Response Of Coupled System Research Articles

Statistical energy analysis for vibro-acoustic coupled system with fuzzy parameters

PurposeThis paper aims to propose a novel statistic energy analysis method with fuzzy parameters to study the dynamic and acoustic responses of coupled system with fuzzy parameters, which can expand the applied range of statistic energy analysis method in engineering to some extent.Design/methodology/approachOn the basis of the property of membership level, the uncertain fuzzy parameters are expressed as the interval forms. Interval mathematics and interval expansion principle are adopted to solve the problem with interval parameters. At last, two numerical examples, which include a two-plate coupled system and a single-partition sound-insulation system, are carried out to demonstrate the feasibility and validity of the presented method.FindingsInterval mathematics and interval expansion principle are adopted to solve the problem with interval parameters.Originality/valueBy integrating the interval analysis, optimization technique and Taylor expansion method, two non-probabilistic, set-theoretical statistical energy analyses are proposed for predicting the dynamical and acoustical response of the complex coupled system with uncertain parameters in high-frequency domain.

Structural-acoustic interaction of a three-dimensional panel–cavity–duct system with non-uniform boundary restraints

Plate drum-silencer has received a lot of research attention due to its excellent low frequency noise attenuation and flow-through characteristics. The majority of existing studies are limited to the classical or uniform elastic boundary conditions, while there is little effort devoted to the study of boundary restraint non-uniformity effect on the vibro-acoustic behavior of such silencing system. Motivated by the current limitation, the structural-acoustic coupling model of a three-dimensional panel–cavity–duct silencer is established, in which the elastic boundary restraint can be set as arbitrary distribution function. Energy principle is formulated to describe the vibro-acoustic dynamics of such 3-D panel–cavity–duct silencing system, with the admissible field functions constructed as the superposition of standard Fourier series and the auxiliary edge/interface smoothed terms. All the coupled system response information can be derived in conjunction with Rayleigh–Ritz procedure. Numerical examples are presented to validate the proposed model through the comparison with those from other approaches. The coupling effects of boundary restraining coefficient and plate bending stiffness on sound attenuation performance of such cavity–backed plate–duct silencer are then discussed and analyzed. The results show that the relationship of translational restraints at the duct entrance and exit, kx0 and kxLx, can be obtained through property inverse proportional functions to achieve the optimal sound attenuation. There will be significant improvement in some special frequency band compared with the uniform restraints distribution, especially for the plate with lower bending stiffness The experimental study is also performed to verify the theoretical prediction from current model. In reality, the arbitrary non-uniform elastic edge restraints represent the most general class of boundary conditions, and can provide more optimal space for such drum silencer design.

A mechanical model of vehicle-slab track coupled system with differential subgrade settlement

Post-construction subgrade settlement especially differential settlement, has become a key issue in construction and operation of non-ballasted track on high-speed railway soil subgrade, which may also affect the dynamic performance of passing trains. To estimate the effect of differential subgrade settlement on the mechanical behaviors of the vehicle-slab track system, a detailed model considering nonlinear subgrade support and initial track state due to track self-weight is developed. Accordingly, analysis aiming at a typical high-speed vehicle coupled with a deteriorated slab track owing to differential subgrade settlement is carried out, in terms of two aspects: (i) determination of an initial mapping relationship between subgrade settlement and track deflections as well as contact state between track and subgrade based on a semi-analytical method; (ii) simulation of dynamic performance of the coupled system by employing a time integration approach. The investigation indicates that subgrade settlement results in additional track irregularity, and locally, the contact between the concrete track and the soil subgrade is prone to failure. Moreover, wheel-rail interaction is significantly exacerbated by the track degradation and abnormal responses occur as a result of the unsupported areas. Distributions of interlaminar contact forces in track system vary dramatically due to the combined effect of track deterioration and dynamic load. These may not only intensify the dynamic responses of the coupled system, but also have impacts on the long-term behavior of the track components.

Study on Earthquake Response of High Voltage Electrical Equipment Coupling System with Flexible Busbar

With the rapid development of technology and society, all walks of life in China are becoming more and more dependent on power systems. When earthquake occurs, the electrical equipment of substation is prone to damage because of its own structural features, top-heavy, and brittleness of main body. At the same time, due to the complex coupling of the soft electrical connection of substation electrical equipment, the negative impact can not be estimated. In this paper, the finite element model of the coupling system of the single unit of high voltage electrical equipment with the connecting soft bus is established and the seismic response is analysed. The results showed that there is a significant difference between the simple analysis for the seismic response of electrical equipment monomer and the analytical results of electrical equipment systems, and the impact on different electrical equipment is different. It lays a foundation for the future development of seismic performance analysis of extra high voltage electrical equipment.

