Dynamic Equations Of System Research Articles

Theoretical and numerical studies on improving absorption power of multi-body wave energy convert device with nonlinear bistable structure

For the energy supplement of deep-sea equipment, we examine a multi-body absolute motion counter-rotating wave energy converter (CR-WEC) in the research. In order to improve the capture efficiency of the absorber, a nonlinear bistable structure is proposed to improve the overall wave-following vibration capability of the CR-WEC. And then, we suggest to employing the harmonic balance method to solve the system dynamics equation in the CR-WEC 2-DOF absolute motion state. Combining the essential assumptions results in an analytical solution that is approximative. The paper also investigates the influence of system-related parameter modifications on absorption efficiency. A multi-degree-of-freedom arrangement with an unaltered overall mass is proposed to further increase the device ability to absorb energy. According to the numerical calculation and simulation results, the combination of 3-DOF state and bistable structure can make the device have the maximum capture width and peak value. In the irregular incident wave under the natural state, the multi-body bistable-linear configuration proposed in this study obtains the highest average absorption power.

Simulation Methods for MEMS S&A Devices for 2D Fuze Overload Loading.

An experimental testing system for the two-dimensional (2D) fuze overload loading process was designed to address the loading issues of recoil overload and centrifugal overload in fuze safety and arming (S&A) device. By incorporating centrifuge rotation energy storage, impact acceleration simulation, and equivalent centrifugal rotation simulation, a block equipped with a fuze S&A device accelerated instantly upon having impact from a centrifuge-driven impact hammer, simulating recoil overload loading. The impact hammer was retracted instantaneously by adopting an electromagnetic brake, which resulted in the centrifugal rotation of the block around its track, to simulate the centrifugal overload loading. The dynamic equations of the experimental testing system and the equations of impact hammer motions were established, whereby the rotation speed of the centrifuge and the braking force of the electromagnetic brake were calculated and selected. A dynamic model of the collision between the impact hammer and block was established using ANSYS/LS-DYNA software for simulation analysis. The acceleration curves of the recoil overload and centrifugal overload with variations in the centrifuge speed, cushion material, and buffer thickness were obtained, which verified the feasibility of the proposed loading simulation method. Two-dimensional overload loading simulation tests were performed using the developed experimental testing system, and the acceleration curves of the recoil overload and centrifugal overload were measured. The test results indicated that the proposed system can accomplish 2D overload loading simulations for a recoil overload of several 10,000× g and centrifugal overload of several 1000× g.

The research of space net control strategy based on the combination of fixed tearing belt and tether brake

In order to solve the rebound motion of space tether net during deployment, a new control strategy based on adding tear tape in the plane and applying tether force out of the plane is proposed. The tether segment of the space tether net is discretized, and the lumped mass model is established. According to the mechanical characteristics of the tether, the system dynamic equation is derived. Then the simulation analysis is made from the perspective of evaluating the effect of the control strategy. Through simulation and comparison, it is found that the control strategy has obvious effect on restraining the rebound movement of the tether net.

A 3-D finite element modeling method for time-varying rotor-support system based on rotating-fixed coordinates

The asymmetry of rotor systems is sometimes evident, such as keyed shafts, crack rotors, two-pole generator rotors and especially shaft-disk-blade systems. Meanwhile, the coupling vibration problem between rotor and support structure is becoming more and more prominent due to the light weight of aero-engines. The design and analysis method for the dynamic characteristics of time-varying rotor-support system with detailed structure is needed. Therefore, a modeling method is proposed by using 3-D finite element for time-varying rotor-support system based on rotating-fixed coordinates. The rotor is modeled in rotating coordinate system and the support structure is modeled in fixed coordinate system respectively. The force, energy and displacement between rotor and support structure are transmitted by bearing mechanical parameters. Thus, the time-varying characteristics of the system are expressed explicitly by bearing mechanical parameters, and the dynamic equation of time-varying rotor-support system can be obtained. Then, Floquet theory and Hill infinite determinant method are used to analyze quasi-mode frequency characteristics and stability of time-varying rotor-support system. The results of a typical asymmetric rotor-support system got by the proposed method were compared with existed methods, and more coupling vibration characteristics such as the coupling vibration of rotor axial motion and support plate bending, the coupling vibration of shaft bending and support plate torsion were obtained.

