Lumped Mass Model Research Articles

Mechanical characteristics analysis of horizontal lifting of subsea pipeline with different burial depths

Different burial depths have different effects on the mechanical characteristics of the horizontal lifting of subsea pipelines. With the consideration of the soil resistance to subsea pipelines, combined with the specific sea condition parameters of a certain sea area, and based on the lumped mass method, the subsea pipeline is discretized into a lumped mass model, the dynamic analysis model of the three-point horizontal lifting of subsea pipelines with different burial depths is established. The stress and bending of the pipelines with different burial depths are analyzed. The calculation results with different burial depths are compared. The variation of mechanical characteristics of the process of lifting horizontal pipelines with different buried depths is obtained. The results show that the change of burial depth has a significant influence on the effective tension of the pipeline. With the increase of the burial depth, the maximum degree of stretching of the pipeline first decreases and then increases. Within a certain depth range, burying the pipeline in the seabed can reduce both the effective tension and the intensity of the fluctuation of the effective tension when the pipeline is lifted. The change of burial depths for the shear action is mainly reflected in the numerical values of the shear force. There is no significant impact on the degree and variation fluctuation of the shear force. The conclusions can provide a certain theoretical reference for the design of the process of horizontal pipeline lifting.

Dynamic characteristics analysis of a dual-rotor system with bolted-disk joint

This article presents a nonlinear vibration characteristics study of a bolted joint dual-rotor system. The motion equations are derived through the lumped mass modeling method and a two-node bolted joint element. Nonlinear time-varying bending stiffness at the joint interface is considered in the numerical integration. Qualitative analysis of the effect of preload on system responses is conducted through changing the value of the transition point of bending stiffness of the bolted joint. Moreover, the transfer path of vibration in the dual-rotor system through inner-shaft bearing was discussed in the present work. The nonlinear differential equations are solved using the Newmark integration method to predict the dynamic characteristics of the dual-rotor system. The results show that the maximum vibration displacement of LP rotor is positively correlated with that of HP rotor as preload changes. Moreover, the maximum amplitude of the time-domain responses of the HP rotor will decrease and the minimum amplitude will increase with the increase of preload. The difference between the maximum and minimum values of the time-domain response will decrease with the increase of preload. This can be explained by the “stiffness hardening” phenomenon of the bolted joint. The research results can help understanding the dynamic properties of the bolted joint dual-rotor system and the vibration transfer path of the rotor system through inner-shaft bearing.

Analysis of contact force and uplift of pantograph–catenary system in overlap section based on numerical simulations and experimental tests

This paper examines the dynamic performance of the pantograph passing through an overlap section of the catenary system, using a China’s high speed railway with the 4-span overlap as an example. The pantograph and catenary system are simulated as a lumped mass model and finite element model, respectively. The model is verified according to EN50318:2018. The model is also assessed against an experimental study of the contact force and uplift of contact wire at 300 km/h. Then the contact force and uplift of contact wire at the speed of 150–350 km/h are calculated. The research shows that when the pantograph passes through the overlap, the maximum contact force increases beyond 14%, the standard deviation of the contact force increases by more than 26%, and the increase of the vertical displacement exceeds 38%, which becomes more apparent with the increase of speed. Under the influence of aerodynamic force, when the running speed increases from 150 to 350 km/h, the mean contact force in the knuckle-downstream and knuckle-upstream orientation increase by 59.49% and 97.85%, respectively. As a result, the contact force and vertical displacement increase greatly when passing through the overlap section, which could affect the current collection quality.

The establishment and validation of pantograph and overhead conductor rail dynamic simulation

Overhead conductor rail which has become the main form of the overhead catenary, is widely used in China’s urban rail transit. In order to understand the vibration behavior of pantograph and conductor rail, it is necessary to carry out the study of the interaction between pantograph and conductor rail. In this paper, we will give a simulation model and calculation method of pantograph and conductor rail at first. The simulation is based on a 3-D finite element model of the conductor rail and a lumped mass model of the pantograph. The main modeling equations and ideas are provided in the simulation process. Finally, a dynamic test for pantograph and conductor rail has been designed for validating the effectiveness of the simulation.