Analysis of a hydraulic coupling system for dual oscillating foils with a parallel configuration

The generators using oscillating foil to extract tidal energy have obvious advantages in shallow water. To get rid of the complicated control system, we proposed a hydraulic system to couple dual foils and realize the self-sustained oscillation motion of the foil. The coupling equations related to the foils' motion and hydrodynamic are established. Computations are performed using the software Fluent with a NACA0015 foil. A User Defined Function is compiled for iteration. The classical Runge-Kutta method is employed to compute the displacement and moving velocity. Computation results demonstrate that the hydraulic coupling system realizes well the self-sustained oscillation motion of foil instead of external control. The response of the coupling system is independent of the initial pitching angle. The damping coefficients have a significant effect on the response of coupling system. The response of coupling system, oscillation amplitude and frequency, declines with the increasing of damping coefficient, especially at relatively low damping coefficient. The energy consumption of pitching motion most appears in the stage of angle decrease. The evolutions of time-averaged power coefficient and energy harvesting efficiency versus damping coefficient are quite similar to that of the oscillation amplitude and frequency.

Study on wind-induced response of fluid-solid coupling system for high bent-type aqueduct

In this paper, the coupling responses of water and high bent-type aqueduct under wind loads were studied by the Arbitrary Lagrangian-Eulerian (ALE) method. The natural vibration characteristics and transversal displacement, stress, overturning force, overturning moment and hydrodynamic pressure of water-aqueduct coupling system were comparatively analyzed in different conditions of water-depth, cross-section shape of aqueduct tank and support bearing. The research results show that the isolated support changes the dynamic characteristics and reduces wind resistance performance of U-shape aqueduct and the dynamic performance is better under the effect of the fluctuating wind but smaller stiffness for U-shape aqueduct than that for the rectangular aqueduct with the same water flux.

Real-time dynamic substructure testing of soil-adjacent structure system based on branch mode method

The concept of inertia coupling terms among substructures was proposed. Based on the branch mode method, the superstructures and foundation soil of one soil-adjacent structure system were divided into different branches. The branch mode method was effectively introduced to real-time dynamic substructure testing (RTDST) by decomposing and transforming the motion equation of the entire system. It was also applied for the interaction coupling terms to exchange data between the physical and numerical substructures. This method decreased the degree-of-freedom of the linear substructure effectively and considered the effects of foundation translation and rotation on the upper structures. One system composed of two adjacent four-story steel structures (S1 and S2, respectively) and foundation soil was presented in this study. S1 was applied on a shaking table as the physical substructure, whereas the foundation soil and S2 were set as two numerical substructures and simulated in a computer. The seismic response of the entire coupling system was analyzed by real-time data exchange among substructures. Test results agree with numerical solutions. The RTDST based on the branch mode method is a feasible and reliable method for the investigation of soil-adjacent structure interaction (SASI) problems, and provides a new way to consider SASI problems in the RTDST.

Stationary random vibration analysis of vehicle-track coupled system with nonlinear stiffness of railpads

According to time-temperature superposition (TTS) and WLF formula, the temperature-dependent and frequency-dependent kinetic parameters of the railpads of WJ-7 fasteners were predicted based on the experimental results at a certain frequency and under the different temperatures. By combining the pseudo excitation method and symplectic mathematics scheme, the impact of railpads frequency-dependent and temperature-dependent stiffness on the random variation of the coupled vehicle-track system was investigated efficiently. The results suggest that, within the range of environment temperature and frequency-dependent extent of railpads in the railway, the PSD peak of the vertical random vibration acceleration of the wheelsets and rail gets the largest increase of 3.3 times at least, and the increment of their 1st dominant frequency also reaches up to 20.6 Hz or more. Therefore, in order to accurately analyze the random vibration responses of the vehicle-track coupled system, experiments must be conducted to obtain the accurate kinetic parameters of the polymer materials like railpads.

