Lumped Mass Model Research Articles

Stabilization of electrostatic MEMS resonators using a stochastic optimal control

Noise-induced motions are a significant source of uncertainty in the response of electrostatic MEMS where electrical and mechanical sources contribute to noise and can result in sudden and dramatic loss of stability. In this manuscript, we present an analysis for the stabilization of an electrostatically actuated MEMS resonator in the presence of noise processes using a stochastic optimal control scheme. A stochastic lumped-mass model that accounts for the uncertainty in mass, mechanical restoring force, bias voltage, and AC voltage amplitude of the resonator is presented. The Ito^ equations, describing the averaged modulations of the resonator's total energy and phase difference, are obtained via the stochastic averaging of energy envelope. The stochastic optimal control law aiming at minimization the pull-in probability of the resonator is determined via the stochastic dynamic programming equations associated with the Ito^ equations. We show that the resulting stochastic optimal feedback control, with a careful selection of its control gain, can be used to suppress the noise-activated pull-in instability of the disturbed resonator. The impact of the time delay inherent in the feedback control input on the control effectiveness is investigated. In addition, the control scheme also shows superior performance in counteracting the deterministic pull-in instability of the resonator operating in the dynamic pull-in frequency band. Good agreement between the theoretical results and numerical simulation is demonstrated.

Application of Absolute Nodal Coordinate Formulation in Calculation of Space Elevator System

The space elevator system is a space tether system used to solve low-cost space transportation. Its high efficiency, large load, reusability and other characteristics have broad application prospects in the aerospace field. Most of the existing mechanical models are based on “chain-bar” and a lumped mass tether model, which cannot effectively reflect the flexible behaviour of the rope of space elevator system. To establish an accurate mechanical model, the gradient deficient beam elements of the absolute nodal coordinate formulation (ANCF) are used to build the mechanical model of the space elevator system. The universal gravitation and centrifugal force in the model are derived. The calculation results of the ANCF model are compared with the results of the finite element method (FEM) and lumped mass (LM) models. The results show that the calculation results of the ANCF method are not very different from the results of the FEM and LM models in the case of axial loading. In the case of lateral loading, the calculation results of the ANCF method are basically the same as the results of the FEM and LM models, but can better reflect the local flexible deformation of the space elevator rope, and have a better calculation stability than FEM. Under the same calculation accuracy, the ANCF method can use fewer elements, and the speed of convergence is faster than the FEM and LM models.

Dynamic behaviors of a hinged multi-body floating aquaculture platform under regular waves

This paper numerically studies the dynamic behaviors of a hinged multi-body floating aquaculture platform under regular waves. A coupled scheme that integrates the boundary element method (BEM) and the lumped-mass model is used to model the frames and the moorings/netting simultaneously. The effect of the hinge-joint rotational stiffness on the motion responses, mooring and hinge-joint forces at different wave steepnesses are examined. The results show that both the wave period and the hinge-joint rotational stiffness affect the pitch response of the multi-body aquaculture platform. However, the hinge-joint rotational stiffness has a predominant influence on the maximum pitch response. Unlike the pitch response, the stiffness has little effect on the heave response. Moreover, with the increase of stiffness, these two individual cages also show distinctive dynamic behaviors. The mooring force decreases with the stiffness and a 14.5% reduction has been obtained at the maximum stiffness. Under the same wave period, the y-direction rotation moment increases alongside the stiffness. When the wavelength is less than 0.9 times the structural span, the increased wave period decreases the y-direction rotation moment. In contrast, the stiffness rarely affects the z-direction hinge-joint force.

Dynamic Modeling and Simulation of Double-Planetary Gearbox Based on Bond Graph

New generations of powertrains are using gearboxes with multiple speed-shift designs to improve fuel efficiency. However, transmission controls and calibration are substantially time consuming, specifically during shift processes. To study the dynamic characteristics of a gearbox with a double-planetary gear train and analyze the influence of external excitation and internal parameters on the dynamic response of a system, dynamic modeling and simulation of the transmission system are conducted. Some physical processes are complex and difficult to express via lumped mass modeling. The dynamic model of a double-planetary gearbox is obtained by adopting the bond graph method based on the working principle analysis of the transmission, as well as the kinematic characteristics of the double-planetary gear train. Subsequently, state equations are deduced from the dynamic model of the power transmission system for simplified calculations, which can effectively facilitate the shift process simulation. The basic case of different shift plans and times is originally analyzed, followed by an analysis of the influence of damping, stiffness, and moment of inertia on transmission systems. The analysis results provide references for the structural design, control strategy optimization, and failure diagnostics of this gearbox type.

