Dynamic Equations Of System Research Articles

Analysis of the influence of the track vertical profile irregularity on the vibration of the vehicle and the track under high speed moving train

A high speed train-track coupling system vertical dynamics model is established by considering the nonlinear wheel-rail contact, and the cross iteration method for solving the train-track nonlinear coupling system dynamics equations is proposed. Four kinds of track irregularities, i.e. the smooth track, the track random irregularity, the short-wave irregularity, and the combined track random irregularity and short-wavelength irregularity, on the vibration responses of the train and the track are analyzed with thismodel. The calculated results show that the vehicle and the bogie passing frequencies are the main excitation sources of the track vibration displacement and velocity, whereas the short-wave irregularity is the main excitation source of the track vibration acceleration. The track random irregularity, the short-wave irregularity and the sleeper spacing have great influence on the wheel-rail force, and the wheelset and the bogie vibration acceleration, while the car-body vibration acceleration is mainly affected by the track random irregularity.

Dynamic response mechanism analysis of hinged FBG acceleration sensor

Considering the influence of the adhesive layer and hinge structure on the dynamic response effect of the hinged fiber Bragg grating (FBG) acceleration sensor, a multi-degree-of-freedom series vibration model and a transfer function were established based on the system dynamic equation. The stiffness calculation formulas of the hinge and adhesive layer were derived based on Castigliano’s second theorem. The results demonstrated that the response time of the sensor could significantly lag when the elastic modulus of the adhesive layer is lower than a certain critical value. The most crucial parameter affecting the dynamic response performance of the sensor is hinge thickness. The jagged oscillations in the sensor response signals can be reduced with the appropriate increase in the thickness, width, and semi-minor axis of the hinge as well as by reducing the semi-major axis of the hinge. However, it could also lead to an increase in the resonance frequency and a decline in sensitivity.

Dual-Attitude Decision-Making Processes of Construction Worker Safety Behaviors: A Simulation-Based Approach.

Workplace accidents are of great concern in the construction industry. Most of those accidents are caused by unsafe behavior in the workplace. Many previous studies have analyzed the causes of workers' unsafe behaviors, but few have investigated workers' feelings of insecurity from the perspective of systematic psychological theory. This study developed an attitude-behavior-intervention feedback loop mechanism of construction workers and used the dual-attitude theory to explain the occurrence mechanisms of unsafe behavior. Using this mechanism, an active-intervention system-dynamics model and a passive-intervention system-dynamics model were designed and simulated. The coefficient of the system dynamics equation in the simulation model involved meta-analysis to combine the correlation coefficients of existing studies, which increased the sample size and improved the statistical test efficiency. The results show that an implicit safety attitude has a more significant impact on safety behavior, and the effect of an active intervention is stronger than that of a passive intervention. Based on these results, this paper presents some feasible suggestions to reduce the probability of unsafe worker behaviors occurring.

Study on impact dynamic characteristics of semi-autogenous mill liner based on improved multivariable method

The impact resistance of semi-autogenous mill liner has an important influence on the reliable operation of the system. The complex dynamic characteristics in the process of collision with abrasive medium are studied by the improved multivariable method proposed in this paper. Firstly, based on manifold element method, the deformation of abrasive medium and lining plate in the contact area is expressed by the coordinates of first-order manifold element basis function, while the deformation of the non-contact region is described by modal coordinates to improve the traditional multivariable method, and the displacement constraint equations as well as the acceleration constraint equations of the collision system are derived, then the Lagrange method is used to establish the impact dynamic equation of abrasive medium and lining plate system. Secondly, a collision test rig between abrasive medium and lining plate was built to verify the correctness and accuracy of the proposed method. Finally, the influence of structural parameters and motion parameters of abrasive medium and lining plate on the dynamic characteristics of collision system is analyzed by parameter analysis method. It is found that when the Poisson’s ratio of abrasive medium to lining plate material exceeds 1.0, the increase amplitude of stress becomes smaller. The increase amplitude of displacement, velocity, acceleration and stress at the collision contact point decreases when the initial velocity of abrasive medium exceeds 3.0 m/s. The stress at the collision contact point changes greatly, and the maximum acceleration occurs in advance when the radius of abrasive medium exceeds 20 mm. When the thickness of liner exceeds 40 mm, the time of maximum acceleration to reach is almost unchanged. The results show that compared with the traditional multivariable method, the improved multivariable method can increase the modeling efficiency and solving accuracy, and lay a theoretical foundation for optimizing the structure of the liner and raising the service life of the system.

