Problem Of Oscillations Research Articles

SOLUSI PERSAMAAN OSILATOR NONLINIER MENGGUNAKAN METODE HOMOTOPI PERTURBASI

The oscillator is an electronic circuit that is widely used in electronic devices. One of the mathematical models that describe the oscillator problem is the conservative nonlinear oscillator equation. In this study, the conservative nonlinear oscillator equation is discussed in the form of where and are odd functions. The purpose of this study is to find a solution to the conservative nonlinear oscillator equation and to know the simulation of the obtained solution. The method used to find the solution to the equation is the homotopy perturbation method which is a combination of the homotopy and perturbation methods. The search for a solution to the conservative nonlinear oscillator equation using the homotopy perturbation method is also modified by the Lindstedt-Poincare method to deal with secular terms. The simulation results show that the greater the value of , the smaller the angular frequency produced and the fewer waves formed.

Study on Burning Surface Regression Algorithm under Erosive Burning Based on CT Images of Solid Rocket Motor Grain

The presence of the erosive burning effect during the operation of a solid rocket motor (SRM) is one of the most important factors affecting the proper operation of the motor. To solve the effects of the operating process of the motor under erosive burning, a synthesis algorithm based on the actual CT images is proposed to combine the Level-set (LS) method with the minimum distance function (MDF) method for the simulation of the burning surface regression of the grain under erosive burning. The Hamilton–Jacobi control equation can be solved exactly for the discrete form of LS. To improve the computational efficiency of the LS method, the minimum distance field is initialized and only the distortion grid is adjusted during the reinitialization. The third-order TVD Runge–Kutta method is used to solve the problem of numerical oscillation and improve the calculation accuracy. The experiments simulate the burning process of the NAWC No. 6 partial grain under erosive burning, which can provide the main basis for the performance design of solid propellant. The experimental results show that the method has good applicability to three-dimensional complex grains. It can realize the simulation of grains under erosive burning and its calculation accuracy is high.

Regulation of the Natural Oscillations Parameters of a Building Spatial Frame in the LIRA Software

Introduction. In recent years many researchers have become interested in applying the various types of finite element method to studying of the buildings oscillation problems. In recent decades the finite element method is being successfully used for natural oscillations analysis along with the physical modeling. The scaled physical modeling and experimental approaches are also suitable for solving the complex problems. The main aim of our research is to identify the dependence of dynamic characteristics of a building frame on geometric characteristics of the frame elements. The objective of this research is to make an analysis and overview of the topic, to determine the scientific deficit, to conduct numerical and experimental studies, to formulate conclusions, to model and analyse the results. The scientific novelty consists in the possibility to use the obtained data on building frame natural oscillations depending on the geometric characteristics of the frame elements as an optimal rigidness ratio. The practical significance of the research consists in development of specific analytical relations for choosing a building frame design solution with an optimal natural frequencies parameter to be used in design and construction practice.Materials and methods. The creation and calculation of the finite element model was carried out in the LIRA software package.Results. As a result of calculation the frequencies and periods of building frame natural oscillations were obtained.Discussion and conclusions. Based on the results of the building natural oscillations analysis the conclusion was made that by changing the frame elements rigidity it’s possible to select its dynamic characteristics to find the optimal design solution of structures.

Modified Filon-type methods for second-order highly oscillatory systems with a time-dependent frequency matrix

We propose a modified Filon-type method for solving second-order highly oscillatory systems with a time dependent matrix. We first transform the second-order problem into a first-order one and then integrate the transformed one by the Filon-type method combined with the waveform relaxation method. The fundamental matrix in the formula of variation of constants can be calculated directly such that our proposed modified Filon-type method do not need to compute the nested integral commutators in the Magnus expansion. The global error of the modified Filon-type method is presented. Numerical examples show that our proposed numerical solver is efficient and accurate for highly oscillatory problems.

On the Quantization of Length in Noncommutative Spaces

We consider canonical/Weyl-Moyal type noncommutative (NC) spaces with rectilinear coordinates. Motivated by the analogy of the formalism of the quantum mechanical harmonic oscillator problem in quantum phase-space with that of the canonical-type NC 2-D space, and noting that the square of length in the latter case is analogous to the Hamiltonian in the former case, we arrive at the conclusion that the length and area are quantized in such an NC space, if the area is expressed entirely in terms of length. We extend our analysis to the 3-D case and formulate a ladder operator approach to the quantization of length in 3-D space. However, our method does not lend itself to the quantization of spacetime length in 1 + 1 and 2 + 1 Minkowski spacetimes if the noncommutativity between time and space is considered. If time is taken to commute with spatial coordinates and the noncommutativity is maintained only among the spatial coordinates in 2 + 1 and 3 + 1 dimensional spacetime, then the quantization of spatial length is possible in our approach.