MATHEMATICAL MODELS, NUMERICAL METHODS AND RESULTS OF STUDY OF TRANSSONIC FLOW AROUND PROFILES OF BLADE SYSTEMS

The aerodynamic characteristics of blade profiles in a transonic flow of an ideal gas are considered, which are obtained on the basis of the numerical solution of the system of gas dynamics equations (laws of conservation) in integral form. The solution is found by stabilizing over time, which avoids complications in the numerical method for a stationary system of variable-type equations with unknown lines of change from elliptic to hyperbolic and vice versa. The peculiarities of the position of the shock wave (jump) depending on the algorithm for calculating the parameter values on the faces of the cells of the difference grid in the finite-volume algorithm are pointed out. The calculation of numerical flows on the faces of the volume is based on the solution of the problem of the decay of an arbitrary discontinuity of parameters on them in a one-dimensional direction along the normal to the face. The choice of the working difference scheme is based on the indicators of accuracy (order of approximation) and complexity (explicit and implicit) of transition to the next time layer. The development of difference schemes of a higher order of approximation allows to obtain more detailed information about gas-dynamic flows on real grids, which was unattainable when using schemes of the first order of accuracy with high scheme (approximation) viscosity and inconsistency of the propagation of disturbances on a heterogeneous background of parameter values (dispersion calculation effects). The results of calculations using S.K. Godunov's scheme of a higher order of approximation, aerodynamic characteristics of the rigid profile and their comparison with experimental data are given. The characteristics of a profile that performs incoherent angular and vertical oscillations according to a given law are studied.

Modeling and characteristic analysis of mid-rear axle hydraulically interconnected suspensions for tri-axle heavy trucks

Truck suspension is a vital component supporting the weight of the vehicle body and plays an important role in transferring wheel load and isolating external vibration. The uneven load distribution between the middle and rear wheels of a tri-axle heavy truck will directly affect the driving stability and safety of the vehicle. To enhance the truck’s wheel load distribution performance and ride comfort, this paper proposes a new coupling suspension system, including an anti-synchronous middle and rear axle hydraulically interconnected suspension (MR-HIS) and the front axle conventional independent suspension (CIS). Considering the load-bearing characteristics of the middle and rear wheels of the tri-axle heavy truck, a five-degree-of-freedom (5-DOF) half-vehicle model of the truck equipped with MR-HIS is constructed. Further, the dynamics equations of the mechanical-hydraulic coupling system are established according to the impedance transfer matrix method and mechanical-hydraulic boundary conditions, and the truck body motion modes are completely decoupled. The modal analysis demonstrates that compared with CIS the proposed MR-HIS system can reduce the body bounce modal stiffness, increase the modal damping ratio, and enhance the dynamic coupling performance of middle and rear wheels. Subsequently, the frequency response analysis is adopted to evaluate the load distribution and vibration isolation performance of the MR-HIS. The comparison analysis results indicate that the proposed MR-HIS system significantly improves the load balance distribution between the middle and rear wheels and suppresses the load transfer to the front wheel, thus the handling stability of the truck is improved. Meanwhile, the body vibration frequency response analysis shows that the MR-HIS can effectively isolate external vibration and improve driving comfort of the tri-axle heavy truck.

Application of the local discontinuous Galerkin method to the solution of the quasi-gas dynamic equation system

Рассматривается решение квазигазодинамической (КГД) системы уравнений локальным разрывным методом Галеркина (ЛРГ). Решаются одномерные задачи Римана о распаде разрыва с известными точными решениями. В решениях задач присутствуют сильные разрывы. Поэтому для обеспечения монотонности решения, полученного ЛРГ методом, введены так называемые ограничители наклона, или лимитеры. Был выбран «моментный» лимитер, сохраняющий как можно более высокий порядок. Проведена модификация лимитера для сглаживания осцилляций на участках постоянства решения.

