Problem Of Oscillations Research Articles

Numerical simulation of tasks of vertical viscoelastic oscillation of suspension systems of frame, engine, cabin and seat

The analysis of the structures of the springing systems of modern vehicles showed that polymer composites are used in vehicles for which the decrease in curb weight is a critical indicator. The use of springs (suspensions) from polymer composites makes it possible to reduce the weight of the elastic element and increase durability while improving the smoothness of movement, reducing noise, and increasing traffic safety. When replacing the steel suspension with a polymer composite suspension, the mass of unsprung parts of the car decreases, and the economic performance of wheeled vehicles improves. The article discusses the problem of vertical viscoelastic oscillations of the suspension systems of the skeleton, engine, cabin, and seat. When considering the suspension's rheological properties, the Boltzmann-Volterra integral model is used. The Koltunov-Rzhanitsyn nucleus is used as a nucleus, which has weakly singular features of the Abel type. The system of integro-differential equations describing the studied process is solved by a method based on the use of quadrature formulas. The effect of the parameters of the hereditary-deformable properties of the suspension on the vibration shape is shown.

DYNAMIC PROBLEM OF AXISYMMETRIC OSCILLATIONS OF CYLINDRICAL SHELLS OF VARIABLE THICKNESS UNDER THE ACTION NON – STATIONARY LOAD

Analyzing the publications in which the dynamic problems of cylindrical shells of non-uniform thickness under the action of various types of loading are considered, a conclusion can be drawn. that there are practically no works devoted to the dynamic behavior of heterogeneous cylindrical shells under non-stationary loads. In this work, the formulation of the dynamic problem of axisymmetric oscillations of a cylindrical shell of variable thickness under the action of non-stationary loading and the algorithm for solving the given problem are considered. In particular, the resulting system of differential equations is based on the theory of Tymoshenko-type shells, while constructing a numerical algorithm, the integro-interpolation method of constructing finite-difference schemes for spatial coordinates is used using Richardson approximations and an explicit difference scheme for time. An example of calculating the dynamic behavior of a variable thickness under non-stationary loading is considered and an analysis of numerous results is given.

Natural and forsed osculations of pipelines in contact with the Wincler medium

In this paper, the pipeline is modeled as a curved rod in contact with the Winkler medium. Linear oscillations of a curved viscoelastic rod lying on the Winkler base are considered. The general formulation of the problem of free oscillations of a spatially curved viscoelastic rod with variable parameters is reduced to a boundary value problem for a system of ordinary integro-differential equations of the 12th order with variable coefficients relative to eigenstates; it can be solved by the method of successive approximations. The relations allowing to present the solution of the boundary value problem for the rod in an analytical form are formulated. It is established that the dimensionless complex frequencies of natural oscillations of a spatially curved rod, while maintaining the elongation of the rod constant, do not depend on it. The Poisson's ratio has little effect on the dimensionless real and imaginary parts of the natural frequencies.

Исследование по динамике многоэтажных зданий

The design of multi-storey buildings is a natural trend in the development of a modern metropolis. Obtaining exact solutions when studying their own and forced oscillations within the framework of a continuous homogeneous medium model (continuum mechanics) with an infinite number of degrees of freedom is often difficult to implement. Therefore, in the article (as part of the modernization of the finite element method), the model of a multi-storey building is discretized and endowed with a finite number of degrees of freedom placed in the middle of the finite elements at the nodes (the mass of finite elements is also placed there), which elastically interact with the finite elements of the model that do not have mass. It is believed that the elements of a multi-storey building work only for bending, which is fully justified by comparing the frequencies of its bending and longitudinal oscillations. The resolving system of differential equations of oscillations of a multi-storey building, in which expressions for energies (potential, kinetic and Rayleigh) are written in quadratures, is obtained using Lagrange equations of the second kind. In the article, the problems of free oscillations of 3- and 100-storey buildings are solved using Green’s functions, stiffness, mass, compliance matrices, etc. The approximate results obtained in the article, when compared with the little-known approximate results obtained by other methods, as well as exact results (direct and indirect methods of boundary elements), showed a good correspondence.