Nonlinear heterogeneous dynamic substructuring and partitioned FETI time integration for the development of low‐discrepancy simulation models

SummaryThis article presents a novel approach to model validation and to the calibration of complex structural systems, through the adoption of heterogeneous (numerical/physical) simulation based on dynamic substructuring (HDS). HDS isolates the physical sub‐system (PS) that contains the key region of nonlinear behavior of interest and is tested experimentally, separate from the remainder of the system, that is, the numerical sub‐system (NS), which is numerically simulated. A parallel partitioned time integrator based on the finite element tearing and interconnecting method plays a central role in solving the coupled system response, enabling a rigorous and stable synchronization between sub‐systems and a realistic interaction between PS and numerical sub‐system response. This feature enhances the quality of benchmarks for validation and calibration of low‐discrepancy models through virtual structural testing. As a proof of concept, we select an old reinforced concrete viaduct, subjected to seismic loading. Several HDS were conducted at the European Laboratory for Structural Assessment in Ispra (Italy) considering two physical piers and related concave sliding bearings as PSs of the heterogeneous system. As a result, the benefit of employing HDS to set benchmarks for model validation and calibration is highlighted, by developing low‐discrepancy FE models of critical viaduct components. Copyright © 2017 John Wiley & Sons, Ltd.

Characteristics analysis of aero-engine whole vibration response with rolling bearing radial clearance

For the influence of rolling bearing radial clearance on the whole vibration in the aero-engine whole system, a real engine rotorbearing- casing whole model is established. The rotor and casing systems are modeled by means of FEM; the support systems are modeled by lumped-mass model; rolling bearing radial clearance and strong-nonlinearity of Hertz contact force at four different supports are considered. The coupled system response is obtained by the numerical integral method. The characteristics of the whole vibration response are analyzed. For rolling bearing at a typical support, the rotor, outer ring of rolling bearing and casing response characteristics at different rotating speeds are analyzed. The changing law of contact forces for each ball and the global contact forces at different speeds are analyzed. The influence of the radical clearance on the contact forces on the whole vibration is analyzed. The results show that the contact forces will be larger and the acceleration amplitude jumps obviously when the radial clearance is increased, and due to the variable stiffness of the rolling bearing, the natural frequency will appear when the stiffness changes fiercely, that is frequency-locked phenomenon. When the radical clearance is larger and the rotating speed is between two critical speeds, the rotor squeezes the outer ring now and then. Reducing the radical clearance can reduce the whole vibration and increase the rotor’s stability.

Elasto-acoustic response damping performance of a smart cavity-coupled electro-rheological fluid sandwich panel

The transient vibroacoustic response mitigation of a rectangular sandwich panel with an adaptive electro-rheological fluid core layer, and backed by a hard-walled reverberant rectangular parallelepiped acoustic enclosure, is investigated. The problem is analyzed in a multidisciplinary framework that involves the thin sandwich electro-rheological fluid-based plate model, the 3D wave equation for the acoustic enclosure domain, the first-order Kelvin–Voigt viscoelastic model for the electro-rheological fluid core material, the pertinent structure–fluid compatibility relation, and the inherently robust sliding mode control strategy. The generalized Fourier expansion method is utilized to set up the fully coupled system equations in the state–space domain, and the fourth-order Runge-Kutta time marching technique is then utilized to compute both uncontrolled and controlled coupled system responses in three basic external loading configurations. It is found that increasing the cavity depth has a substantial restraining effect on the overall sound pressure response levels, while the electro-rheological fluid-panel displacement response amplitudes experience only moderate reductions. Also, a purely passive electro-rheological fluid-based system is observed not to be very effective for vibroacoustic response suppression of the cavity-coupled structural system, while the overall success of the applied sliding mode control methodology in reasonable reduction of both panel displacement and sound pressure time response amplitudes is demonstrated. Furthermore, the control system authority with regard to the acoustic cavity pressure (panel displacement) is found to moderately (slightly) decrease as the cavity depth increases. Limiting cases are considered and accuracy of the suggested analytical model is checked against the output of an FEM package as well as with the accessible literature results. Moreover, the main components of a prospective experimental platform for verifying the performance of proposed vibroacoustic control system are briefly described.

