Dynamic Response Of System Research Articles

Numerical modeling and validation of earthquake soil structure interaction: a 12-story building in Ventura, California

Presented is a validation study for high fidelity numerical modeling of earthquake soil structure interaction (ESSI) for a building, hotel structure in Ventura, California. A detailed finite element (FE) model of the ESSI system, featuring the 12-story concrete structure, pile group foundation, and underlying soil, is developed using the Real-ESSI Simulator (Jeremić et al., The Real-ESSI Simulator System 1988–2022, 2022a). The domain reduction method (DRM) (Bielak et al., Bulletin of the Seismological Society of America, 2003, 93(2), 817–824; Yoshimura et al., Bulletin of the Seismological Society of America, 2003, 93(2), 825–841) is used to apply seismic loads, in this case the 1994 Northridge earthquake motions. Direct comparison between simulation results and California Strong Motion Instrumentation Program (CSMIP) recordings shows a high level of agreement in acceleration and displacement responses at all instrumented locations. Sensitivity study on a number of modeling choices and analysis parameters is conducted to investigate controlling factors for the ESSI response. For example, the soil-structure interaction effect and structural damping ratios are shown to have significant influence on system dynamic response. In addition, the soil inelasticity is shown to be highly influenced by the magnitude of seismic motion. Both effects are important for validation as they contribute to sensitivity of response to parametric variability.

Simulation of transient dynamic response of a locomotive considering its flexibility and rigidity

Time-domain or transient dynamic response method is the most traditional method used to evaluate the dynamic response of a vibratory system subjected to deterministic inputs. The inertia or damping effects are very crucial in the time scale of loading. The present work determines the time domain analysis of railway locomotive using finite element analysis for Indian tracks. The track inputs are modelled as an ellipsoidal bump, and variations in displacement at different key locations of the truck and carbody models are plotted subjected to standard loading conditions. The response plot of the front and rear locations of the locomotive truck and carbody indicate that these regions are more responsive to wheel inputs in comparison to the mid portion due to unbalanced mass distribution. In the further study vertical-lateral random inputs are measured through track recording car and modelled to express in the form of PSD. These random inputs are provided to finite element modelled flexible bogie frame, and acceleration response is determined. The results obtained are compared with the same obtained from rigid bogie frame formulated using an analytical model. The results obtained from the flexible and rigid body models are found to be in good agreement.

Study on dynamic characteristics of urban rail transit vehicle considering faulty axle-box bearings under variable speeds

Axle-box bearing is the key component of urban rail transit vehicles, and its performance status seriously affects the operation safety and stability of the train. Therefore, analyzing the dynamic response of a vehicle system by considering axle-box bearings is the premise of ensuring its safety. Besides, vehicles generally run under the condition of variable speeds, which leads to more complex dynamic response for the vehicle system. Accordingly, studying the influence of faulty axle-box bearings on the vehicle system under variable speeds can reflect the running situation of trains more realistically. In this paper, a dynamics model of axle-box bearings is considered in the vehicle-track coupling model, and the dynamic response of the vehicle system with faulty bearings under variable speeds is analyzed. Firstly, a vehicle-track coupling dynamics model considering axle-box bearings is established, which considers the coupling effect between axle-box bearings and other vehicle components. The bearing inner race is fixedly connected with the axle shaft, and the bearing outer race is fixedly connected with the axle-box housing. Then, an outer race defect model and an inner race defect model of axle-box bearings are respectively established to simulate the internal fault excitation which is often generated in the running process of train bearings. Finally, considering faulty axle-box bearings and variable speeds, the dynamic response of the vehicle system is simulated by the proposed model, whose effectiveness is validated through the theoretical analysis and field tests. The test results show that the axle-box bearing with an outer or inner race defect has a certain influence on the dynamic response of the vehicle system under variable speeds.