Vibration and stability analysis of drivelines with self-excitation of non-constant velocity couplings

In this research, a drivetrain system consisting of three shafts coupled by two joints is considered. This drivetrain system is able to transfer out-of-plane motion. To yield a more realistic model, the interconnected shafts are simulated by the finite element method. The dynamic stability is also analyzed using a computational method called monodromy matrix. Finally, the unstable areas are identified and the effects of various system parameters are discussed. Furthermore, the distributed parameter model is compared with a basic lumped mass model that is common in two-axis shafts. Moreover, there are several unstable areas, which have not been found using lumped mass models. Subsequently, the finite element model is feasible to examine the torsional vibrations of multi-axis driving shafts.

Hydrodynamics of a dual-module pontoon-net floating breakwater system: Numerical simulations and prototype tests

Floating breakwaters with a mooring system have been widely applied to protect marine infrastructures (e.g., artificial beach or island, aquaculture farm or marine vessels in harbors) from being destroyed by severe waves. In this paper, an innovative cylindrical dual pontoon-net floating breakwater was developed to enhance the wave attenuation capacity. This dual-module floating breakwater system was constructed as the prototype for on-site testing. A fully nonlinear time-domain model based on the coupled iterative solutions of the fluid integral equation and the pontoon-net dynamic equations was proposed to simulate the interactions between waves and the floating breakwater system. The flow field around the nets was simulated by introducing a porous-media model with Darcy’s law, while the deformation of the flexible nets was solved by using the lumped mass model. The instantaneous free surface was captured using the mixed Eulerian-Lagrangian (MEL) approach which employs an improved moving-grid technique based on the spring analysis to re-mesh the instantaneous water surface and the body wetted surface. On-site tests were also conducted to evaluate wave transmission performance of the floating breakwater system and to validate the numerical model. The comparisons show that the numerical solutions are in good agreement with the measured data. The effects of incident wave direction, wave period, wave height, net height, net number and net porosity on the hydrodynamic performance of the floating breakwater system were emphatically examined.

Experimental Analysis and Theoretical Modelling of Polyurethane Effects on 1D Wave Propagation through Sand-Polyurethane Specimens

ABSTRACT This paper shows the experimental results of impact hammer tests conducted on sand and composite sand-polyurethane samples at different confining pressures. It was found that polyurethane can mitigate the propagation of waves generated by an impact, thereby influencing seismic isolation. Also, accelerations in the composite samples were reduced in relation to the percentage of polyurethane present. A theoretical lumped-mass model (calibrated based on the experimental results) interpreted the experimental results and enabled an in-depth parametric analysis. This analysis shows that the proposed isolation method is efficient, as the damping coefficient of the polyurethane and the soil/polyurethane impedance ratio increased.

Suspended cable model for layout optimisation purposes in floating offshore wind farms

The cable layout optimisation for floating offshore wind farms is a complex task due to the number of elements involved and their nature, such as dynamic cables with buoyant sections. The first step is defining a model of the suspended cables that connect wind turbines between them or to cables on the seabed (risers). A lumped mass model and the finite element method are used to find the static position and mechanical stresses of the cables, keeping a balance between computational time and the quality of the results. The model allows the inclusion of standard ancillary equipment such as bend stiffeners, buoyancy modules, clamps and tethers in order to simulate multiple configurations: double hanging, single hanging (catenary), lazy wave, steep wave and tethered wave. The external actions considered are marine growth and currents and the main cable properties are taken into account to calculate its weight, buoyancy, tensions, moments and drag forces. The information obtained after the simulation includes cable tensions, curvature, laid and suspended lengths and tether tension, when applicable. Next steps include the optimisation of the suspended cables and the full network in the farm.