Numerical coupling strategy using HOS-OpenFOAM-MoorDyn for OC3 Hywind SPAR type platform

The coupled (Potential theory and Navier–Stokes) solver is applied to simulate the interaction of sea waves with substructure of floating offshore wind turbines (FOWT) platform, notably similar to the OC3 Hywind SPAR structure. The intention is to develop a numerical tool that allows the study of the survivability of floating structures in extreme sea states. In this study, the moorings are modeled in two ways. One is by considering the mooring lines as a linear spring with defined spring stiffness, and another is by coupling the solver (foamStar) with a lumped-mass mooring dynamics model (MoorDyn). MoorDyn represents mooring line behavior subject to axial elasticity, hydrodynamic forces, and vertical contact forces with the seabed. The coupled model has been validated against the experiments carried out as part of the SOFTWIND project. The numerical model results of free surface elevation, floating body motions and mooring tensions are compared with the experiments. For wave cases with mild and moderate amplitudes, mooring in the form of a stiffness matrix is sufficient. However, dynamic mooring simulation (MoorDyn) is required for the extreme sea state conditions.

Convolutional Neural Network-Based Rapid Post-Earthquake Structural Damage Detection: Case Study.

It is necessary to detect the structural damage condition of essential buildings immediately after an earthquake to identify safe structures, evacuate, or resume crucial activities. For this reason, a CNN methodology proposed to detect the structural damage condition of a building is here improved and validated for two currently instrumented essential buildings (Tahara City Hall and Toyohashi Fire Station). Three-dimensional frames instead of lumped mass models are used for the buildings. Besides this, a methodology to select records is introduced to reduce the variability of the structural responses. The maximum inter-storey drift and absolute acceleration of each storey are used as damage indicators. The accuracy is evaluated by the usability of the building, total damage condition, storey damage condition, and total comparison of the damage indicators. Finally, the maximum accuracy and R2 of the responses are obtained as follows: for the Tahara City Hall building, 90.0% and 0.825, respectively; for the Toyohashi Fire Station building, 100% and 0.909, respectively.

Dynamic Behavior of the Net of a Pile–Net-Gapped Enclosure Aquaculture Facility

A pile–net enclosure aquaculture facility, deployed in inshore waters, is a sustainable and ecological aquaculture pattern for rearing fish and other aquatic animals of economic value in China. It is essential to study the maximum force on and deformation of the net system of a pile–net enclosure facility to prevent its failure, since successful aquaculture is highly dependent on the longevity of the net system. In this study, a pile-net enclosure aquaculture facility with a gapped pile-net configuration was numerically investigated based on the lumped mass model. A Newton’s second-law-based motion equation was solved using Euler’s method. Finally, MATLAB was used to visualize the results. The results highlight that the force of a net system significantly increases with ocean loads, and the load of the entire net is mainly from the top half of the net. Moreover, the maximum force of the vertical rope occurs at the connection of the top channel steel. The maximum force of the horizontal rope and net twine occur in the rope near the still-water level and at the connection of the top channel steel, respectively. Thus, the net at those positions should be reinforced to prevent its failure.

Dynamic Modeling and Transient Response of a Rigid-Body Inductrack Maglev System

Abstract The Inductrack system provides a novel way to achieve magnetic levitation by using Halbach arrays of permanent magnets (PMs). Due to the complexities of the nonlinear electro-magneto-mechanical coupling in the system, most previous analyses of the Inductrack system rely on steady-state results and consequently cannot fully capture the dynamic behaviors of the system in transient scenarios. In this article, a new three degrees-of-freedom (3DOF) transient model of the Inductrack system is proposed. This model describes the rigid-body motion of the Inductrack vehicle with axial (longitudinal) and vertical (transverse) displacements and pitch rotation, and it is derived without any assumption of steady-state quantities. Compared to a recently available 2DOF lumped-mass model developed by the authors, the inclusion of the pitch rotation in the new model results in a much more complicated mechanism of electro-magneto-mechanical coupling. Numerical results show that the pitch rotation can have a significant effect on the dynamic response and stability of the Inductrack system, which necessities vibration control for the safe operation of the Inductrack system.