Application of optimal control for wind integrated power system

<div align="center"><span>This paper presents the modeling and application of an optimal controller for frequency and tie-line power stability for a two-area interconnected hydro-thermal power plant having tandem compound non-reheat turbines integrated with wind power generation having doubly fed induction generator (DFIG) wind turbines in each area. The power system is interconnected using AC tie-lines. The designed optimal controller was implemented and the system dynamic responses for three power system model states were obtained considering a 1% load fluctuation in one of the areas. The optimal control strategy presented in this paper depends on formulating an error value and finding the feedback gains corresponding to each state of the system, which are easily attainable as outputs. The analysis was undertaken and verified by calculating the performance index value, the closed ring real and imaginary values, finding the feedback gains, and through graphical simulations of the three system models under investigation. The output of the optimal controller was enhanced when the DFIG-based wind turbines were installed in each area combined with a superconducting magnetic energy storage (SMES) unit and a thyristor control phase shifter (TCPS).</span></div>

Euler-buckled beam based nonlinear energy sink for vibration reduction of flywheel system under different excitations

This study develops a new class of Euler-buckled beam based nonlinear energy sink (EBNES) with three configurations, which is expected to attenuate the disturbance effects and further enhance vibration suppression under launching and on-orbit loads simultaneously. The effects of different arrangements on amplitude-frequency responses of the primary system are derived and analyzed through complexification-averaging method, and the approximate solutions are verified by fourth-order Runge Kutta method. Comparison results exhibit that the EBNES-I is much more effective with enhanced vibration reduction performance and stability in a broad frequency range. Furthermore, a two-degree-of-freedom dynamic model of the flywheel system, which integrates the EBNES-I and the supporting structure in satellite, is established. The vibration reduction and bifurcation behaviors of the proposed EBNES-I are investigated, and the efficiency of the proposed EBNES-I in vibration reduction of the flywheel is compared to that of a traditional cubic-stiffness-type NES. It is found that the EBNES-I exhibits a good vibration reduction performance on the dynamic responses of the flywheel system in launching and on-orbit stage simultaneously. Additionally, the bifurcations of the coupled system are studied in order to investigate the influences of gravity and excitation amplitudes on the stability of the EBNES. Calculation results provide conditions for occurrence of the saddle-node (SN) and Hopf bifurcations.

Investigation on the Damping Effect of FST System under Moving Load Using the Track–Tunnel-Layered Saturated Ground Model

In this paper, a single-tier beam-spring-damping system and a two-tier beam-spring-damping system are adopted to simulate the FT (fixed track) and FST (floating slab track) system, respectively. The tunnel is modeled as an infinitely long Euler—Bernoulli beam embedded in the layered saturated soil. By solving the governing equations of the saturated soil and employing the TRM (transmission and reflection matrices) method, the frequency response function of the tunnel-layered saturated soil model is obtained. Making use of the interaction between the tunnel and track systems, the track system is coupled with the tunnel-layered saturated ground model. The solutions for the dynamic response of the track system–tunnel-layered saturated ground model under moving loads in the time–space domain are obtained using the inverse Fourier integral transform. To evaluate the damping effect of the FST system on the vibration of tunnel and soil, four damping coefficients are defined and the vibration results of the FT system–tunnel-layered saturated soil model are compared with those of the FST system–tunnel-layered saturated soil under different moving loads and soil conditions. The numerical results show that both the vibration displacement and acceleration amplitude are attenuated after using the FST system, and the damping coefficient of acceleration is about 30% greater than that of the displacement. In addition, the damping effect of the FST system on the ground surface vibration is associated with the embedded depth of the tunnel and the soil stiffness.

Impact of wheel profile evolution on the lateral motion characteristics of a high-speed vehicle navigating through turnout

The wheel-rail contact asymmetry on the left and right sides of the wheelset while navigating high-speed vehicles through turnouts can lead to lateral motion of the wheelset, ultimately resulting in substantial vibrations in the vehicle system. This study employs the trace method to examine the changing pattern of the wheel-rail equivalent conicity in the turnout area as the wheel profile evolves. A coupled system dynamics model containing flexible turnouts is established. Specifically, the model examines the lateral position of wheel-rail contact points, the lateral motion of the wheelset, and the lateral vibration acceleration of the vehicle system. The study indicates that the lateral motion characteristics of high-speed trains passing through turnouts are influenced by the degree of wheel wear. When the wheels are slightly worn (for mileage below or equal to 100,000 km), the lateral dynamic responses of the vehicle system are affected by the inherent structure of the turnout. When the wheels are severely worn (for mileage above or equal to 150,000 km), the lateral dynamic response of the vehicle system is no longer affected by the inherent structure of the turnout.