Optimal Earthquake Intensity Measures for Probabilistic Seismic Demand Models of Base-Isolated Nuclear Power Plant Structures

The purpose of this study is to evaluate the optimal earthquake intensity measures (IMs) for probabilistic seismic demand models (PSDMs) of the base-isolated nuclear power plant (NPP) structures. The numerical model of NPP structures is developed using a lumped-mass stick model, in which a bilinear model is employed to simulate the force-displacement relations of base isolators. In this study, 20 different IMs are considered and 90 ground motion records are used to perform time-history analyses. The seismic engineering demand parameters (EDPs) are monitored in terms of maximum floor displacement (MFD), the maximum floor acceleration (MFA) of the structures, and maximum isolator displacement (MID). As a result, a set of PSDMs of the base-isolated structure is developed based on three EDPs (i.e., MFD, MFA, and MID) associated with 20 IMs. Four statistical parameters including the coefficient of determination, efficiency (i.e., standard deviation), practicality, and proficiency are then calculated to evaluate optimal IMs for seismic performances of the isolated NPP structures. The results reveal that the optimal IMs for PSDMs with respect to MFD and MID are velocity spectrum intensity, Housner intensity, peak ground velocity, and spectral velocity at the fundamental period. Meanwhile, peak ground acceleration, acceleration spectrum intensity, A95, effective peak acceleration, and sustained maximum acceleration are efficient IMs for PSDMs with respect to MFA of the base-isolated structures. On the other hand, cumulative absolute velocity is not recommended for determining the exceedance of the operating basis earthquake of base-isolated NPP structures.

Numerical Simulation Study on Environment-Friendly Floating Reef in Offshore Ecological Belt under Wave Action

An artificial floating reef is an important part of the coastal ecological corridor. The large-scale construction of floating reefs by optimizing mooring methods can effectively improve the ecological effects of coastal projects. The artificial floating reef belongs to coastal engineering, and wave resistance is fundamental to its structural design. In this paper, the method for processing coupling forces and motion, the method for judging the floating reef out of water surface, and the method for correcting velocity and acceleration of water mass points are elaborated in detail by using the finite element method and lumped-mass mooring model. By comparing and analyzing the results of physical experiment and numerical simulation, the correctness of the numerical model is verified. Finally, the diachronic variation of pitching angle of floating reef, the tension of the mooring rope, and the total tension of the fixed points of the fishing net were analyzed by the dynamic response numerical mode with a new type of mooring. The purpose of the current study was to provide a basis for the optimization of structure shape, the matching of floating body, and the counterweight of artificial floating reef.

Recommendations for regularization in the inverse estimation of ice-induced propeller moments for ice-going vessels

To date, the insufficient quantification of ice-induced propeller moments leads to uncertainty and over-design of ship propulsion systems. Recent developments document the use of lumped mass models and inverse solutions of the external ice-induced propeller moments from indirect measurements on the propulsion shaft. However, these inverse solutions suffer from instability. This article studies various regularization methods which are required in the inverse solution process to insure the stability of the solution. The study focuses on the success rates of the regularization methods. Specifically, the success rate of the automatic selection of a regularization parameter within the inverse solution algorithm was evaluated. Full-scale measurements of the shaft-line of an ice-going vessel were used as inputs for the regularization of the inverse problem. It was found that the Tikhonov regularization method was the most reliable for the analysed case studies. Furthermore, the solution times for the regularization methods were considered. The limitations of the lumped mass inverse model used with the regularization methods are presented and discussed, suggesting that the model is not ideally suited for the application.

Platform Motions and Mooring System Coupled Solver for a Moored Floating Platform in a Wave

In advance of building moored floating offshore platforms, in recent years, there has been a greater demand for two-way coupled simulations between a motion solver based on the viscous flow theory and a mooring line model, including cable dynamics. This paper introduces open-source libraries such as MoorDyn (the lumped-mass mooring line model) and OpenFOAM (the computational fluid dynamics libraries). It describes the methods by which they can be coupled bi-directionally. In each time step, the platform motions calculated by OpenFOAM are transferred to MoorDyn as the boundary conditions for the mooring system analysis. In contrast, MoorDyn calculates the restoring force and moment due to the mooring system and transfers them to OpenFOAM. The restoring force and moment act on the platform as the external force and moment for the platform motions in the next time step. The static tension and profile of the mooring system, dynamic tension of the mooring system, and free decay motions of the floating buoy in the still water were simulated to check the accuracy of OpenFOAM and MoorDyn. The coupled solver was used to produce simulations of the moored decay motions of the floating buoy in the still water and the moored motions with the Stokes 5th order wave. All simulation results were compared and showed good agreement with the numerical solution and experiment results. In addition, the characteristics of each solver were investigated.