Sorting strategy to retune the disordered periodic structures regarding vibration reduction in band gaps

Periodic structures exhibit frequency band gaps, in which the propagation of certain waves is attenuated. A periodic structure can be designed such that its band gaps cover the excitation frequencies and its vibration can be reduced. However, perfectly periodic structures do not exist in reality due to inevitable deviations in the material and geometric properties. The vibration reduction performance can be significantly altered by the disorder, as reported by various authors. Therefore, it is favorable to find approaches that can retune disordered structures to the best possible state. In this way, robust vibration reduction performance can be achieved. In this study, a sorting strategy is proposed to rearrange the disordered unit cells. The aim is to reduce the performance change of vibration reduction. Specifically, a diatomic lumped-mass model has been used, where one mass coefficient in each unit cell is subject to random error. The forced response is computed, and the frequency-averaged spatially maximum amplitude is used as the indicator to quantify the influence of the disorder. Then, we reveal the importance of the deviation at different unit cells by a global sensitivity analysis. A variance-based approach termed Sobol’s sensitivity analysis is used. The results show that the deviation in the unit cell nearest to the excitation source is of the greatest importance. A theoretical interpretation from the perspective of wave propagation is given. Eventually, a simple sorting strategy is proposed, and the rule is to ensure that the unit cell in the first position has the smallest deviation. This strategy can significantly improve the similarity of the dynamic characteristics between the nominal and disordered structures. Overall, the conducted work provides a reference to the manufacture and assembly of periodic structures and a further understanding of the vibration reduction in band gaps.

Output-only structural damage identification using hybrid Jaya and differential evolution algorithm with reference-free correlation functions

To solve the optimization-based structural damage identification problem, a novel hybrid algorithm based on Jaya and differential evolution algorithm (HJDEA) is proposed to detect, locate and quantify structural damages by effectively incorporating the powerful local exploitation capacity of Jaya algorithm and global exploration capability of differential evolution. Meanwhile, Hammersley sequence initialization and Lévy flight search mechanism are introduced into HJDEA to further improve convergence rate and refining the quality of the best solution. Four different algorithms, genetic algorithm, particle swarm optimization, Jaya and the proposed HJDEA are employed for comparative study. In addition, the objective function is established by adjacent acceleration correlation function so as to avoid false identification caused by defining improper reference point. The performance of the proposed damage identification strategy based on HJDEA and adjacent acceleration correlation function is investigated with numerical examples involving an 8-DOF lumped mass model and a cantilever beam, as well as an experimental study of the ASCE benchmark structure under white noise excitation. Results show that the proposed hybrid identification method is accurate, efficient and robust in the identification of the damage existence, location and severity of stiffness and mass parameters even with partial output-only responses and 20% noise-polluted measurements.

Improving the Seismic Response of Tall Buildings: From Diagrid to Megastructures and Mega-Subcontrol Systems

Background: Diagrid structures, widely used for the tall buildings of the third millennium, are characterized by a very effective behaviour in the elastic field due to the grid triangulation. In particular, under horizontal actions, axial forces and deformations mainly arise in the structural members of the diagrid, thus resulting in the reduction of the shear lag effect and racking deformations. The response to incremental horizontal actions beyond the plastic threshold, however, shows a poor plastic redistribution capacity, with consequent low values of global ductility, in spite of a significant design overstrength. Objective: In this paper, it is proposed to exploit the high elastic efficiency of the diagrid type and use a vibration control system, based on mass damping mechanism with large mass ratios, to reduce a priori the inelastic demands due to seismic actions. Methods: Starting from the analysis of the seismic behavior of archetype diagrid buildings, a case study is selected to assess the effectiveness of the proposed motion-based design approach. For this purpose, the diagrid is first transformed into a megastructure (MS) configuration by densifying the diagonal elements at the most stressed corner areas and transfer floors, suitably chosen. Then, the exterior mega-frame is detached from interior sub-structures, thus allowing for a relative motion between the two structural portions according to a “mega-sub-structure control system” (MSCS), which activates the mass damping mechanism. Results: Time-history analyses carried out on simplified lumped-mass models confirm the effectiveness of the proposed strategy in reducing the seismic response. Conclusion: Finally, the practical feasibility of the MSCS and engineering solutions for the relevant structural organization are discussed.