Nonlinear vibration analysis of beam-like bridges with multiple breathing cracks under moving vehicle load

The beam-like bridges with small and medium spans are designed to mainly sustain the moving vehicle. Hence, the dynamic behavior of bridges under vehicular loading can provide important information for the bridge design, assessment, and maintenance. Cracks, as one of the most common damage in the bridge structures, alter the bridge dynamic characteristics and therefore responses to the moving vehicle. This paper proposes a novel semi-analytical approach for nonlinear vibration analysis of the beam-like bridges with breathing cracks subjected to vehicular loading, taking into account the dynamic interactions between the vehicle and cracked bridge. The Dirac’s delta function is utilized to represent the local stiffness change at the crack location, leading to closed-form solutions of mode shapes of the cracked beam. The breathing process of the crack, causing eigenproperties of the beam to change over time, is characterized by the time-varying curvature of the bridge. Subsequently, the nonlinear dynamic equation of the vehicle-cracked bridge interaction system is established, which is solved through a formulated double-iterative numerical scheme. Eigenvalues and dynamic responses of the bridge with open crack presented in the literature are compared with those obtained from the proposed approach for purposes of validation. The effects of various crack parameters, vehicle speed, and bridge surface irregularity are investigated through a parametric study. In addition, the detection of breathing cracks is also discussed. The results show that the proposed approach can be used to effectively obtain the nonlinear vibration characteristics and dynamic responses of the beam-like bridge with general boundary conditions and different crack numbers, locations, depths, and initial status under moving vehicle. Moreover, the approach has the potential to be incorporated into the vibration-based bridge damage detection.

Analysis of the effect of squeeze film damper on the bending-torsional coupling vibration characteristics of dual-rotor system

The study of the vibration reduction characteristics of SFD to the bending-torsional coupled vibration of the dual-rotor system can provide support for the structural design of aero-engines. Based on the overall eccentric disc model, the bending-torsional coupling dynamic equation of the dual-rotor system is established in this paper. The amplitude and nonlinear periodic characteristics of the dual-rotor system are obtained by combining Newmark-β method and Newton-Raphson method. The results show that the vibration reduction effect of SFD on bending-torsional coupling vibration is closely related to the speed. The vibration reduction effect of SFD is weak at the first-order critical speed range and below, and reduces the torsional amplitude by 70 % at the second-order critical speed range and above. SFD kept the bending-torsional coupling vibration of the dual-rotor system stable in a stable 5-period motion state.

Phonon and Optical-roton Branches of Excitations of the Bose System

For a system of a large number of Bose particles, a chain of coupled equations for the averages of field operators is obtained. In the approximation where only the averages of one field operator and the averages of products of two operators at zero temperature are taken into account, there is derived a closed system of dynamic equations. Taking into account the finite range of the interaction potential between particles, the spectrum of elementary excitations of a many-particle Bose system is calculated, and it is shown that it has two branches: a sound branch and an optical branch with an energy gap at zero momentum. At high density, both branches are nonmonotonic and have the roton-like minima. The dispersion of the phonon part of the spectrum is considered. The performed calculations and analysis of experiments on neutron scattering allow to make a statement about the complex structure of the Landau dispersion curve in the superfluid $$^4$$ He.

State-unknown single parameter learning adaptive output feedback control for ship dynamic positioning

This paper focuses on the ship adaptive dynamic positioning output feedback control considering the thruster system dynamics, solving the problems of the ship output end affected by measurement noise, unmeasurable ship speed, unknown time-varying disturbance, model parameter ingestion, and input saturation simultaneously. First, a high-gain state observer is used for online estimation of the unknown ship speed, and an update gain technique is introduced to ensure the speed of state construction and reduce the effect of measurement noise. In addition, a single-parameter learning neural network is used to solve the unknown time-varying disturbance and ship model parameter ingestion problem. Furthermore, the thruster system dynamic equation is considered to solve the thruster system dynamic characteristics. Finally, the finite-time auxiliary dynamic system is used to deal with the input saturation problem. The analysis process shows that the control method can make the ship finally reach and stay in the desired position and desired heading, and all control variables in the designed dynamic positioning system are consistent and eventually bounded. The simulation results show that the proposed dynamic positioning control method is effective.