Experimental investigation on the nonlinear dynamic responses of the coupled floating submerged artificial seabed-mooring system in internal solitary waves

A new deepwater artificial seabed (DAS) production system is developed as a competitive offshore field development solution in deep and ultra-deep waters. This paper experimentally investigates the acting mechanism of ISWs on the nonlinear dynamic responses of the coupled floating submerged artificial seabed-mooring (ASM) system in a large-scale density-stratified flume. A compositive method for measuring and analyzing the interactions between the ASM system and the ISW is proposed. On this basis, the spatio-temporal features of the dynamic motion responses, the mooring tension variations and the flow field surrounding the ASM coupling system are characterized. The minute motion responses of the test model are captured by a charge-coupled device camera and subsequently processed using a developed image processing method. The temporal tension variations in the mooring lines are measured utilizing a non-contact optical measurement technique. The fluid-structure interaction characteristics between the flow field and the test model are revealed through the particle image velocimetry technique. In addition, the effects of crucial environmental factors on the nonlinear coupled dynamic responses of the ASM system are systematically explored in the experiments. The results indicate that the nonlinear dynamic responses of the ASM system in ISWs are characterized by the significant surge motion (maximum: 14.7% of the water depth), the coupled heave motion with the surge response, and the considerable mooring tension variation (maximum: 31.8% of the pre-tension), especially with the test model located within the density pycnocline.

Dynamic analysis of a dual rotor bearing system passing through critical speed

This research aims to investigate the dynamic response of a dual rotor-bearing system for passing through critical speeds. The Newmark- β method for solving the nonlinear lateral vibration of rotor-bearing systems is approached and the effects of various parameters including shaft crack, unbalanced mass, shaft bow, and support parameters are shown. A model, including shaft cracks, rotor unbalance, and shaft bow, is established using the finite element method with six degrees of freedom per node. The results provide a detailed feature analysis of the support parameters in a dual rotor-bearing system when it is coupled with various faults to pass through the critical speeds.

Refined Equivalent Modeling Method for Mixed Wind Farms Based on Small Sample Data

For equivalent modeling of mixed wind farms (WFs), existing clustering indicators cannot consider the complex coupling characteristics between different types of wind turbines (WTs). In this paper, a refined equivalent modeling approach based on artificial intelligence technology is proposed. Firstly, the electromechanical transient performance of mixed WFs is analyzed. The WT type, wind speed and direction, and voltage dip are considered the dominant factors affecting the external dynamic response of mixed WFs. Secondly, the equivalent node model is established, including the selection of independent and dependent variables. Then, the multiple artificial neural networks (ANNs) are trained one by one based on small sample data, to fit the nonlinear relationship between the dependent variables and the independent variables. Finally, the dynamic response of the power systems with a mixed WF is simulated in the MATLAB platform. A comparison of the errors in electromechanical phenomena demonstrates that the proposed model can reflect the external characteristics of the test mixed WF in different wind conditions and voltage dips.

Nonlinear Dynamic Responses of Rigid Rotor Supported by Thick Top Foil Bearings

This study focuses on thick top foil bearings (TTFBs), which can prevent top foil from sagging and significantly reduce the load capacity of gas foil bearings (GFBs). However, the limited research on the dynamic responses of TTFB-rotor systems has hindered their wide application of TTFBs with high load capacity. To address this, an integrated nonlinear dynamic model is developed to analyze the linear dynamic responses of a rigid rotor supported on TTFBs. The model incorporates time domain orbit simulation, considering unsteady Reynolds equations, foil deformation equations, thick top foil motion equations, and rotor motion equations. A symmetrical test rig is used to validate the model, and three types of TTFBs with different bump foil stiffness are tested, with experimental results aligning with the model predictions. This study also investigates the effects of nominal clearance, static load, and unbalance on TTFB-rotor systems. The results indicate that unbalance has minimal impact on subsynchronous vibrations. However, larger bump foil stiffness, increased normal clearance, and higher static load contribute to improved stability and higher maximum stable speed of the TTFB-rotor system. Moreover, other relevant parameters reducing the bearing attitude angle can further enhance the system’s stability.