Operational transfer path analysis with regularized total least-squares method

Operational transfer path analysis (OTPA) uses only operational responses to characterize the paths, so it is efficient and widely used in various engineering fields. However, the operational responses are inevitably contaminated by errors, which seriously reduce the accuracy of OTPA. To reduce the influence of errors and improve the accuracy of OTPA, a Tikhonov regularized total least-squares method (RTLSM) which is based on the Tikhonov regularized least-squares method (RLSM) is used to estimate the transmissibility matrix, and then the individual contributions are calculated. The total least-squares method takes into account not only the influence of the errors in the target point responses but also the influence of the errors in the indicator point responses. Tikhonov regularization is introduced to regularize the total least-squares method to improve the ill-conditioning of the indicator point response matrix in the process of estimating the transmissibility matrix. An OTPA simulation on a lumped mass model and an OTPA experiment on an aluminum plate are studied to test the performance of the RLSM and RTLSM. Both simulation and experimental results show that the RTLSM is better than the RLSM in OTPA, and improved the accuracy of OTPA effectively.

A disturbance observer based lumped-mass catenary model for active pantograph design and validation

ABSTRACT To understand and thus improve the dynamic behaviour of the railway pantograph-catenary system, researchers have developed a number of approaches to the catenary modelling. The Finite Element (FE) approach provides a high degree of accuracy, but at the cost of significant computing time. In contrast, researchers in active pantographs generally use relatively simple (and fast running) lumped-mass catenary models. This paper aims to improve on the models available for the design and validation of active pantographs. Firstly, the veracity of the classic lumped-mass model is assessed and a new catenary model is proposed, by augmenting the lumped-mass model with a dynamics-matched mass and a disturbance which can be found using a disturbance observer (DO). Open-loop, passive pantograph, results show that the proposed model can represent the dynamic behaviour exhibited in the FE catenary very well. Secondly, two PID controllers are designed for an active pantograph, and tested with the FE, classic and DO-based lumped-mass catenary models. It is shown that if a controller is validated on the classic lumped-mass model, the credibility will be low. In contrast, the new DO-based model is found to deliver more robust results, providing efficient simulations for active pantograph design and validation.

CFD simulation of floating body motion with mooring dynamics: Coupling MoorDyn with OpenFOAM

It is increasingly popular to use Computational Fluid Dynamics (CFD) models to study floating structures subjected to ocean waves, especially when it comes to applications of floating offshore wind turbines and Wave Energy Converters (WECs). Mooring dynamics are currently lacking in most of these applications. This paper presents a coupled simulation study of moored floating body motion by coupling two open-source libraries: a finite volume CFD toolbox, OpenFOAM, and a lumped-mass mooring model, MoorDyn. The instantaneous floating body position and velocity are passed from the body motion solver in the CFD model to the mooring model to calculate the fairlead kinematics. The mooring reaction forces, which are calculated by MoorDyn after updating the mooring system states, are then returned to the body motion solver to update the floating body motion. Both mesh deformation and overset mesh methods are used as the mesh motion solver in the CFD model to account for the floating body motion. The coupled model was validated against experimental measurements for a floating box moored with four catenary lines under the action of regular waves, which came from a preliminary test campaign for WECs. Apart from the lumped-mass mooring model, the present work also coupled a quasi-static mooring model and a finite element model with the floating body motion solver in OpenFOAM. The mooring line tensions predicted by these models were compared. The coupled model equipped with three mooring line codes may be further used to carry out survivability studies of FOWTs and WECs subject to severe sea states.