An improved Hamiltonian finite element method for three-dimensional nonlinear dynamics of towed system

An improved Hamiltonian nodal position finite element method without any coordinate transformation is developed to numerically analyse the three-dimensional nonlinear dynamics of towed system, in which the dynamic equation of towed system is derived and built in global system. The medium resistance effect is taken into consideration, the deformation of towing cable is modelled using logarithmic strain theory, the coupling force between towed system and the surrounding medium is modelled by Morison formulation. The dynamic canonical equations of towed system would be updated for each time step due to the strong nonlinearity of the flexible towing cable. A first-order Symplectic difference scheme is formulated and applied to solve the canonical equations. The Symplectic conservation and high efficiency features of the proposed method are firstly validated by the solution of a U-turn towed system dynamics, the results are compared with the ones retraced by LS-DYNA. A linear towed system experiment in air environment is reconstructed and calculated to further validate the robustness of the proposed method, in which the air resistance influence is of the essence.

A simplified analytical model of equipment-pipe-shell structure

In addition to being directly connected to the base, the mechanical equipment in the ship is often connected to the shell through attachment elements such as pipelines. There are multiple vibration transmission paths in the system, and there is still a lack of in-depth theoretical research on this type of system. To study the vibration transmission characteristics of the system, a simplified analytical model of equipment-pipe-shell structure is proposed. The equipment and shell are approximated by rigid bodies, and the pipe is represented by an elastic cylindrical shell. In addition to the pipe, the equipment is also connected to the shell through several vibration isolators. Travelling wave solution is used to express pipe response, and the forces on the equipment and the shell can be obtained through the continuity condition at both ends of the pipe and the internal forcedisplacement relationship. By solving the system dynamic equation, the response of any point in the system can be obtained. The comparison of the analytical model calculation results and finite element simulation results verifies the accuracy of this analytical model.

Method of an Asymptotic Analysis of the Nonlinear Monotonic Stability of the Oscillation at the Problem of Damping of the Angle of Attack of a Symmetric Spacecraft

One of the current directions in the development of the modern theory of oscillations is the elaboration of effective methods for analyzing the stability of solutions of dynamical systems. The aim of the work is to develop a new asymptotic method for studying the nonlinear monotonic stability of the amplitude of plane oscillations in a dynamic system of equations with one fast phase. The method is based on the use of the method of variation of an arbitrary constant, the averaging method, and the classical method of mathematical research of the function of one independent variable. It is assumed that the resulting approximate analytical function is defined and twice continuously differentiable on the entire considered interval of change of the independent variable. It describes the nonlinear and monotonic evolution of the oscillation amplitude on the entire considered interval of change of the independent variable. In the paper, this method is applied to the problem of nonlinear monotonic aerodynamic damping of the amplitude of oscillations of the angle of attack during the descent of a symmetric spacecraft in the atmosphere of Mars. The method presented in this paper made it possible to find all characteristic cases of nonlinear monotonic stability and instability of the oscillation amplitude of the angle of attack. In addition, one should speak of a symmetrical quantity of different cases of stability and instability, located on different sides of the zero value of the first average derivative of the angle of attack.

Experimental and numerical study on vibration and structure-borne noise of composite box-girder railway bridges

ABSTRACT This paper adopts a proficient approach to evaluate vibration and structure-borne noise and makes up for the steel-concrete composite (SCC) box girder vacancy in the SCC structure. First, the dynamic equation of the train-rail system is established, the pseudo-response of the system in the frequency domain is appropriately assessed by pseudo excitation method (PEM), and the frequency spectra of the wheel-rail force as well as the forces transmitted to the bridge are obtained. Next, applying the force to the finite element method (FEM), boundary element method (BEM), and statistical energy analysis (SEA) model. The vibration and structure-borne noise of the SCC box girder are calculated in the frequency domain. Then, the effectiveness of the method and model is verified through the comparison of the field experimental results. Finally, the effect of the ground reflection in the SEA model is considered using the sound ray-tracing method for the first time.