Coupling effects of boundary restraining stiffness and tension force on sound attenuation of a cavity-backed membrane duct silencer

In this paper, the vibro-acoustic model for predicting the sound attenuation performance of a cavity-backed membrane duct silencer is established via an improved Fourier series method, in which the membrane vibration and cavity acoustic fields are both constructed as the superposition of standard Fourier series and supplementary polynomials to tackle the differential discontinuity issues encountered at such elastic edge restraint and/or coupling interface. The energy formulation is employed to describe the whole structural-acoustic interaction among the membrane vibration, cavity sound field as well as the sound propagation in duct environment. The coupled system response under the upstream plane wave excitation is then solved through the Rayleigh-Ritz procedure. Numerical examples are then presented to illustrate the correctness and effectiveness of the proposed model. The predicted results from the current method are compared with those derived from other approach and experimental measurement available in literature, satisfactory agreements are observed for these validation studies. Based the model established, the coupling effects of boundary restraining stiffness and tensile force on the sound attenuation performance of such cavity-backed membrane duct silencer are discussed and analyzed, the results show that there exists an optimal window of these two parameters matching. This work can provide some useful insight for the effective design of such membrane silencing system.

The Response of Irregular Enclosure with Different Excitation

This paper presents a theoretical investigation into the response of the coupled system which consists of a regular or irregular enclosure with different excitation, including noise reduction level and panel vibration energy level. The results show that the noise reduction level curves appear changes in medium and high frequency region when the enclosure change from regular rectangular to irregular trapezoidal, but there is small variation in panel vibration energy. Compared with the incident plane wave perpendicular to the flexible wall, more panel modes are excited by the oblique plane wave, and it means that more noise go through the flexible wall into the enclosure.

Finite Element Analysis of DSSI Effects for a Building of Strategic Importance in Catania (Italy)

Structural response to earthquakes has to be definitely considered a multidisciplinary subject, depending on many factors among which local site effects and dynamic interaction between soil, foundations and structures. The present paper deals with the multidisciplinary Dynamic Soil Structure Interaction (DSSI) analysis concerning the INGV building in Catania (Italy) by means of FEM 2D modelling. The building is a masonry structure situated in an area characterized by a high seismic hazard. The dynamic analysis was performed by adopting seven different accelerograms, scaled at the same PHA with reference to the estimated seismicity of the investigated area. Linear visco-elastic constitutive models were adopted for both the soil and the structure; nevertheless, soil non-linearity is taken into account according to EC8, adopting degraded shear modulus and increased damping ratio. The dynamic response of the system was analysed in the time and frequency domains. The main goals of the paper are: i) to investigate the amplification input effects, considering and not considering the DSSI; ii) to highlight the influence of soil layer variation in the coupled system response; iii) to compare the obtained results with the ones given by simpler 1D free-field soil analyses; iv) to compare the acceleration spectra obtained by 1D and 2D analyses with those provided by Italian technical code, NTC08. The performed analyses show the influence of DSSI in the seismic response of the system in terms of PHA and frequency contents.

Pumps modelling of a sodium fast reactor design and analysis of hydrodynamic behavior

One of the goals of Generation IV reactors is to increase safety from those of previous generations. Different research platforms have been identified the need to improve the reliability of the simulation tools to ensure the capability of the plant to accommodate the design basis transients established in preliminary safety studies. The paper describes the modelling of primary pumps in advanced sodium cooled reactors using the TRACE code. Following the implementation of the models, the results obtained in the analysis of different design basis transients are compared with the simplifying approximations used in reference models. The paper shows the process to obtain a consistent pump model of the ESFR (European Sodium Fast Reactor) design and the analysis of loss of flow transients triggered by pumps coast–down analyzing the thermal hydraulic neutronic coupled system response. A sensitivity analysis of the system pressure drops effect and the other relevant parameters that influence the natural convection after the pumps coast–down is also included.

Aeroelastic Responses of Ultra Large Wind Turbine Tower-Blade Coupled Structures with SSI Effect

By a case study on a new-generation 5MW ultra large wind turbine system, the finite element model of the blade-nacelle-tower-foundation coupled structure with soil-structure interaction (SSI) and blade rotational centrifugal force is established. The harmonic superposition method and modified blade-element momentum theory are used to predict the aerodynamic loads with the consideration of tower-blade aerodynamic and model interaction, and modification of steady wind. Then the modal superposition method is adopted to solve the wind turbine coupling dynamic equation, in which the blade speed and aerodynamic force were updated though iteration to obtain the aeroelastic loads. At last, based on the previous work of “consistent coupling method”, which can fully consider the structure background mode, resonant mode, and the coupling effect between them, the aeroelastic responses of the wind turbine-blade coupled system are investigated. For completeness, the action mechanism of SSI effect and aeroelastic effect on the wind-induced responses are discussed through parameter analysis. The research conclusions can provide a scientific foundation for wind-resistance design of the ultra large wind turbine systems.