A Method of Qualitative Analysis for Determining Monotonic Stability Regions of Particular Solutions of Differential Equations of Dynamic Systems

Developing stability analysis methods for modern dynamical system solutions has been a significant challenge in the field. This study aims to formulate a qualitative analysis approach for the monotone stability region of a specific solution to a single differential equation within a dynamical system. The system in question comprises two first-order nonlinear ordinary differential equations of a particular kind. The method proposed hinges on applying elements of combinatorics to the traditional mathematical investigation of a function with a single independent variable. This approach enables the exact determination of the different qualitative scenarios in which the desired solution changes, under the assumption that the function values monotonically diminish from a specified value down to a finite zero. This paper outlines the creation and decomposition of the monotone stability region associated with the solution under consideration.

Research on Dynamic Modeling Method of Single Linkage Flexible Robotic Arm

In this paper, a dynamics modeling method is proposed for a single-link flexible robotic arm. Firstly, the dynamic equation of the flexible manipulator system is deduced by using the Lagrange equation, secondly, the nonlinear model of the single-link flexible robotic arm is obtained by separating the spatio-temporal variables using the assumed modes method, and the model is verified by the Quanser flexible robotic arm experimental platform. Finally, the model is modified for the dead zone of the actuator found in the experimental process, which improves the accuracy of the model.

A New 8D Lorenz-like Hyperchaotic System: Computer Modelling, Circuit Design and Arduino Uno Board Implementation

This paper presents the construction of Matlab-Simulink and LabView models for a novel nonlinear dynamic system of equations in an eight-dimensional (8D) phase space. The Lyapunov exponent spectrum and Kaplan-York dimension were calculated with fixed parameters of the 8D dynamical system. The presence of two positive Lyapunov exponents indicates hyperchaotic behavior. The fractional Kaplan-York dimension shows the fractal structure of strange attractors. An adaptive controller was used to stabilize the 8D chaotic system with unknown system parameters, and an active control method was derived to achieve global chaotic synchronization of two identical 8D chaotic systems with unknown system parameters. Using the results from Matlab-Simulink and LabView models, a chaotic signal generator for the 8D chaotic system was implemented in the Multisim environment. The simulation results of chaotic behavior in the Multisim environment demonstrate similar behavior compared to simulation results from Matlab-Simulink and LabView models. To visualize the new 8D chaotic system, we employed an Arduino Uno board along with eight light-emitting diodes (LEDs). Furthermore, we demonstrated the capability to simulate the new 8D chaotic system in the Proteus 8 environment using the Arduino Uno microcontroller. This advancement in the understanding and implementation of chaotic systems opens doors to numerous possibilities in the realm of secure communication and control systems.

Расчет движения подвижного состава по железнодорожному пути сеточно-характеристическим методом

The application of a grid-characteristic method is proposed for numerical simulation of the movement of rolling stock along a railway track laid on an earth and a bridge. In the study, the railway track is presented using a dynamic system of equations of the theory of elasticity of hyperbolic type. The grid-characteristic method relies on the characteristic properties of the system under consideration and uses finite-difference schemes of high order of accuracy to obtain a space-time solution. The features of railway structures are considered by changing the boundary conditions and conditions at the contact borders. To simulate the areas of contact of wheel pairs of rolling stock with the rail – the "wheel-rail" system – a previously developed pressure boundary condition is applied, modified so as to consider multi-element rolling stock. As a result of computer simulation of the movement of rolling stock along the railway track of various types, full-wave stress distribution in the track structure is obtained, which makes it possible to predict dangerous sections of rolling stock movement.

Dynamics modelling and influencing factor analysis of a rocket-launcher coupling system considering uncertain parameters

Vibration characteristic is an important factor affecting the motion of rocket in the launcher and its firing performance. In this paper, a rocket-launcher coupling dynamics model is proposed by applying the transfer matrix method for multibody systems. Considering manufacturing error and nonlinear contact force, the dynamics equations of the rocket-launcher coupling system during the whole process of firing are deduced. Combined with the dynamics model and equations, a dynamics simulation system is developed with uncertain parameters. The uncertain parameter description scheme and probability sampling scheme are proposed to obtain dynamics characteristic and firing performance of the system. The relevant tests are carried out to verify simulation results. Then, the factors affecting the firing performance are discussed. In view of the analysis results, the influence weight of initial disturbance on firing precision is 85% under the condition of full-loading continuous firing, and the swing angular velocity of rocket at muzzle is the main influence factor.