Development and analysis of magnet-engaged piezoelectric energy generator under friction-induced vibration

Piezoelectric energy transducers, which can be an efficient solution for the power supply of wireless devices, have been widely researched. This study investigated the characteristics of a magnet-engaged nonlinear piezoelectric energy generator stimulated by friction-induced vibration (FIV), in two distinct design configurations (in-parallel and in-series). A mathematical model was developed, and the dynamic response of the mechanical system and voltage output from the piezoelectric shear deformation were solved using an iterative method. A friction model considering the Stribeck effect was introduced to describe the friction motion. The emergence of a stick-slip motion induced limit cycle and its vanishing delineates the unstable and stable regions of the system, respectively. A critical sliding velocity vc splits the regions. When the sliding velocity exceeds vc, the system remains in stable region with exclusive slip friction behavior. Parameter studies were conducted to explore the effect of decay factor β, dynamic friction coefficient μk, static friction coefficient μstatic, and normal force FN on vc. The results indicate that increasing β and μk can reduce the unstable region and generation of FIV, whereas, increasing FN and μstatic can promote the occurrence of FIV. The energy generation was evaluated by a transient charging simulation that has been experimentally validated in a previous study. The influence of β, μk, μstatic, and FN on the energy generation was also investigated relative to the operating velocity range (OVR) and sum of root mean square charging power (SRCP). The in-parallel systems exhibit a higher SRCP within the same OVR, whereas the in-series systems are more likely to excite FIV with a wider OVR. Additionally, the simulation results of fluctuating working conditions show that both fluctuating FN and v0 have negative effects on the energy generation. The nonlinear in-series system exhibits better robustness with the least affected SRCP and almost unchanged OVR under fluctuating FN and v0.

Analysis of Train-Track-Bridge Coupling Vibration Characteristics for Heavy-Haul Railway Based on Virtual Work Principle.

This paper introduces an innovative model for heavy-haul train-track-bridge interaction, utilizing a coupling matrix representation based on the virtual work principle. This model establishes the relationship between the wheel-rail contact surface and the bridge-rail interface concerning internal forces and geometric constraints. In this coupled system's motion equation, the degrees of freedom (DOFs) of the wheelsets in a heavy-haul train lacking primary suspension are interdependent. Additionally, the vertical and nodding DOFs of the bogie frame are linked with the rail element. A practical application, a Yellow River Bridge with a heavy-haul railway line, is used to examine the accuracy of the proposed model with regard to discrepancy between the simulated and measured displacement ranging from 1% to 11%. A comprehensive parametric analysis is conducted, exploring the impacts of track irregularities of varying wavelengths, axle load lifting, and the degradation of bridge stiffness and damping on the dynamic responses of the coupled system. The results reveal that the bridge's dynamic responses are particularly sensitive to track irregularities within the wavelength range of 1 to 20 m, especially those within 1 to 10 m. The vertical displacement of the bridge demonstrates a nearly linear increase with heavier axle loads of the heavy-haul trains and the reduction in bridge stiffness. However, there is no significant rise in vertical acceleration under these conditions.

Magneto-thermo-elastic coupling vibration and bifurcation characteristics of functionally graded rotating cylindrical shell

The magneto-thermo-elastic coupling vibration of rotating ferromagnetic functionally graded cylindrical shell is investigated in this paper. Based on the physical neutral surface theory and Donnell's theory, the expressions of kinetic energy and strain energy are obtained by introducing geometric nonlinearity. The magneto-thermo-elastic vibration equations of the rotating ferromagnetic functionally graded cylindrical shell in multi-physical field are derived via the Hamilton's principle. Considering the magnetization effect of ferromagnetic shell in magnetic field, the expression of magnetization force is obtained according to the nonlinear magnetic constitutive relation. For simply supported boundary conditions, Galerkin's method is used to obtain the discretized ordinary differential equations, and the static deflection of the shell under static load is solved. The steady-state response of the system during primary resonance and the stability of solutions are given by the multi-scale method and the Lyapunov stability theory. Through numerical examples, the characteristic curves and surfaces of amplitude are plotted, and the parameter ranges corresponding to regions of multi-valued solutions and stable solutions are determined. The system dynamics laws describing the coupling effect between multiple parameters such as force, magnetism, heat, and rotational speed are evaluated. The Global bifurcation diagrams and the maximum Lyapunov exponent spectrums under different control parameters are plotted to analyze the effect of parameter changes on the dynamic response of system. The results show that the vibration characteristics of the system are significantly influenced by the external physical fields, in addition to the shell size and material volume fraction. Slight changes in parameters can lead to violent changes in the dynamic response of the system, exhibiting intermittent, jumping, and chaotic characteristics.