Oscillation characteristics and trajectory stability region analysis method of hierarchical control microgrids

To address the broadband oscillation problem caused by isomerized power electronic devices in microgrids, an oscillation characteristic and stability region analysis method was proposed for hierarchical control structure microgrids based on the dynamic time-varying fast and slow scale analysis method. From the perspective of control, the controller was combined with the main circuit, and a nonlinear dynamic model of the microgrid hierarchical control grid-connected inverter was established. Then, the dynamic time-varying fast and slow scale analysis method was used to obtain the Hopf bifurcation oscillation trajectory. Furthermore, and combining with three-dimensional and Hopf bifurcation, considering the correlation between the main circuit parameters and controller parameters as the starting point, the trajectory instability region analysis method is proposed. Finally, the instability mechanism of the hierarchical control structure microgrid is revealed using the above methods. These methods provide a theoretical basis for the correct selection of the main circuit structure parameters and controller parameters of the microgrid.

Intrinsic oscillations of viscoelastic three-layer truncated conical shell

Conical shells are used in rocket engineering, construction, aircraft engineering and shipbuilding. The purpose of the present work is to carry out a technique, algorithm and programs for obtaining resonant frequencies and waveforms for circular viscoelastic three-layer conical shells. On the basis of the Lagrange variation equation integral-differential equations of own vibrations are obtained. Based on the method of finite elements, a method for solving the problem of eigen-wear oscillations of the truncated three-layer shell with handedly and freely resting edges was carried out. The problem comes down to solving algebraic equations a large order. Obtained a frequency equation with complex output parameters. The proper oscillations of truncated conical shells are investigated, some characteristic features are revealed. Solving the frequency equation by the Muller method, complex roots are determined. It is established that as the elastic modulus of the shell increases, the real and imaginary parts of the natural frequencies increase accordingly. Paying attention to the rheological properties allows you to increase the values of frequency up to 15%.

Application of matrices for transfer function values calculation in mechanical systems

The paper describes the formalism and methodology that can be employed for calculation of transfer function in distributed parameter elastic mechanical systems. Generalized formalism for derivation of transfer function matrices is presented as developed in accordance with the Hilbert-Schmidt theorem. Matrix-based method to determine elastic mechanical system transfer function is offered. The solution of the problem of forced harmonic oscillations of an elastic body of a mechanical system with the presence of friction is considered. The described technique can be applied to find the transfer functions of technological equipment in order to determine the dynamic characteristics of the system.

Analysis of flexural oscillations of the shaft of saw cylinder on the elastic bearing supports of the fiber cleaner

The results of analysis of flexural oscillations of the shaft of saw cylinder on the elastic bearing supports of the fiber cleaner are presented in the article. A design diagram, a mathematical model of flexural oscillations of the shaft of saw cylinder on the elastic bearing supports of the fiber cleaner are given. Analytical and numerical solutions of the problem of oscillations of the saw cylinder shaft are given. The main parameters of the system are substantiated.

Oscillations of the outer bush of composite roller of the thread guide in the sewing machine

The diagram of thread guide with composite rollers in a sewing machine is given in the article. Based on solving the problem of oscillations of the outer bush of the compound roller of the thread guide, the dependence of changes in the amplitude of deformation values of cushioning bush has been obtained. Values of stiffness coefficient of cushioning bush of compound roller have been substantiated.

Fifth Order Improved Runge-Kutta Nystrom Method Using Trigonometrically-Fitting for Solving Oscillatory Problems

In this paper, the Trigonometrically Fitted Improved Runge-KuttaNystrom method is proposed as a novel method with four stages and fifth order for solving oscillatory problems. This method is intended to integrate second-order initial value problems using the trigonometrically fitting approach. To increase the method'saccuracy, the principal frequency of the problem푤∈ℝ, is used. It is discovered that the new method is more precise when compared with the other existing Runge-Kutta Nystrom and IRKN5 methods. To show how well the TFIRKN5 method works, test problems for second-order ordinary differential equations (ODEs) are solved. The numerical outcomes show that the novel approach outperforms methods that have already been published.

