations, the filament oscillates without decay with a period of 36.4 ± 0.3 min for almost 4 h before eruption. During oscillations, four quasi-periodic jets emanate from a magnetic cancellation site near the filament. The time interval between neighboring jets is ∼68.9 ± 1.0 min. Numerical simulations constrained by the observations reproduced the decayless longitudinal oscillations. However, it is surprising to find that the period of the decayless oscillations is not consistent with the pendulum model. Conclusions. We propose that the decayless longitudinal oscillations of the filament are maintained by quasi-periodic jets, which is verified by the hydrodynamic simulations. More importantly, it is found that, when it is driven by quasi-periodic jets, the period of the filament longitudinal oscillations also depends on the driving period of the jets, not on the pendulum period alone. With a parameter survey in simulations, we derived a formula by which the pendulum oscillation period can be derived using the observed period of decayless filament oscillations and the driving periods of jets.

The investigation of a physical pendulum motion, which move along a horizontal axis

The article presents a study of the physical pendulum, taking into account the force of friction in the kinematic pair, as a result of which oscillations are damped. Graphs of the dependence of the pendulum deflection angle α and the angular velocity on time for different values of the velocity v have been given. It has been established that the speed of the sleeve significantly reduces the amplitude and angular velocity of the pendulum, and the frequency of its oscillations does not depend on the presence of dry friction in the system. The dependences of the change in the amplitude of pendulum oscillations have been given and the results of numerical integration of the differential equation of pendulum motion have been obtained. The graphical dependences of the pendulum deflection angle and the movement of the sleeve x along the horizontal axis from time to time have been obtained at different values of the coefficient of friction. It has been found that during the first five seconds of the system movement, the axial speed of the sleeve is practically independent of the coefficient of friction (at f = 0.3… 0.5). To verify the obtained results, an experimental laboratory installation has been designed and manufactured. Theoretical studies are satisfactorily consistent with experimental data, with an error not exceeding 16%. The obtained dependencies can be used in the design and study of various mechanisms, the motion of which is described by similar differential equations. Such mechanisms include inertial conveyors, the gutter of which performs in addition to longitudinal and transverse oscillations. In addition, the proposed technique can be used in the study of the motion of bulk materials in an inclined cylinder, which performs torsional oscillations around the axis of symmetry.

The investigation of a physical pendulum motion, which move along a horizontal axis

The article presents a study of the physical pendulum, taking into account the force of friction in the kinematic pair, as a result of which oscillations are damped. Graphs of the dependence of the pendulum deflection angle α and the angular velocity on time for different values of the velocity v have been given. It has been established that the speed of the sleeve significantly reduces the amplitude and angular velocity of the pendulum, and the frequency of its oscillations does not depend on the presence of dry friction in the system. The dependences of the change in the amplitude of pendulum oscillations have been given and the results of numerical integration of the differential equation of pendulum motion have been obtained. The graphical dependences of the pendulum deflection angle and the movement of the sleeve x along the horizontal axis from time to time have been obtained at different values of the coefficient of friction. It has been found that during the first five seconds of the system movement, the axial speed of the sleeve is practically independent of the coefficient of friction (at f = 0.3… 0.5). To verify the obtained results, an experimental laboratory installation has been designed and manufactured. Theoretical studies are satisfactorily consistent with experimental data, with an error not exceeding 16%. The obtained dependencies can be used in the design and study of various mechanisms, the motion of which is described by similar differential equations. Such mechanisms include inertial conveyors, the gutter of which performs in addition to longitudinal and transverse oscillations. In addition, the proposed technique can be used in the study of the motion of bulk materials in an inclined cylinder, which performs torsional oscillations around the axis of symmetry.

CALCULATION OF A TRAJECTORY FOR THE MOVEMENT OF A LOAD OF SWINGING SPRING

Pendulum oscillations in the vertical plane of a suspended weightless spring, while maintaining the straightness of its axis, are considered. In the literature, this type of pendulum is called a swinging spring. The required trajectory of the load of the swinging spring is modeled using a computer using the values ​​of the mass of the load, the stiffness of the spring and its length without load. In addition, the initial values ​​of the parameters for initiating oscillations of the oscillating spring are used: the initial angle of deviation of the spring axis from the vertical, the initial rate of change of this angle, as well as the initial parameter of the spring elongation and the initial rate of change of the elongation. The calculations were performed using the Lagrange equation of the second kind. Variants of finding conditionally periodic trajectories of movement of a point load of a swinging spring with a movable attachment point are considered.
 The relevance of the topic is determined by the need to research and improve new technological schemes of mechanical devices, which include springs. In particular, the study of the conditions for separating from chaotic vibrations of mechanical structure elements and determining the rational values ​​of parameters to ensure periodic trajectories of their vibrations.
 Calculation options are given to obtain periodic trajectories of cargo movement, when the given parameters are:
 - the length of the spring without load and its stiffness with an unknown value of the mass of the load;
 - the length of the spring without load and the value of the mass of the load with an unknown spring stiffness;
 - the value of the mass of the load and the stiffness of the spring with an unknown length of the spring without load.
 The results can be used as a paradigm for studying nonlinear coupled systems, as well as for calculating options for mechanical devices, when it is necessary to dissociate themselves from chaotic movements of loads, and provide periodic trajectories of their movement.