Global optimization of excitation directions for scavenging energy based on a cross-jointed L-shape multidirectional piezoelectric energy harvester

Energy harvesting technology can collect energy from environmental vibrations, but it is still challenging because the vibration from an environment is random and the directions vary. In this study, a novel cross-coupled L-shaped vibration piezoelectric energy harvester (CL-VPEH) was proposed to collect energy from different environmental vibration directions. This CL-VPEH consists of a vertical beam and a horizontal beam joint crosswise with two laminated piezoelectric layers. Finite element analysis was performed to study the voltage output and resonant frequency. A simplified lumped mass model of CL-VPEH under excitation from an arbitrary direction was built to describe its working principle and multi-directional energy-harvesting ability. The experimental results demonstrate that the CL-VPEH shows good agreement with the numerical and analytical solutions. The experimental results validate the CL-VPEH’s multidirectional energy harvesting ability. Using the lumped mass model, the performance of the CL-VPEH under every single-direction excitation is investigated. A weak power output area is found with a frequency range of 10 Hz − 25 Hz, which should be avoided in future applications of this kind of multiple-directional excitation energy harvesting.

Evaluation of two complementary modeling approaches for fiber-reinforced soft actuators

Although robots are increasingly found in a wide range of applications, their use in proximity to humans is still fraught with challenges, primarily due to safety concerns. Roboticists have been seeking to address this situation in recent years through the use of soft robots. Unfortunately, identifying appropriate models for the complete analysis and investigation of soft robots for design and control purposes can be problematic. This paper seeks to address this challenge by proposing two complementary modeling techniques for a particular type of soft robotic actuator known as a Fiber-Reinforced Elastomeric Enclosure (FREE). We propose that researchers can leverage multiple models to fill gaps in the understanding of the behavior of soft robots. We present and evaluate both a dynamic, lumped-parameter model and a finite element model to extend understanding of the practicability of FREEs in soft robotic applications. The results of experimental simulations using a lumped-parameter model show that at low pressures FREE winding angle and radius change no more than 2%. This observation provided confidence that a linearized, dynamic, lumped-mass model could be successfully used for FREE controller development. Results with the lumped-parameter model demonstrate that it predicts the actual rotational motion of a FREE with at most 4% error when a closed-loop controller is embedded in the system. Additionally, finite element analysis was used to study FREE design parameters as well as the workspace achieved with a module comprised of multiple FREEs. Our finite element results indicate that variations in the material properties of the elastic enclosure of a FREE are more significant than variations in fiber properties (primarily because the fibers are essentially inextensible in comparison to the elastic enclosure). Our finite element analysis confirms the results obtained by previous researchers for the impact of variations in winding angle on FREE rotation, and we extend these results to include an analysis of the effect of winding angle on FREE force and moment generation. Finally, finite element results show that a 30^{circ } difference in winding angle dramatically alters the shape of the workspace generated by four FREEs assembled into a module. Concludingly, comments are made about the relative advantages and limitations of lumped-parameter and finite element models of FREEs and FREE modules in providing useful insights into their behavior.

Hybrid modeling approach for the tether of an airborne wind energy system

The design of controllers for the automatic operation of airborne vehicles is challenging. Especially in the emerging research field of airborne wind energy, where tethered aircraft convert energy from wind at higher altitudes into electricity, the development of robust and safe control systems will be a critical success factor. Typically, these systems consist of one or more controlled aircraft, a ground station, and one or more tethers that transfer aerodynamic forces acting on the wings to the ground. To understand these systems and control them for real-time simulations, suitable tether models must extend the classical flight mechanical models. In this paper, a hybrid approach is presented, combining an elastic spring model with a catenary model of the tether. In particular, for real-time simulations in a model-in-the-loop environment where a static modeling approach is sufficient, this hybrid model is intended to provide an alternative to the commonly used spring models. Furthermore, such a static tether model neglects high-frequency dynamic oscillations that can occur with dynamic lumped mass models. As consequence, the focus is on primary influences such as stiffness and sag due to external loads. The developed hybrid model is analyzed and compared with the spring model for a simulated tethered flight. It can be concluded that this hybrid static model, although subject to strong assumptions such as symmetrical tether sag, represents the tether more accurately. For example, it allows a more precise design of the flight controller before conducting any flight tests. This model can be used as a reasonable alternative to the simple spring model whenever a static modeling approach of the tether is adequate.