A decoupled approach for determination of the joint probability density function of a high-dimensional nonlinear stochastic dynamical system via the probability density evolution method

The joint probability density function (PDF) of multiple response processes of a system is a crucial topic in the fields of science and engineering. It is adopted to describe the dependent uncertainty propagation in complex stochastic dynamical systems, including the displacement and velocity of one degree of freedom (DOF), and the nonlinear probabilistic dependencies between multiple variables. However, the partial differential equations (PDEs) governing the time evolution of joint PDFs for multiple stochastic processes are often high-dimensional and coupled, making them analytically or numerically intractable for systems with high dimensionality. The probability density evolution method (PDEM) has provided a new perspective from the standpoint of random events description of the principle of preservation of probability. For an n-dimensional system, if merely the joint PDF of m processes is needed, where m is not larger than n, then it is sufficient to solve the generalized density evolution equation (GDEE), i.e., the Li–Chen equation, in m dimensions. This approach is particularly convenient for cases where n is large while m is small. However, for cases where m is not less than two, it is still challenging to avoid solving high-dimensional PDEs. This paper proposes a new method for the determination of joint PDF of multiple responses based on the principle of preservation of probability. To capture the joint PDF of m processes, the m-dimensional PDE can be transformed into m one-dimensional PDEs, significantly reducing the computational complexity of numerical implementation. The proposed method gives an enhanced version to the PDEM, enabling it to not only determine the individual probabilistic response, but also efficiently determine the dependent probabilistic distribution of multiple responses of high-dimensional stochastic dynamical systems without solving the coupling PDE. It reduces the computational cost from exponential growth of m powers to linear growth. Some numerical examples are presented to verify the effectiveness of the proposed method. Finally, problems for future investigations are discussed.

Extended‐state‐observer‐based adaptive robust control of a single‐axis hydraulic shaking table

AbstractThe shaking table test has been widely recognized as one of the most reliable methods for assessing the dynamic response of structures and systems when exposed to a range of vibrations. Replicating these vibrations, recorded as acceleration signals, necessitates precise controller designs. However, traditional controller designs primarily rely on linear system assumptions, leading to complications in incorporating parametric uncertainty and uncertain non‐linearity. This paper presents a novel approach to the acceleration trajectory control problem of single‐axis hydraulic shaking table systems from a non‐linear perspective. This strategy employs a controller combined with an extended state observer (ESO) and adaptive control, offering a design that more closely reflects real‐world scenarios and requires less parameter adjustment. The ESO estimates the uncertain non‐linearity using the displacement signal, while the parametric uncertainty is tackled through adaptive control. The proposed controller's effectiveness is validated through theoretical proof using Lyapunov analysis. The analysis demonstrates that asymptotic tracking performance is guaranteed when the uncertain non‐linearity is time‐invariant. Moreover, with time‐variant uncertain non‐linearity, the controller can also ensure both prescribed transient tracking performance and final tracking accuracy. Comparative experiment results underscore the superior performance of the proposed controller.

Study on the structural stability of the rail pad and its influence on the dynamic response of the vehicle-track coupled system

This paper investigates the structural stability difference between Grooved Rail Pads (GRP) and Mesh-Type Rail Pad with Damping Blocks (MTRPDB), along with their impact on vehicle-track coupled systems. Firstly, the different loading tests reveal that both Rail Pad (RP) types exhibit increased static/dynamic stiffness when with higher loading. The MTRPDB maintains superior structural stability and vibration absorption under large loading, and the fatigue tests confirm its better fatigue resistance. Then, finite element analysis demonstrates that MTRPDB outperforms GRP with a higher bearing capacity and lower stress level under large loading. Moreover, MTRPDB can better maintain a linear stiffness under identical working conditions. Finally, the dynamic analysis reveals that an increasing number of RP failures negatively impact train safety, and the car body acceleration significantly rises with more RP failures. Furthermore, the MTRPDB exhibits lower dynamic responses compared to GRP across different speed conditions, indicating its superior vibration absorption capacity.