Studi Eksperimen Bandul dalam Menentukan Percepatan Gravitasi Bumi dan Memahami Konsep Gerak Harmonik Sederhana

This research is a pendulum experimental study in determining the acceleration of Earth's gravity and understanding the concept of simple harmonic motion. This research was conducted at the Physics Laboratory of the University of Muhammadiyah Lamongan. This study aims to examine the benefits of conducting pendulum experiments with the simple pendulum swing method and in determining the acceleration of Earth's gravity, the period of oscillation and concepts in simple harmonic motion with variations in the mass of the pendulum, namely 150 grams, 75 grams and 35 grams. The results of the analysis of this study obtained the acceleration of Earth's gravity 9.79 m/s where the mass and length of the pendulum do not affect the value of gravity. While in simple harmonic motion in the form of pendulum oscillation is influenced by the length of the string. The pendulum oscillation will experience energy dissipation in maintaining its equilibrium position due to the gravity of the earth.

Galerkin method, ansatz method, and He’s frequency formulation for modeling the forced damped parametric driven pendulum oscillators

The forced damped parametric driven pendulum oscillators are analyzed numerically via the Galerkin method (GM) and analytically using both ansatz method (AM) and He’s frequency formulation. One of the most important features of the obtained numerical approximation using GM is that it can recover a large number of different oscillators related to the problem under study. Moreover, the mentioned equation is solved analytically via both AM and He’s frequency formulation. Also, the analytical approximations can recover many different oscillators related to the problem under consideration. Both analytical and numerical approximations are compared with each other and with Runge–Kutta (RK) numerical approximation by estimating both maximum global distance and residual errors. The proposed method can help many authors interested in studying the dynamic problems to explain the mechanics of oscillating to different oscillators in physics, plasma models, engineering, and biological systems.

The Stone Guest. The Soviet Rediscovery of Formal Linguistics Towards the Early Chomsky

After Stalin’s death, Soviet linguistics seemingly steered in a new direction, enthusiastically adopting mathematical methods within the upsurge of interest in machine translation. This fostered the acceptance of formal models disjointed from the rigid dictates of dialectical materialism and paved the way for the rediscovery of the scientific legacy of (post-)structuralist Euroamerican schools. In the eyes of the protagonists of this epistemological change, linguistics seemed to be freed from the traditional methodological constraints imposed by philology and literature. This short-lived yet intense period, however, is characterized by the polyphonic coexistence of several ideas and personalities, whose research activity can be properly understood and evaluated only from a broader historical perspective, encompassing both earlier and later stages, thus substantially curtailing the explanatory power of historical and thematic periodization. The study aims at examining the salient characteristics of the scientific environment surrounding the early critical reception of Noam Chomsky’s Syntactic Structures in the Soviet Union. By tackling specific terminological and epistemological issues, it is argued that the evolution of Soviet linguistics was not defined by abrupt saltational processes, but rather by a constant pendular oscillation which – depending on cultural, political, and historical circumstances – would grant temporary priority to some scientific approaches and orientations at the expense of others.

Study of adaptive control law of overhead crane using its model

Nowadays, cargo cranes are widely used in various areas of industries. Many of cranes use suspended load fastening, which is associated with load swinging during transportation. Load swinging is most often caused by acceleration or deceleration of the crane trolley, less often it occurs due to external disturbances, such as wind. One of the key directions of the development of this kind of cranes is the development of an automated control system that can dampen pendular oscillations of the load. At present, a considerable number of control systems have been developed, but most of them require preset adjustment of specific parameters of the transported load. The task of this study is to develop and debug a control algorithm using a model of an overhead crane of previously developed adaptive control law that can provide fine positioning and damping of load oscillations under the current parametric uncertainty. The study using the pilot plant will allow us to determine and analyze the features of the implementation of the control law before its application for industrial cranes. An adaptive control law is studied using the model of overhead crane under conditions of a current parametric uncertainty of the load and external disturbances. This control method is based on an adaptive control approach with an identifier and an implicit reference model using “simplified” adaptation conditions. A previously developed adaptive control law for an overhead crane is described. An experimental model of an overhead crane is described. An algorithm for adaptive control of an overhead crane model has been developed. The first experimental studies of the proposed control method have been carried out. They confirm its performance in real conditions. The results of experimental tests have shown the effectiveness of the adaptive control law. The system ensures fine motion of the load in a short period of time, dampens the pendular oscillations of the load during acceleration and deceleration of the trolley, as well as during external disturbances. The adaptive control law allows you to move the load to the designated position and dampen the pendular oscillations with minimal preset adjustment of the control system. Since the identification of parameters occurs at the current time, the changes of the parameters of the load and the length of suspension do not affect the quality of control.