Development of a numerical mooring line model for a floating wind turbine based on the vector form intrinsic finite element method

The utilization of renewable energy has great significance to reduce CO2 emissions. Floating offshore wind turbines (FOWTs) is regarded as most cost-effective solution to harness the offshore renewable energy in deep-water. Fully coupled analysis is regarded as the state-of-art simulation method for FOWT's design and analysis. Until now, various methods (lumped mass model, quasi-static model, finite element model et al.) are used in mooring line modelling in the fully coupled simulation for FOWTs. In this paper, a new dynamic model for catenary mooring line is proposed based on the vector form intrinsic finite element (VFIFE) method. This method is designed to calculate motions of a system, which the motion may include large rigid body motions and large geometrical changes, or very large deformations. The inertia and hydrodynamic and the seabed interaction are contained in this model. Newton's law of particle is assumed to derive the governing equations of motion. An explicit algorithm is used to calculate the numerical results. The feasible and accurate of the dynamic model are verified by comparing with the experimental data and other validated codes. In the comparisons the results of VFIFE method has a good agreement with the references. Thus, the dynamic model proposed in this paper is capable for the dynamic analysis of mooring lines. Furthermore, the influence of the forced motion frequency (and amplitude) of mooring system on the hysteresis loop area is studied, which reveals the mechanism of the energy dissipation from the viscous damping of fluid and the gravitational potential energy of the line.

Surge Response Analysis of the Serbuoys-TLP Tension Leg Platform under the Action of Wave–Current Coupling

A new type of tension leg platform (TLP) connected to a series of buoys (Serbuoys-TLP) has been proven to effectively suppress the surge response of the platform during wave conditions. However, in the complex marine environment, it is more relevant to study its motion response to the action of waves and currents. Considering the tension tendon as a lumped mass model, a DUTMST 2.0 time-domain simulation program was written, based on MATLAB, which can accurately calculate the surge response of the Serbuoys-TLP under wave–current coupling conditions. The suppression efficiency of the Serbuoys-TLP on the surge response was analyzed under different current velocities and wave parameters, and the results showed that the suppression efficiency by the Serbuoys-TLP of surges was higher under the action of waves and currents compared with the action of waves. In addition, the surge response of the platform under the two conditions of wave–current combination and wave–current coupling was also investigated, where wave–current coupling considers the effect of the current’s velocity on the wave period, while the wave–current combination does not consider it, which means that the wave and current are linearly superimposed. The results show that the surge response of the platform will be overestimated without considering the coupling effect of waves and currents. The effect of wave–current coupling has a greater impact on the surge response of the Serbuoys-TLP than that of conventional TLP. Therefore, in the design of new floating structures, the motion performance in response to the effect of wave–current coupling should be paid full attention.

Switching Kalman filter for damage estimation in the presence of sensor faults

Bayesian filtering based approaches for diagnosis of structural damage have been widely employed in structural health monitoring (SHM) research. The approach however may lead to an inaccurate alarm/decision due to the presence of faulty sensor/s. Nevertheless, sensor faults are inevitable during real field SHM in which sensor may malfunction or get detached from the structural surface, registering completely irrelevant information as measurement. Eventually, such erroneous information induce error in the estimation which leads to an inaccurate, sometimes divergent and impractical solution. The current study deals with Bayesian filtering based structural damage detection in the presence of one or multiple (consecutive) sensor faults. The damage detection is addressed with joint state-parameter estimation approach while a switching filtering strategy is employed for sensor fault detection. Switching approach employs multiple possible sensor fault models which are subsequently integrated to the measurement model of the joint estimation approach. The selection of the competent model (/switching between model ensembles) is undertaken recursively based on their likelihood against measured response. The proposed approach is tested on a numerical lumped mass model of a shear frame building, followed by a laboratory experiment on a cantilever beam. It has been perceived that estimation of health for structures measured with faulty sensors can actually lead to a false (positive and negative) alarm which can, however, be avoided by the employment of the proposed approach. The performance of the proposed approach is further established for healthy and damaged system with pre-existing and sudden sensor faults.