Vibration Control of the Steel-Concrete Composite Box Girder Bridge with Slip and Shear-Lag Effects by MTMDs under the Train-Bridge Interaction

Steel-concrete composite girder bridges, in essence, are thin-walled structures, the dynamic responses of which will be greater than those of a typical Euler–Bernoulli beam under the train-bridge interaction because of the shear lag and interface slip. Thus, in this study, the dynamic analysis model of a train-composite box girder bridge-multiple tuned mass damper (MTMD) coupling system is proposed, with the derived dynamic equations of this time-varying system. Meanwhile, the program is compiled using the Newmark-β method for the solution, combined with the optimization toolbox to solve the complex optimization design problems of MTMDs involved. Finally, factors affecting the vibration-damping effect are studied, such as the mass ratio of MTMDs, the number of trains, and the slip and shear lag of the composite box girder bridge.

Event-triggered nonlinear information fusion preview control of a two-degree-of-freedom helicopter system

This research presents a novel nonlinear information fusion preview control (NIFPC) method for the flight control problem of two-degree-of freedom (2-DOF) helicopter system. First, according to the information fusion optimal estimation methodology, the system performance index and the system dynamic equation are converted to several information equations about the control input, and then the control input is directly derived by fusing these information equations via the centralized information fusion optimal estimation. In the limited bandwidth, transmitting a large number of sampled data through the network will increase the computational and communication burden of the system. In order to overcome this difficulty, event triggering mechanism is introduced. The asymptotic convergence of system performance index is guaranteed by Lyapunov stability theory. Numerical simulation and experiment results have been provided to demonstrate the effectiveness of the proposed control scheme.

A comprehensive methodology to obtain electrical analogues of linear mechanical systems

Electrical analogues of linear mechanical systems have traditionally been obtained using a set of rules that can potentially be tedious when applied to complex systems. In addition, such rules do not cover all the possibilities of mechanical systems including rotational and translational generalized coordinates. The present work establishes a comprehensive and systematic methodology for obtaining the electrical analogue of any mechanical system modelled by rigid bodies, springs, and dampers. The method is simple and straightforward. First, the dynamic equations of the mechanical system are derived into matrix form. These equations are then translated to the electrical domain by means of the electromechanical analogy and, finally, the electrical circuit is obtained by direct inspection of the matrices. In addition, the method can deal with a combination of translational and rotational coordinates in the definition of the mechanical model. To support the proposed method, and beyond the planar vehicle models found in the literature, the electrical analogue of a linear 3D 7-DOF full car model is presented in this work.

A distributed approach for solving AC–DC multi-objective OPF problem

This paper first proposes an optimization model for Multi-Objective Optimal Power Flow (MO-OPF) problem in AC–DC networks. The considered objective functions are the fuel cost, active power losses, and environmental emission. The AC and DC power flow equations, the converter operating limits, the voltage magnitude limits, and line capacity limits are considered in the proposed AC–DC MO-OPF model. Then an equivalent Gradient Dynamical System (GDS) for the AC–DC MO-OPF model is derived. Each equilibrium point of this GDS is a Karush–Kuhn–Tucker (KKT) point of the original AC–DC MO-OPF model. In Theorem 1, we derive condition under which this KKT point is a saddle point of the original AC–DC MO-OPF problem. The equivalent GDS has the property that it can be solved using a distributed solution algorithm. Every bus in the AC–DC power grid is considered as a local agent in the proposed distributed GDS algorithm, which only obtains information only from its neighbors. In Theorem 2, we prove that proposed distributed approach is locally convergent to the saddle point of the original AC–DC MO-OPF problem. To show the performance of our distributed approach to solve our developed AC–DC MO-OPF model, the simulation results based on several test systems are provided.

Traversable wormholes in [formula omitted] gravity with vanishing speed of sound

In this manuscript, we explore the existence of traversable wormholes (WHs) in the framework of f(R,T) (R is the Ricci scalar and T is the trace of energy–momentum tensor (EMT)) gravity with non-exotic matter and hypothetical condition of stability inside the WH throat. To this end, we choose two different suitable shape functions and obtain the necessary condition for overall stability of fluid evolution threading WH throat. To close the dynamical system of equations, we consider the power-law form of the f(R,T) model and adopt the Padé approximants to characterize rational shape function b(r)r. We consider the lowest Padé order, i.e., P(0,1), and obtain the negligible fluid perturbations inside the WH throat, which implies stable solutions. We determine the suitable bounds on model parameters for the above discussion. Finally, we conclude that only small deviations from general relativity (GR) are permitted where one can find the WH solutions with vanishing sound speed hypothesis in f(R,T) theory.