Dynamic Analysis of Overhead Transmission Line under Turbulent Wind Loading

This paper compares the dynamic response of a test transmission line with the response due to static loads given by Eurocode. Finite element design software SAP2000 was used to model towers and power-lines. Nonlinear dynamic analysis including the large displacement effects was carried out. Macroscopic aspects of wind coherence along element length and integration time step were investigated. An approach is presented to compare the probabilistic dynamic response due to 7 different stochastically simulated wind fields with the response according to EN-50341. The developed model is used to study the response recorded on a test line due to the actual wind speed time history recorded. It was found that static load as calculated from EN-50341 underestimates the response of conductor cables. The response of coupled system considering towers and cables was found to be different from response of only cables with fixed supports.

Dynamic Analysis of Overhead Transmission Lines under Turbulent Wind Loading

Transmission tower-line systems are designed using static loads specified in various codes. This paper compares the dynamic response of a test transmission line with the response due to static loads given by Eurocode. Finite element design software SAP2000 was used to model the towers and lines. Non-linear dynamic analysis including the large displacement effects was carried out. Macroscopic aspects of wind coherence along element length and integration time step were investigated. An approach is presented to compare the probabilistic dynamic response due to 7 different stochastically simulated wind fields with the response according to EN-50341. The developed model will be used to study the response recorded on a test line due to the actual wind speed time history recorded. It was found that static load from EN overestimated the strength of conductor cables. The response of coupled system considering towers and cables was found to be different from response of only cables with fixed supports.

On the Early Response of the Climate System to a Meltwater Input from Greenland

Abstract The early response of the atmosphere–ocean system to meltwater runoff originating from the Greenland ice sheet is studied using a coupled atmosphere–ocean general circulation model (AOGCM). For this purpose, AOGCM ensemble simulations without and with associated ocean freshening around Greenland are compared. For freshwater perturbations initiated in northern winter, the mean response for the first three months shows the emergence of negative sea surface temperature (SST) anomalies in the Denmark Strait, in association with enhanced oceanic advection by the East Greenland Current. The response also shows negative SST anomalies in the North Atlantic associated with enhanced westerlies at the ocean surface. Additionally, the baroclinic atmospheric cyclonic circulation east of Greenland intensifies, and anticyclonic circulations with equivalent barotropic structures develop over western Europe and the North Pacific Ocean. Simulations by the atmospheric component of the AOGCM indicate that atmosphere–ocean interactions contribute significantly to enhance the response. The sensitivity of the coupled system response to the timing of freshwater perturbation is also studied. For freshwater perturbations initialized in northern summer, the response during the following winter is similar, but stronger in magnitude. In the Northern Hemisphere, the atmospheric response resembles the Arctic Oscillation (AO) mode of variability. The association between anomalies in the Denmark Strait SSTs and in the atmosphere east of Greenland is consistent with that observed during previous great salinity anomaly (GSA) events. The results obtained highlight the importance of atmosphere–ocean interaction in the early climate response to Greenland melting, the teleconnections with the North Pacific and the contribution of GSA events to North Atlantic Oscillation (NAO) variability.

Study on Wind Vibration Control Effect of the Tower and Tower-Line Coupling System of the Transmission Tower

Currently, the Chinese code calculate the wind loads of transmission towers and lines separately, the code methods make the loads of ground wire which was regarded as external loads force on the transmission tower, without considering the coupling effect between the tower and line, this method does not accord with the actual working state of the transmission tower. Therefore, according to the actual state of tower-tower-line coupling, this article established the finite element model of its system. What’s more, on the basis of different layout of damper system, the dynamic response and vibration reduction effect of the tower-line coupling system under different conditions were studied in this paper. The results show that, both can reduce the system’s vibration effectively while considering the tower-line coupling and with the consideration of different damper layout schemes at the same time. The third scheme which is tower head lower half part edge member bar plus dampers had the most significant vibration reduction effect. The research results can be reference for engineering design and engineering practice, it also has a certain theoretical and practical significance.