Improved method for analysing the dynamic response of gear transmission systems

PurposeThe purpose of this paper is to propose an improved method which can shorten the calculation time and improve the calculation efficiency under the premise of ensuring the calculation accuracy for calculating the response of dynamic systems with periodic time-varying characteristics.Design/methodology/approachAn improved method is proposed based on Runge–Kutta method according to the composition characteristics of the state space matrix and the external load vector formed by the reduction of the dynamic equation of the periodic time-varying system. The recursive scheme of the holistic matrix of the system using the Runge–Kutta method is improved to be the sub-block matrix that is divided into the upper and lower parts to reduce the calculation steps and the occupied computer memory.FindingsThe calculation time consumption is reduced to a certain extent about 10–35% by changing the synthesis method of the time-varying matrix of the dynamics system, and the method proposed of paper consumes 43–75% less calculation time in total than the original Runge–Kutta method without affecting the calculation accuracy. When the ode45 command that implements the Runge–Kutta method in the MATLAB software used to solve the system dynamics equation include the time variable which cannot provide its specific analytic function form, so the time variable value corresponding to the solution time needs to be determined by the interpolation method, which causes the calculation efficiency of the ode45 command to be substantially reduced.Originality/valueThe proposed method can be applied to solve dynamic systems with periodic time-varying characteristics, and can consume less calculation time than the original Runge–Kutta method without affecting the calculation accuracy, especially the superiority of the improved method of this paper can be better demonstrated when the degree of freedom of the periodic time-varying dynamics system is greater.

New continuous-discrete model for wireless sensor networks security

A wireless sensor network (WSN) is a group of "smart" sensors with a wireless infrastructure designed to monitor the environment. This technology is the basic concept of the Internet of Things (IoT). The WSN can transmit confidential information while working in an insecure environment. Therefore, appropriate security measures must be considered in the network design. However, computational node constraints, limited storage space, an unstable power supply, and unreliable communication channels, and unattended operations are significant barriers to the application of cybersecurity techniques in these networks. This paper considers a new continuous-discrete model of malware propagation through wireless sensor network nodes, which is based on a system of so-called dynamic equations with impulsive effect on time scales.

Fuzzy Sliding Mode Control with Moving Sliding Surface of Rotary Inverted Pendulum

In this study, considering the dynamic equations of the rotary inverted pendulum system and the motor dynamics, pendulum angle is controlled with fuzzy logic sliding mode control method which has moving sliding surface using state variables in Matlab program. The sliding surface of sliding mode control method is selected as moving. A fuzzy logic structure is used to calculate the slope of slip surface. The boundary values of the membership functions in the fuzzy logic structure have been optimized using genetic algorithm codes in Matlab program. The sum of the squares of the errors is preferred as the objective function. Inputs of the fuzzy logic structure are the error of the pendulum angle and the derivative of pendulum angle error. In the fuzzy logic structure, the slope of sliding surface of sliding mode control structure is obtained as an output. From the results, it was seen that the pendulum angle reached the desired reference value around the first second and the error was approximately zero. In addition, it has been observed that the motor torque value is at the levels of 20 Nm and the motor current value is at the levels of 3 ampers. It has been obtained from the results that the motor values are at reasonable levels close to the values in practical applications. When the motor is selected according to these obtained values, there won't be a problem with the implementation of this control method in real-time applications of the rotary inverted pendulum system

Mathematical Model of Spatial Motion of the Controlled Parachute-Tether System of the Wind Kite Type

Mathematical modeling is created for the mathematical task of spatial motion of the controlled parachute-tether system of the “wind kite” type. The mathematical model parachute-tether system consists of a model of the main para-chute and a model of the braking parachute. The parachutes are connected by the tether. The model of the main para-chute is supposed to be the solid body. This solid body has two planes of symmetry. The braking parachute is the solid body with axial symmetry. The tether model is an absolutely flexible elastic thread. The tether is connected by ideal hinges with the main parachute and braking parachute. The control of the main parachute is carried out by changing the length of the control slings. Changing the length causes deformation of the dome. This is the reason for the change in its aerodynamics. Maneuvering of the main para-chute occurs in the vertical plane, when the length of the control slings changes simultaneously. Maneuvering of the main parachute in space is carried out when the length of the control slings changes, when the slings are given a travel difference. The system of dynamic and kinematic equations is designed for calculating the controlled spatial movement of the main parachute, braking parachute and tether. The option exists when the mass of the tether and the forces applied to the tether cannot be neglected. The motion of the tether is represented by the equations of motion of an absolutely flexible elastic thread in projections on the axis of a natural trihedron. The mathematical model is represented by a system of ordinary differential equations and par-tial differential equations. The problem is solved using various numerical methods. The solution is possible with the help of an integrated numerical and analytical approach as well.