Dynamic Response and Running Safety of High-Speed Railway Train–Track–Bridge System Under Near-Fault Pulse-Type Ground Motion

The pulse effect of near-fault ground motion has asevere threat to high-speed railway train running on bridge. Current research generally relies on numerical simulation and lacks physical test data. In this paper, a scale indoor physical test of high-speed train running on bridge is conducted and dynamic characteristics of high-speed railway train–track–bridge system under near-fault pulse-type ground motion are explored. The bridge of the physical test is excited by shaking table with lateral inputs of near-fault pulse-type ground motion, pulse-free ground motion and far-field ground motion. A corresponding numerical model is established and validated by the test data. Then, the influence regularities of pulse effect on system dynamic response and running safety indexes are explored under different peak ground acceleration (PGA) and train speeds using data of the physical tests and the numerical simulation comprehensively. Results suggest that compared to the near-fault pulse-free ground motion and the far-field ground motion, the near-fault pulse-type ground motion leads to larger lateral beam displacement, lateral train acceleration, and running safety indexes in different degrees. And from the data results of this paper, its lateral wheel–rail force and derailment coefficient are the first to break through the limit values. By studying the parameter sensitivity of lateral train acceleration, it was found that under the near-fault pulse-type ground motion, the lateral train acceleration is significantly more sensitive to changes of train speed and PGA. From the perspective of energy, the near-fault pulse-type ground motion results in spectrum intensity (SI) indexes which are larger and improve faster with the increase of PGA than other ground motions. This indicates that it inputs significantly more energy into the high-speed railway train–track–bridge system, although it may not excite larger lateral beam acceleration.

Optimizing direct power control of DFIG-based WECS using super-twisting algorithm under real wind profile

In this study, we address the optimization of the direct power control of a doubly fed induction generator within a wind conversion system under actual wind conditions. The primary objective is to enhance the dynamic response of the wind energy conversion system (WECS) while minimizing the impact of wind fluctuations on power generation. To achieve this goal, we introduce a novel control methodology based on the super-twisting algorithm (STA). This approach allows for effective regulation of both reactive and active power output in the WECS. We employ comprehensive simulations using a detailed model of the WECS and real wind profiles to evaluate the efficacy of the STA-based control strategy. Our simulations demonstrate that the adopted STA-based control strategy successfully tracks the desired power set-point and effectively mitigates the adverse effects of wind power fluctuations and uncertainties on the WECS power output. Specifically, it exhibits superior performance in managing transients and rejecting disturbances compared to a conventional approach employing a switching table and hysteresis controller. These results suggest the practical viability and potential applications of the STA-based control strategy in real-world wind energy systems.

A comprehensive study on natural characteristics and dynamic responses of a dual-rotor system with inter-shaft bearing under non-random uncertainty

Aeroengines are usually designed with a dual-rotor configuration for the rotating part. A dual-rotor system has coupling characteristics introduced by an inter-shaft bearing, and the rotating direction of the rotors has critical influences on the performance. It becomes more complicated when the inevitable uncertainties of the dual-frequency excited dynamical system are considered. This paper delivers a comprehensive study of the natural characteristics and dynamic responses of a dual-rotor system with an inter-shaft bearing considering the non-random parametric uncertainties under co- and counter-rotating conditions. To this end, the finite element modeling and the deterministic solutions of a dual-rotor system are established. Then, the polynomial surrogate function is constructed for the desired natural characteristics and dynamic responses under non-random uncertainty. The polar interpolation technique is implemented to compute uncertain shaft orbits, overcoming difficulties in the traditional frequency-sense measure. Intensive case studies for different interval uncertain parameters are carried out and the results are comparatively discussed. It is found that the mass unbalance uncertainties only affect the respective modes excited by the rotor where the unbalance is located. The shaft stiffness has global uncertainty effects on the Campbell diagram, mode shapes, time history, shaft orbit and responses. Uncertainties in the inter-shaft bearing stiffness and speed ratio generally influence higher-order modes. The results of the present work gain insights into the modal characteristics and dynamical behaviors of the dual-rotor system under complex parametric uncertainties.