Interaction of FACTS devices with loads dynamics in the transport networks and interconnection

This paper introduced analysis and improvement of power networks stability. It focused on the impact of flexible AC transmission systems (FACTS) device interaction with the other components of the network. It investigated the impact of dynamic charges on the ability of FACTS to eliminate power oscillations problems. A small-signal analysis, frequency analysis and non-linear time simulations using EUROSTAG made it possible to study these problems. Other, research has shown that the damping loops of the power oscillations effects using classical techniques of sensibility are not robust in relation to the variations of load models. Thus, this paper proposed a method based on the sensitivity of the eigenvalues and it takes into account the variations of the load models. The method calculates an optimal phase compensator based on a weighted average of the sensitivity of the target mode. It considers the variations of sensitivity as a function of the uncertainty in the load model. According to the obtained results, this method is effective in most stability problems.

Adaptive Mesh Refinement for Dam-Break Models using the Shallow Water Equations

The 2D shallow water equations are a common tool for the simulation of free surface fluid dynamics in civil engineering. However, the nonlinear structures of the equations' straightforward implementations lead to numerical problems, such as spurious oscillations and unphysical diffusion. Therefore, this research compared several strategies to overcome these problems, using various finite element formulations and combinations of stabilization methods and mesh options. The accuracy and performance of numerous approaches are examined on models of dam-break in one and two space dimensions. The analytical solution checks the numerical, derived shock wave heights and velocities for the 1D classical benchmark. The result showed that streamlined diffusion and shock capturing stabilization deal with the classical problems of spurious oscillations and numerical diffusion but still indicate similar problems locally in the vicinity of steep fronts and shock waves when used on fixed meshes. As adaptive meshing is the most promising method to deal with such situations, several concerned options are examined in detail. It is important to fine-tune the method to the model's needs, i.e. to adapt the maximum number of mesh refinements, the indicator functions, and the starting mesh. The use of adaptive meshing techniques leads to accurate solutions for the usual parameter range in 1D and 2D, requiring less computational resources than simulations on fixed meshes. Meanwhile, meshing reduces the model size of the 2D dam break model adaptive by almost one order of magnitude and the execution time by a factor of 20.

Suppression of eddy-current effects in beam injection using a pulsed sextupole magnet with a new ceramic chamber

At the Photon Factory storage ring (PF ring) of the High Energy Accelerator Research Organization (KEK), a pulsed sextupole magnet (PSM) has been used for top-up injection for the first time. Following its successful operation at the KEK, this new injection scheme was expanded to one with a nonlinear kicker in BESSY II and was then applied at UVSOR and Aichi SR in Japan. Also, the PSM system in the PF ring was improved by introducing a rectangular shape for the magnet's bore to strengthen the magnetic field. However, this upgraded PSM was not implemented for user operation because it induced a horizontal oscillation of the stored beam with a maximum amplitude of 5.0 mm. This oscillation was assumed to be caused by eddy currents originating from the uniform inner coating of the ceramic chamber. We, therefore, developed a modified ceramic chamber with a new patterned coating designed to suppress the eddy current--induced magnetic field. The pattern shape was optimized to suppress this magnetic field and, simultaneously, to reduce the resistive wall impedance. A fine-line pattern-coating process, originally developed for a ceramic chamber with an integrated pulsed magnet, was modified for application with the magnet's chamber of the sextupole. The maximum horizontal oscillation amplitude was suppressed by a factor of 16 by using the new PSM chamber without any issues related to beam instability. Details of the historical background of the upgrading of the PSM system, an investigation of the cause of the abnormal oscillation problem, the development of the new process for coating the ceramic chamber, and the results of the beam-response measurements for the new ceramic chamber installed in the PF ring are reported in this article.

The tri-coloured free-tree theory for symplectic multi-frequency ERKN methods

Symplectic ERKN methods have been shown to be a very powerful tool that can solve oscillatory Hamiltonian problems with high accuracy and efficiency. However, in order to obtain a symplectic ERKN method, it is necessary to solve a large system of equations which are derived from order conditions and symplectic conditions. In this paper, it is found that for symplectic ERKN methods, order conditions can be greatly simplified. A compact set of order conditions are then expressed in algebraic format, instead of the original functional format, specially for symplectic ERKN methods.The corresponding tri-coloured free-tree theory is developed. Furthermore, we present several approaches for constructing symplectic ERKN methods, by solving relatively small systems of algebraic equations. This is crucial, in particular, in the construction of high-order ERKN methods.