Theoretical and experimental research on damping performance of suspended multiple mass pendulums damper

Conventional suspended mass pendulum damper (SMPD) include suspended single mass pendulum damper (SSMPD), tandem suspended multiple mass pendulums damper without springs (TSMP), and parallel suspended multiple mass pendulums damper without springs (PSMP), these types of SMPD have the advantages such as clear mechanism, simple construction, and good damping effect, but they have a narrow tuning frequency band and the pendulum length needs to be set too long for low-frequency super tall structures and too short for high-frequency tall structures, limiting their application in practical engineering. Because of this, the paper proposes connecting the spring to the mass pendulum, forming a tandem suspended multiple mass pendulums damper with spring (TSMP-S) and a parallel suspended multiple mass pendulums damper with spring (PSMP-S), and establishing structural system dynamics equations and performing the dynamic characterization of the TSMP-S and PSMP-S, obtain their frequency resolved solutions to explain the damping mechanism. In order to study the vibration-damping performance of these two types of SMPD, through numerical simulations to compare the damping effect of the conventional SMPD, TSMP-S, and PSMP-S on the controlled structures, and a series of shaking table tests on controlled and uncontrolled structures to verify the effectiveness of SSMPD, TSMP, PSMP, TSMP-S and PSMP-S for damping control of controlled structures under conventional earthquake and earthquake at four types of sites. Numerical simulations and shaking table test results in both show that the TSMP-S has the best damping effect, with the advantages of increasing the tuning frequency band, achieving multi-order vibration control, and flexible adjustment of the pendulum length, which is suitable for actual engineering.

An Adaptive Frequency Sampling Algorithm for Dynamic Condensation-Based Frequency Response Analysis

This paper proposed an efficient and adaptive frequency sampling algorithm for frequency response analysis using dynamic condensation-based reduced-order modeling. For the degree of freedom-based model reduction method, the reduced-order basis becomes a frequency-dependent matrix since the relationship between master and slave degrees of freedom stems from partial equations of a second-order dynamical system. Such frequency-dependency makes the analysis inefficient for investigating the frequency response of the system. Considering that the coverage of a local reduced-order basis at a single frequency varies depending on the frequency, a new frequency sampling algorithm was proposed with a strategy of constructing multiple local reduced-order models (ROMs) at sample frequencies. For adaptive sampling, the frequency range of a local ROM was evaluated, and a new sample was added if there was a gap between two adjacent ROMs. As a result, the accuracy of the local ROM can be estimated, and the efficiency in the online stage was greatly enhanced. The proposed method was verified by performing frequency response analysis with several numerical examples, including a large-scale structural and dynamic system.

A new LBFNN algorithm to solve FPK equations for stochastic dynamical systems under Gaussian or Non-Gaussian excitation

In this paper, a new Logistic Basis Function Neural Network (LBFNN) algorithm is proposed and applied to solve Fokker–Planck–Kolmogorov (FPK) equations for stochastic dynamical systems under random excitation. Our attention is focused on the transient solution of the systems under Non-Gaussian excitation. Firstly, we built a neural network by using Logistic probability functions as the basis functions, in which the weighted coefficients are unknown and to be determined. After that, considering the constraint from FPK equation and the normalization condition from the weighted parameters, we construct the loss function to be comprised by these two parts. The innovation of our algorithm is that unknown weighted parameters in LBFNN can be obtained by solving a set of algebraic iteration formulas instead of testify by sample data. Four examples with different dimensions and different excitations are discussed to identify the availability of the LBFNN algorithm. All results show that LBFNN algorithm is not only capable to get transient solutions of the systems under Gaussian white-noise, but also enable us to get the transient solutions in the case of Non-Gaussian excitation. Other techniques including Exact expressions, Gaussian radial basis function neural network (RBFNN) and Monte-carlo simulation are utilized in order to examine the accuracy of the LBFNN algorithm. The good agreements in different comparisons demonstrate the validity and the strength of the LBFNN algorithm.