Time dependent nature of the Neptune’s arc configuration

By distinguishing the main arc Fraternite from the minor arcs Egalite (2,1), Liberte, Courage, the conservative restricted three-body system is extended to a non-conservative restricted four-body system with the central body Neptune S, the primary body Galatea X, a minor body Fraternite F, and a test body s. Through the equations of motion, it is shown that the locations where the force is null (null points) along the orbit of s correspond to the locations of Egalite (2,1), Liberte, and Courage. Even if all the arcs were captured by three-body CER sites initially, the orbits over the CER potential maxima would be unstable for the minor arcs due to the disturbing force of Fraternite with finite mass, allowing them to be relocated to the four-body null points. On the other hand, the minor arcs do not have the mass to destabilize Fraternite from its three-body CER site, which is enlarged from 8.37 degrees to 9.7 degrees thus accounting for the Fraternite’s span. In this non-conservative restricted four-body system, s is under the effects of the potentials of X and F, therefore the null points are not absolutely stable as the Lagrangian points. The potential of X drives a long period harmonic pendulum oscillation through Φ s x = [ ( n + 1 ) θ s − n θ x − ϕ s ] centered over a four-body null point with T = 1 , 000 d , while the potential of F drives a much longer period singular pendulum oscillation through Δ θ s f centered over Fraternite with T f = 40 , 000 d . In this four-body system, the dynamics of these two oscillations generates a time alternating symmetric arc configuration about Fraternite with a century long time scale. The non-conservative nature of this system could account for the time varying intensity, configuration, and disappearance of the minor arcs.

Centrifugal controller of rotation frequency for vertical axis wind turbines

The market for small vertical axis wind turbines (VAWTs) continues to grow rapidly, filling up especially the low wind potential locations. Since the Saudi Government has announced to install 9 GW of wind power by 2032, this ambitious plan could be at least partially improved by the small wind turbines, taking into account the low annual mean wind speed on the most Kingdom of Saudi Arabia territory.However, the safety and durability of most commercially available VAWTs have not been adequately addressed with respect to the turbine over speed in high wind speed conditions.The presented research gives a methodology for calculating a cost-effective dynamic braking controller, based on a centrifugal mechanical activation spring-load mechanism with a pendulum. The analysis is focused on a small two-tier 3 kW Darrieus VAWT, where a mechanically activated friction brake is deployed as the turbine rotational speed approaches a red line. The proposed method makes a small turbine absolutely safe on any available wind speed and/or during accidental electric load switch off. The analysis was made for a typically high continental wind speed of 25 m/s.The paper presents the calculation model in VisSim software. Controller parameters were developed as the result of the research conducted on a functional turbine of the specific size in the model. The experiments covered two different cases: with a relatively low spring stiffness coefficient (400 N/m), showing the periodical oscillations of a controller pendulum on the cut-out speed and a high spring stiffness coefficient (4000 N/m), which the VAWT rotor can be surely braked at.The paper is intended to provide the mathematical basis for the scientific analysis, as well as providing practical implementation information to engineers building similar turbines, including Savonius, Darrieus, H-Darrieus, helix shape, V-type, and any other types of rotating rotors. The estimated capacity utilization factor (CUF) of any VAWTs, when using the proposed centrifugal mechanical controller, can be increased twice to 82% for on-land small VAWTs.

Comprehensive observations on pendulum oscillation using stereo vision

We have developed a stereo vision system for observing real objects for experimental physics demonstration. The stereo vision observes objects from two different points of view. An observer can identify the distance and velocity of an object based on at least two different points of view. This paper demonstrates our comprehensive observation in a pendulum oscillation experiment to test the stereo vision system where a stereo camera is in a forward view position. The stereo camera produces stereo images. We use automatic object tracking techniques to obtain the 3D position of the pendulum in real space based on the sequential stereo images of the pendulum movement. The experimental results in a 3D graph that shows the trajectory of the pendulum oscillation. We confirm the common understanding of the oscillation movement by obtaining the graph of the pendulum oscillation as a function of time. We can obtain the oscillation motion parameters such as amplitude, angular frequency, frequency, period, and initial phase. Also, we can show the damping oscillation phenomena and the damping factor.