Research on Flexible Virtual Inertia Control Method Based on the Small Signal Model of DC Microgrid

Renewable energy is usually connected to the DC micro-grid by a large number of power electronic devices, which have the advantages of a fast system response, but the disadvantage to reduce the inertia of the system, which makes the stability of the system worse. It is necessary to increase the inertia of DC micro-grid so that it can recover and stabilize well when it receives a disturbance. In this paper, a small-signal model of DC micro-grid with constant power load (CPL) is established, and a flexible virtual inertial (FVI) control method based on DC bus voltage real-time variation is proposed, by controlling the DC/DC converter of the energy storage system, the problem of system oscillation caused by introducing voltage differential link to the system is solved. Compared with the droop control method, the FVI control method can increase the inertia of DC micro-grid system, reduce the influence of small disturbances, and improve the stability of the system. Finally, the validity of the FVI control method based on small signal model is verified in dSPACE.

Design and performance analysis of a charge controller for solar system using MATLAB/SIMULINK

The energy utilization of a Photovoltaic (PV) module is determined by the maximum power the module harnesses from the sun. A static PV module can only harness maximum power from the sun at a particular time in a day as the sun revolves. This simply means that if the PV module can be designed to move in such a direction to harness maximum power from the sun, then its energy utilization efficiency will be highly improved over the period the Sun is available. This design can be achieved by employing Perturb and Observe (P and O) algorithm for maximum power point tracking (MPPT). In this study, Propotional and Integral (PI) controller along with P and O is proposed to solve the problem of low efficiency and irregular output oscillations. The simulation is carried out in the MATLAB/SIMULINK environment and the result shows that by incorporating the PI controller into the system, the efficiency of 99.96% at the maximum power point was attained.

Decoupled power-based sliding mode control modeling enhancement for dynamic stability in doubly-fed induction generator-based wind turbines

Low-voltage ride through (LVRT) capability is the principal method used to counteract voltage dips and over-current, which are caused by various balanced and unbalanced faults. However, in providing LVRT capability during faults, oscillations that occur in parameter changes should be damped for a short time. In this study, a decoupled power-based sliding mode control (SMC) in doubly-fed induction generator (DFIG)-based wind turbines was developed in order to eliminate the oscillation problems that may occur during balanced and unbalanced faults. Besides, while the stator electromotive force model in DFIG is developed with the aim of improving simulation performance and enabling ease of calculation, the rotor electromotive force model is developed to dynamic stability in the system during various faults. The results obviously indicated that the proposed decoupled power-based SMC and stator-rotor electromotive force models enhanced the LVRT capability of the grid-code requirement and quickly restored dynamic stability to the system.

A novel dual switch DC/DC converter without reverse recovery problem

The traditional dual switch forward converter has a very large filter element and all the diodes on the primary and secondary sideshow the problem of reverse recovery and voltage oscillation. Therefore, this paper proposes a novel dual switch DC/DC converter with only one capacitor as the output filter, which reduces the number of magnetic elements and improves the power density. Besides, zero current turned on of main switches and zero current turned off of all diodes is achieved to solves the problem of parasitic oscillation and reverse recovery of the diodes. In this paper, the detailed analysis of the dual switch converter’s operating principle and characteristics are analyzed. Finally, according to the proposed converter, a prototype has been established in the lab, and the experimental results verify the validity of the analysis.

Behaviors of the long penetration mode with a hot counterflowing jet

When an aircraft flies at hypersonic speeds, a large aerodynamic drag and a significant amount of aerodynamic heat are generated around it. As an active flow control technology, counterflowing jets can effectively reduce the drag and heat flux and have therefore attracted broad attentions. However, the oscillation problem that accompanies counterflowing jets remains to be studied further. The present study aims to investigate the oscillation properties of the flow around a hypersonic vehicle with a hot counterflowing jet using a numerical solver with a single-temperature multi-component chemical reaction model. A hypersonic hemispherical-nosed is selected and the solver is developed on the OpenFoam platform. The drag reduction efficiency, the flow field structure, and the flow instability characteristics for different jet temperatures are discussed in detail. It is found that a high-temperature jet can reduce the amplitude of the drag force significantly and even suppress the flow oscillation, and the drag reduction efficiency per unit mass increases with the jet temperature. For the same efficiency, a high-temperature jet has a smaller mass flow rate which may reduce the load of flight and lead to savings in space and cost. Therefore, within the allowable range of heat flux, increasing the jet temperature might be a more effective method for reducing drag and stabilizing the flow field than increasing the jet pressure ratio as usually thought. It is hoped that the present results serve to advance the application and the development of hypersonic counterflowing jet technology.