From main axes control to flexible body control of large telescope structures

AbstractAstronomers have to point their telescopes with extreme high precision to their targets on the sky. The early craftsmen, which built their telescope mounts, were masters in mechanics and developed sophisticated axis mechanisms based on clockwork motors for the hour angle. The situation changed with the growth of the size of the optical telescopes, the upcoming of large radio telescopes, the related transition to elevation over azimuth mounts and the introduction of electrical main axes drives. The new telescopes were equipped with gears of high transmission ratios, and the dynamics of the motor control was limited by mechanical resonances between the rotors of the motors and the mass of the telescope structure. Early layout tools for the controllers were lumped mass models for the telescope structure including gear stiffnesses and inertias of rotors and brakes, with the free rotor and locked rotor frequencies as critical characteristics influencing the servo loop performance. Nowadays, static and dynamic analysis is performed with the help of finite element models, and the axes controllers are optimized with end‐to‐end models. The emergence of large radio telescopes initiated the development of additional compensation methods for environmental influences as temperature and wind on the shape of the reflectors and their pointing to the sky. Additional active elements on the telescope as surface actuators and subreflector positioners, and additional state sensors on the structure allow the identification and compensation of structural deformations. The method is called flexible body control (FBC). The increasing size of the optical telescopes initiated the development of new mirror technologies as thin meniscus or segmented mirrors in sizes not feasible with the passive supported thick meniscus mirrors. These mirrors need active elements as shape actuators, segment positioners, and wavefront and edge sensors. The method is called active optics (AcO). Astronomical observations in the visible are disturbed by atmospheric blur, and the operability is depending of the active compensation of that blur, based on a fast wavefront sensor analyzing an artificial star and an additional fast wavefront corrector. The method is called adaptive optics (AdO). The following text gives an overview on the historic development of telescope control systems from the viewpoint of the telescope mount and its axes control systems, finally culminating in FBC applications. Actual examples are the large millimeter telescope LMT/GTM in Mexico, the advanced technology solar telescope DKIST in Hawaii, and the airborne telescope of SOFIA, the Stratospheric Observatory for Infrared Astronomy with its base in Palmdale, California.

Lumped Mass Model for Flexible Cable: A Review

Model of a flexible cable plays a great role in the applications of underwater towing system, mooring line system, etc. A complete mathematical model is a basis to accurately describe the dynamic characteristics of flexible cable. This article presents a state of art comprehensive review of lumped mass model. First, the mathematical principle of the lumped mass model, including geometric simplification, force analysis, and solution, are systematically summarized.Second, the dynamic response of cable under different boundary conditions is introduced, and boundary conditions are categoried. Third, the numerical solution of the lumped mass model are assessed. Finally, based on the application of guide dog robot, the authors discussed the research future and trends. The authors aim to ealize human-robot interaction through a flexible cable.

Numerical and experimental analysis of the effect of eccentric phase difference in a rotor-bearing system with bolted-disk joint

Bolted joints are widely used in industrial rotating machines to fasten the adjacent disks together and affect system dynamic properties. Therefore, there is a strong need to study their influence on the response of such systems. This paper investigated the effect of the eccentric phase difference of the disk and bolted-disk joint on rotor dynamics, which takes into account the time-varying bending stiffness of the bolted joint. The bolted-disk joint is modeled as a two-node element based upon the energy theorem and Lagrange’s principle, where the relative lateral displacement stiffness, relative bending stiffness, and coupling stiffness between the adjacent disks are considered. And then the dynamic model of the rotor-bearing system is derived based on the proposed bolted joint element and lumped mass modeling method. Combining with the Newmark-β integration scheme, the established model allows the dynamic response characteristics of the rotor-bearing system with the bolted joint to be predicted, and the impact of eccentric phase difference in the rotor system on the response to be investigated. The validity of the simulation results was confirmed by experiment. Through the modeling method proposed in this paper and obtained results, the bifurcation characteristics of the bolted joint rotor system can be predicted.