MODELING STABILITY OF DIFFERENTIAL-DIFFERENCE EQUATIONS WITH DELAY

Differential-difference and differential-functional equations are mathematical models of ma\-ny applied problems in automatic control and management systems, chemical, biological, technical, economic and other processes whose evolution depends on prehistory. In the study of the problems of stability, oscillation, bifurcation, control, and stabilization of solutions of linear differential-difference equations, the location of the roots of the corresponding characteristic equations is very important. Note that there are currently no effective algorithms for finding the zeros of quasipolynomials. When studying the approximation of a system of linear differential-difference equations, it was found that the approximation of nonsymptotic roots of their quasi-polynomials can be found with the help of characteristic polynomials of the corresponding approximating systems of ordinary differential equations . This paper investigates the application of approximation schemes for differential-difference equations to construct algorithms for the approximate finding of nonsymptotic roots of quasipolynomials and their application to study the stability of solutions of systems of linear differential equations with many delays. The equivalence of the exponential stability of systems with delay and of the proposed system of ordinary differential equations is established. This allowed us to build an algorithm for studying the location of non-asymptotic roots of quasi-polynomials, which are implemented on a computer. Computational experiments on special test examples showed the high efficiency of the proposed algorithms for studying the stability of linear differential-difference equations.

MODELLING AND ANALYSIS OF INITIAL STRESS STATE IN A THIN-WALL CYLINDER WITH VARIABLE CHARACTERISTICS

A linearized model of prestressed elastic body vibrations is described in terms of the nonsymmetric Piola stress tensor, and a weak statement of the original problem is given. With the help of the Lagrange variational principle, we construct a statement of the problem of steady axisymmetric oscillations of a thin-walled (shell-like) cylinder with variable material properties in the presence of an inhomogeneous prestress field. The motion equations, essential and natural boundary conditions are formulated. Integral characteristics are introduced that average the change in prestresses and material properties over the shell thickness. On the basis of the model presented, the problem on steady-state vibrations of a functionally graded prestressed cylindrical shell is numerically investigated via the shooting method; the influence of the laws of change in material modules and prestress components on dynamic characteristics (e.g., amplitude-frequency characteristics, natural vibration frequencies) is analyzed, a comparative analysis of the solutions is carried out depending on the thin-walled parameter. For the considered cylindrical shell with axial inhomogeneity, based on the acoustic sounding data, we study the inverse problem of restoring two laws of prestress inhomogeneity characterizing the nonuniform initial stress-strain state of tension or inflation. As additional information, we consider the measurement data of the displacement components on the cylinder's surface, given in a set of points at a certain frequency of steady-state oscillations; in such a case, the material characteristics are considered to be known and may depend on the axial coordinate, which makes it possible to set an arbitrary functional gradient along the axis of the cylinder. The mode of probing loading is determined by specifying the traction type and oscillation frequency. Explicit formulas for the desired laws of prestress inhomogeneity are obtained, and computational experiments are carried out to restore them. A high accuracy of reconstruction is revealed far from the ends of the cylinder when probing at a frequency in the vicinity of the first resonance.

Genetic Algorithm Assisted Parametric Design of Splitting Inductance in High Frequency GaN-Based Dual Active Bridge Converter

Splitting and placing interfacing inductance on both sides of the transformer has been proven to be an effective method, which extends the zero-voltage switching region for all the switching devices in the dual active bridge (DAB) converter. With the trend toward operating in higher frequency, achieving higher power density and higher efficiency, the converter model becomes more complex due to the non-negligible parasitic components that brings new challenges to DAB converter design. Traditional analytical methods have made it hard to imitate the proposed converter easily and precisely. Thus, artificial intelligence techniques are able to be utilized to assist the design process. When considering the converter system as a gray-box model, the metaheuristic algorithm can be implemented for the targeted design inside such a gray-box. In this article, a genetic algorithm (GA) is employed in the DAB converter parametric design with an explicit fitness desire to help in discovering the high frequency oscillation (HFO) problem. Consequently, the splitting inductance tuning method is proposed for eliminating the HFO problem and minimizing inductors’ loss. The methodology of implementing GA into converter parametric design, and the proposed splitting inductance tuning method are introduced and verified with a 1 MHz gallium nitride high-electron-mobility transistor based DAB converter prototype. The comparitive experimental results prove the effectiveness of the splitting inductance tuning method and achieve 4% efficiency enhancement with 200 W power delivering.

Basis of the parameters of the spin extractor tool on the interned spinning machine

The article presents an effective new constructive scheme and the principle of operation of the exhaust device of the ring spinning machine. The mathematical model and the results of solving the problem of oscillations of the axis of the composite squeezing roller of the drawing apparatus of the spinning machine have been determined. The recommended values of the roller parameters are given. Based on the analysis of the research results and the conditions for obtaining high-quality yarn, the recommended parameter values for each squeezing rollers were determined.