Analytical and experimental analyses of nonlinear vibrations in a rotary inverted pendulum

Gaining insight into possible vibratory responses of dynamical systems around their stable equilibria is an essential step, which must be taken before their design and application. The results of such a study can significantly help prevent instability in closed-loop stabilized systems by avoiding the excitation of the system in the neighborhood of its resonance. This paper investigates nonlinear oscillations of a rotary inverted pendulum (RIP) with a full-state feedback controller. Lagrange’s equations are employed to derive an accurate 2-DoF mathematical model, whose parameter values are extracted by both the measurement and 3D modeling of the real system components. Although the governing equations of a 2-DoF nonlinear system are difficult to solve, performing an analytical solution is of great importance, mostly because, compared to the numerical solution, the analytical solution can function as an accurate pattern. Additionally, the analytical solution is generally more appealing to engineers because its computational costs are less than those of the numerical solution. In this study, the perturbative method of multiple scales is used to obtain an analytical solution to the coupled nonlinear motion equations of the closed-loop system. Moreover, the parameters of the controller are determined using the results of this solution. The findings reveal the existence of hardening- and softening-type resonances at the first and second vibrational modes, respectively. This leads to a wide frequency range with moderately large-amplitude vibrations, which must be avoided when adjusting a time-varying set-point for the system. The analytical results of the nonlinear vibration of the RIP are verified by experimental measurements, and a very good agreement is observed between the results of both approaches.

Влияние искровых разрядов на множественные соударения двух стальных шаров в колыбели Ньютона

The spark discharges influence on multiple collisions of two balls in Newton’s cradle was studied experimentally. The single pendulum dynamics without collisions as well as the dynamics of two pendulums with collisions was video-recorded. A non-monotonic oscillations' damping of the pendulums (the so-called beating effect) was observed both in collisions with spark discharges and without them. The pendulum oscillations' damping was investigated. It was found that collisions between balls increase the damping coefficient, and spark discharges decrease the damping coefficient.

Адаптивное управление мостовым краном по скорости перемещения тележки

A method is proposed for automatic control of the speed of an overhead-type crane trolley with direct tracking of the horizontal movement of load in conditions of current uncertainty of load parameters and external disturbances. The purpose of the control is to find the precise positioning of the transported cargo with the damping of its pendulum oscillations and the parrying of external disturbances. The dynamics of an overhead crane when moving a trolley along one axis is described. The proposed control method is based on an adaptive control scheme with an identifier and an implicit reference model using «simplified» adaptability conditions. The stability of a closed control system is proved and the conditions for this are determined. For the current identification of load parameters, the recursive least squares method with a forgetting factor is used. This control method was developed specifically for research and debugging on an experimental layout, so all the parameters of the crane and load were approximated to the layout during calculations. The results of computer simulation the proposed control method with different mass-inertial properties of the load, the length of its suspension and perturbations in the Matlab Simulink software environment are presented. The results showed the high efficiency of the proposed adaptive control system. It ensures accurate movement of the load in a short period of time, prevents the load from swinging during acceleration and braking of the cart, and is also able to fend off external disturbances, for example, the impact of wind. The developed approach can be recommended for any crane installations using a suspended load.

Optimization of oscillation damping modes of spatial double pendulum. I. Formulation of the problem

The paper discusses the issues of optimal damping of oscillations of a spatial double pendulum, whose joint axes are not collinear to each other. As options for damping, both simply passive damping associated with the influence of viscous friction, and combined passive and active damping are considered, and active influences are formed according to the principle of collinear control. The analytical solution of the system motion equations is given for both cases in the framework of the linear model, and it clearly demonstrates the damping of motions on the natural oscillation modes of the original conservative model. The optimization criteria characterizing the efficiency of the damping processes of system movements are considered. It is noted that in order to obtain the most strongly marked damping modes, the degree of stability should be maximized or the integral energy-time indicator should be minimized. In addition, the main advantages and disadvantages of these optimization criteria are discussed. This article is the basis for further research, which will be presented as a separate article “Optimization of oscillation damping modes of spatial double pendulum. II. Solving the problem and analyzing the results”.

Theory of Harmonic Oscillations: A Gross Error in Physics

Theory of Harmonic Oscillations: A Gross Error in Physics

Flatness-based feedforward and modal model-predictive state-feedback control of a double pendulum bridge crane

In some industrial crane applications the payload is fixed at a hook by lifting slings such as belts or chains. The payload mass is typically much larger than the hook mass yielding small but high-frequent double pendulum oscillations. The main control goal for such cranes is to actively damp the single pendulum motion. Such double pendulum cranes are often approximated by single pendulum models. However, this may yield control or observation spillover effects. The influence of neglecting the double pendulum motion on feedforward control is analyzed in this paper by simulations. Therefore, a flat parametrization is derived which can be applied to both single and double pendulum cranes by simply adjusting two parameters. Besides, a modal state-feedback controller (in combination with modal state estimation) is suggested to avoid observation spillover effects without the need of damping high-frequent double pendulum oscillations at the same time. The feedback control performance is validated experimentally on a laboratory bridge crane.