Seismic performance assessment of NPP concrete containments considering recent ground motions in South Korea

Seismic fragility analysis, a part of seismic probabilistic risk assessment (SPRA), is commonly used to establish the relationship between a representative property of earthquakes and the failure probability of a structure, component, or system. Current guidelines on the SPRA of nuclear power plants (NPPs) used worldwide mainly reflect the earthquake characteristics of the western United States. However, different earthquake characteristics may have a significant impact on the seismic fragility of a structure. Given the concern, this study aimed to investigate the effects of earthquake characteristics on the seismic fragility of concrete containments housing the OPR-1000 reactor. Earthquake time histories were created from 30 ground motions (including those of the 2016 Gyeongju earthquake) by spectral matching to the site-specific response spectrum of Hanbit nuclear power plants in South Korea. Fragility curves of the containment structure were determined under the linear response history analysis using a lumped-mass stick model and 30 ground motions, and were compared in terms of earthquake characteristics. The results showed that the median capacity and high confidence of low probability of failure (HCLPF) tended to highly depend on the sustained maximum acceleration (SMA), and increase when using the time histories which have lower SMA compared with the others.

The Effect of Rainfall Intensity to Landslide Run-Out Prediction and Velocity: A Parametric Study on Landslide Zones in West Java-Indonesia

Assessment and management of landslide risk require the knowledge of landslide run-out distance and velocity. However, the landslide volume as the basis for calculating landslide run-out distance and velocity is governed by slip surface development during rainfall. Thus, it is necessary to understand how rainfall characteristics influence landslide run-out and velocity. This paper presents a parametric study to clarify the effect of rainfall intensity on landslide run-out and velocity of two steep volcanic cut-hillslopes in West Java, Indonesia. The landslide volumes were estimated from the potential sliding surface obtained from slope stability analysis under a rainfall infiltration. The landslide run-out and velocity were then calculated using an energy conservation formula in a lumped mass model. This study shows that the slip surface developed at a different depth in each slope, depending on the rainfall intensity. As a result, the landslide run-out and velocity of both cut-hillslope are significantly different and, in general, decrease to reach a constant value with increasing rainfall intensity. Thus, the results of this study can be used as a guideline to assess the rainfall-induced landslide movement, especially in cut-hillslopes.

Dynamic analysis of an array of semi-rigid “sea station” fish cages subjected to waves

The dynamic behaviour of an array of 6 × 6 semi-rigid “sea station” fish cages is studied under the effect of waves. The semi-rigid sea station system is discretized into a lumped mass model, that is used as the dynamic simulation model. The tension in the mooring lines of the mooring system is obtained in the time domain for different wave directions. The rotations of three degrees of freedom of each semi-rigid sea station under different wave directions are analysed, and the spectral density function of the mooring tension is obtained by Fast Fourier Transform of the time domain response. The results provide a basis for the design of the semi-rigid sea station system and have a certain guiding significance for the specific engineering practice.

Effects of Soil-Structure Interaction on Seismic Response of Fixed Base and Base Isolated Liquid Storage Tanks

ABSTRACT A detailed numerical framework for seismic analysis of liquid storage tanks considering soil-structure interaction (SSI) is presented. Lumped mass model for the tank and finite element approach for the soil domain are adopted. Effects of SSI on seismic performance of ground supported and elevated liquid storage tanks, with fixed base and base isolated conditions, are studied under near-field and far-field ground motions. Effect of SSI on fixed base tanks is found to be similar under different types of ground motions. Nevertheless, effectiveness of isolation systems with different stiffness characteristics depends on soil type, tank slenderness ratio, and ground motion types.

Hydrodynamic performance of the floating fish cage under extreme waves

Extreme waves with large wave heights may cause the biomass loss and catastrophic damage to the offshore fish cage. This study investigates the hydrodynamic response of fish cage under extreme waves. Focused waves based on the NewWave theory are simulated to represent such extreme waves in this study. Based on the lumped-mass model, the fish cage is numerically simulated to analyze the motion and load characteristics in extreme waves. The results indicate that the fish cage volume dramatically decreases in extreme waves. The extreme wave results in large motions and mooring loads. Different extreme wave crest locations give rise to different net cage responses. The fish cage attacked at the leeward side suffers from larger motions and mooring loads than the upwind side. With the increase of the steepness, surge motions and mooring loads sharply increase. The preceding waves before the highest crest greatly influence the peak values of motions and loads. Results imply that not only the crest location but also the load histories should be carefully examined when investigating the extreme response.