Моделирование распространения квазипериодических осцилляций в корональной плазме

In the general problem of oscillations observed in the solar corona, a particularly intriguing position is occupied by quasi-periodic oscillations, which are often observed in coronal holes. Most often, periods are observed in pairs of close values. Among the possible explanations of this phenomenon, we consider the dispersion of acoustic waves under the influence of thermal conductivity. The possibility of the appearance of pairs of periods may be due to the existence of a minimum at the group velocity, which is realized under the conditions available in the corona. We show how this works, and also claim that this mechanism can serve for the purposes of coronal seismology to determine the parameters of coronal plasma.

Statement and general technique for solving problem of oscillation of a hereditarily deformable aircraft

This article provides a general statement and a technique for solving the problem of oscillations of a hereditarily deformable aircraft in a gas flow with a finite number of degrees of freedom. Using the Lagrange equations and the variational principle of the hereditary theory of viscoelasticity, the equations of motion of the problem under consideration are derived. The generalized forces acting on the aircraft in the subsonic flight mode are determined according to the stationarity hypothesis. As a result, closed interconnected weakly singular integro-differential equations are obtained that describe the mathematical model of the problem with a finite number of degrees of freedom. General schemes for the numerical solution of these equations are outlined. As an example, the flexural-torsional-aileron flutter of the transient process of a hereditarily deformable wing with a finite freedom number is considered.

Research on Small-Loop Transient Electromagnetic Method Forward and Nonlinear Optimization Inversion Method

The small-loop transient electromagnetic (TEM) method has great application prospects in shallow surface geophysical exploration. However, the theoretical research on the forward and inversion of this method is obviously lagging behind, which seriously affects the application effect in practical engineering. For the oscillation problem of the small-loop TEM response calculated by using the forward theory of the conventional TEM methods, the dipole integral superposition method was proposed to solve the problem in this article. The transmitter source is divided into an infinite number of electric dipoles, and the calculation expressions of the electromagnetic field components satisfied by the electric dipoles are deduced, and the forward calculation problem of the layered model of the small-loop TEM method is solved. For the small-loop TEM method inversion problem, the simulated annealing (SA) method was presented for inversion calculation in this article. First, the influence of the selection of the initial temperature on the inversion result of the SA algorithm was analyzed. Then, we demonstrate the algorithm’s flexibility by choosing different initial models and search ranges and concluded that the different initial models and search ranges do not affect the inversion results of the SA algorithm. Next, the typical layered models were established, and the SA algorithm was used to carry out calculations. The research results show that the SA algorithm is an excellent global optimization algorithm, which can easily jump out of the local minima and converge to the global minima. Finally, we processed the measured data through inversion calculations and compared it with the results of the other three methods to verify the effectiveness and accuracy of the SA algorithm for small-loop TEM data processing. The research content solves the theoretical problem of the small-loop TEM method forward and inversion, promotes the development of the small-loop TEM method technology, and objectively and effectively solves practical engineering application problems.

Distributionally Robust Differential Dynamic Programming With Wasserstein Distance

Differential dynamic programming (DDP) is a popular technique for solving nonlinear optimal control problems with locally quadratic approximations. However, existing DDP methods are not designed for stochastic systems with unknown disturbance distributions. To address this limitation, we propose a novel DDP method that approximately solves the Wasserstein distributionally robust control (WDRC) problem, where the true disturbance distribution is unknown but a disturbance sample dataset is given. Our approach aims to develop a practical and computationally efficient DDP solution. To achieve this, we use the Kantrovich duality principle to decompose the value function in a novel way and derive closed-form expressions of the distributionally robust control and worst-case distribution policies to be used in each iteration of our DDP algorithm. This characterization makes our method tractable and scalable without the need for numerically solving any minimax optimization problems. The superior out-of-sample performance and scalability of our algorithm are demonstrated through kinematic car navigation and coupled oscillator problems.

Approximate Solution of a Neutrosophic Nonlinear Van der Pol Oscillator Problem by Semi Analytical Method Using Thick Function

In this paper, an analytical method (Homotopy perturbation method HPM) is used for solving the initial value problem represented by a neutrosophic nonlinear Van der Pol oscillator equation (N-VDP) arising in applied dynamics using the thick function. We find the solutions of the (N-VDP) equation by HPM and then compare the numerical results with fourth order Runge-Kutta method (RK4). The results showed that the HPM lead to accurate and efficient results. Furthermore, these results of the HPM scheme and RK4 are implemented in Matlab.