FREQUENCY OF NON-LINEAR DYNAMIC RESPONSE OF A POROUS FUNCTIONALLY GRADED CYLINDRICAL PANELS

In this article, a nonlinear dynamical investigation of porose functionally graded cylindrical panels using a proposed analytical model is carried out. The material's properties are considered to be porosity-dependent and graded in the thickness direction, corresponding to a power-law distribution. The classical shell theory, with the geometrical shape of nonlinear in von Karman–Donnell, is employed to get the Lagrange motion equations. By applying the Galerkin procedure, the system of nonlinear dynamic vibration equations is found. The natural frequencies and dynamic amplitude vibrations are obtained by using the fourth-order Runge–Kutta approach. In numerical analyses, the effects of porosity factor, power-law index, porous FGM thickness, frequency–amplitude relation, and excitation force on the dynamic response of thin functionally graded porous cylindrical panels are investigated. Through the obtained results, it is discovered that the porosity coefficients have important effects on the natural frequencies and amplitude of the nonlinear dynamic response of the FG structures. It leads to a reduction in natural frequencies by 5.74 % at 10% pores.

Charge transport in quantum dot sensitized solar cells: A mathematical model

In this paper, charge transport in quantum dot (QD) thin films is modeled by considering trap-state assisted tunneling among the QD thin films. Multiple parameters associated with traps like density, position, and capture/emission rates which can significantly affect tunneling, have been considered in the model. The model is further extended to the quantum dot sensitized solar cells (QDSSC), and the effects of tunneling rate variation in accordance with the trap-states at the QD-QD interfaces and/or in the shell of QDs is analyzed. In the proposed model, multiple silicon QD layers as active material are considered, which are sandwiched between ZnO as electron transport layer (ETL) and a MoO3 as hole transport layer (HTL). The model couples drift–diffusion framework for charge transport in ETL and HTL, and a system of rate equations for carrier dynamics among the QDs and their interfaces with ETL and HTL. Our analysis shows that the variations in trap-state concentration significantly affect the charge extraction and recombination scenario in the active layer of QDSSC, consequently producing a direct impact on device characteristics.

Vibration Reduction of a Timoshenko Beam with Multiple Parallel Nonlinear Energy Sinks

A nonlinear energy sink is a promising device to reduce structural vibrations. In this work, the vibration reduction performances of multiple parallel nonlinear energy sinks attached to a short beam are investigated based on the Timoshenko beam theory. The dynamic equations of a vibration reduction system subjected to a harmonic excitation are established. The frequency responses are analyzed based on Galerkin discretization and the harmonic balance method, and the accuracy is verified by the Runge–Kutta method. An optimization method based on the genetic algorithm is proposed for the number, location, and cubic stiffness of the nonlinear energy sinks. The study reveals that, with the same total mass, multiple parallel nonlinear energy sinks can achieve a larger vibration reduction ratio than a single nonlinear energy sink. The parameter influences of the nonlinear energy sinks are revealed, and unstable responses with large cubic stiffness are presented. The optimal locations of the multiple parallel nonlinear energy sinks are related to low-order modal shapes. A larger reduction ratio on the resonant amplitude can be achieved compared to a uniform distribution of the nonlinear energy sinks. The optimal locations and cubic stiffness are related to the number of nonlinear energy sinks. In the studied case, the optimal number of nonlinear energy sinks was two.

Key characteristics of generic bond graphs for planetary gears

This paper deals with generalized power flow models of compound planetary gear trains based on standard planetary gears. In this context, the Bond Graph approach provides an optimal tool for a large variety of structures. Starting with compound gears based on two standard planetary gears, two kinds of parameter definitions are discussed and two specifications for power ratio and efficiency are compared. Next, the influence of elastic shaft connections is clarified. Essential methods for these findings are the use of symmetry and the definition of sub-systems and, if applicable, of scalar or vectorial models. The second part deals with the effect of the number of constraints on constructions based on three standard planetary gears. Typical consequences, such as the number of free running elements, of complete Willis equations or of self-locking impacts, are systemized and illustrated by means of reference instances. It is shown by example that constructions featuring five external shafts would avoid such effects. Corresponding outcomes for the equivalent dynamic system equations, the parameter definitions and the Bond Graph modelling are given.