Solution for the simple harmonic oscillator problem via unilateral Fourier transform

Solution for the simple harmonic oscillator problem via unilateral Fourier transform

On the oscillation of first-order differential equations with deviating arguments and oscillatory coefficients

<abstract><p>In this work, we study the oscillation problem of first-order differential equations with deviating arguments and oscillatory coefficients. We generalize and improve the work of Kwong <sup>[<xref ref-type="bibr" rid="b30">30</xref>]</sup> such that the delay (advanced) and the coefficient functions do not need to be monotone and nonnegative, respectively. This method essentially improves many known oscillation conditions. The significance and the substantial improvement of our results are shown by two illustrative examples.</p></abstract>

Harmonic State-Space Based AC-Side Impedance Model of MMC and High Frequency Oscillation Characteristics Analysis

Recently, high-frequency oscillation of the modular multilevel converter (MMC) based high-voltage direct current (HVDC) projects has attracted great attentions. In order to analyze the small-signal stability, this paper uses the harmonic state-space (HSS) method to establish a detailed frequency domain impedance model of the AC-side of the HVDC transmission system, which considers the internal dynamic characteristics. In addition, the suggested model is also used to assess the system's high-frequency oscillation mechanism, and the effects of the MMC current inner loop control, feedforward voltage links, and control delay on the high-frequency impedance characteristics and the effect of higher harmonic components. Finally, three oscillation suppression schemes are analyzed for the oscillation problems occurring in actual engineering, and a simplified impedance model considering only the high-frequency impedance characteristics is established to compare the suppression effect with the detailed impedance model to prove its reliability.

Sharp results for oscillation of second-order neutral delay differential equations

The aim of the present paper is to continue earlier works by the authors on the oscillation problem of second-order half-linear neutral delay differential equations. By revising the set method, we present new oscillation criteria which essentially improve a number of related ones from the literature. A couple of examples illustrate the value of the results obtained.

Solving non-Hermitian Dirac equation in the presence of PDM and local Fermi velocity

We present a new approach to study a class of non-Hermitian ([Formula: see text])-dimensional Dirac Hamiltonian in the presence of local Fermi velocity. We apply the well-known Nikiforov–Uvarov method to solve such a system. We discuss applications and explore the solvability of both [Formula: see text]-symmetric and non[Formula: see text]-symmetric classes of potentials. In the former case, we obtain the solution of a harmonic oscillator in the presence of a linear vector potential while in the latter case we solve the shifted harmonic oscillator problem.

PLL-Less Active/Reactive Power Control of Photovoltaic Energy Source with Applying pq-Theory in Single-Phase Grid System

Converter systems are applied to manage active/reactive power control of photovoltaic (PV) source during integration with the electric grid system. The control algorithm of the conventional converter system consists of a reference generation unit, a dc-link voltage control loop, two power control loops and a phase lock loop (PLL) system. PLL unit is used to lock in phase angle of the electric grid, and to perform the coordinate transformation for calculations of the active/reactive powers. However, the control algorithm has a slow dynamic response because of utilisation of a PLL structure. In addition, additional complex mathematical computations are required with the use of a PLL algorithm. Furthermore, the interaction of the PLL and the power control loops may lead power oscillation problems under weak grid, and also result in instability of the PV system. In this study, to avoid the aforementioned issues and to enhance the power flow capability of the grid-connected PV panels, a PLL-less control algorithm in pq-theory is studied for the active/reactive power management and the grid synchronization. In addition, the mathematical formulations of the current control algorithm are presented in detail. To show the effectiveness of the PLL-less controller, a PV system model with using real PV panel groups is designed and constructed in a simulation environment. The proposed control method is tested under various operation cases such as dynamic environmental conditions, reactive power support and voltage variations. The proposed method shows efficient performance under applications of the different operation situations.

Эффективный метод построения амплитудно-частотных характеристик оболочки

Timoshenko type equations are used, taking into account the transverse shift. The shell has the properties of constructive anisotropy. Forced oscillations in the frequency range, including the first significant low-frequency resonances, are considered. The internal scattering of vibrational energy is taken into account by the method of complex amplitudes. The influence of a number of parameters on the amplitude-frequency characteristics (frequency response) of input compliance is investigated. A semi-analytical method of constructing a solution is used. In the case of a cylindrical shell freely supported at the ends, Fourier series are used in two coordinates. The problem of forced oscillations is solved by decomposing the amplitudes of displacements according to their own forms of oscillations. At the same time, the separation of equations for determining coefficients by harmonic numbers is provided. The algorithm on this basis allows you to quickly build the amplitudefrequency characteristics necessary for analysis.