Lumped Mass Method Research Articles

Modeling and modal analysis of non-uniform multi-span oil-conveying pipes with elastic foundations and attachments

This paper studies the parametric modal characteristics of non-uniform multi-span oil-conveying pipes, considering many combined factors such as the various foundations that pipes rest on, the accessary masses attached to the pipes, and the flow moving inside the pipes. A new modified lumped-mass transfer matrix method (LTMM) is proposed to derive the governing equation of the system, where we simplified and modeled all the combined factors as lumped masses and springs that can be treated in uniform ways. The boundary is also modeled in a similar lumped-spring strategy. In such a way, the system with combined factors and various boundary conditions is eventually modeled as a “Free-Free” pipe with only lumped masses and springs. Numerical results are illustrated to testify the accuracy and efficiency of the proposed method, and a general case with combined factors affecting the modal characteristics is discussed. It can be presented that rotary inertia and concentrated mass can affect different order mode shapes; under different foundation parameters, the differences between mode shapes are remarkable while the positions of the nodes do not change much, even under classical boundary condition. The results through modal analysis can afford the basis for the vibration analysis, fault diagnosis and prediction, and the optimization design of the dynamic characteristics of the structure.

Experimental Test and Numerical Analysis of a Structure Equipped with a Multi-Tuned Liquid Damper Subjected to Dynamic Loading

Tuned liquid dampers (TLDs) have many advantages in controlling building vibrations, among which multi-tuned liquid dampers (MTLDs) appear to have better stability and effectiveness. However, the tank wall was assumed to be rigid in the past by ignoring the fluid-structure interaction (FSI) at the interface, resulting in simplified calculation for the design of the TLDs. Moreover, the fluid in the tank was considered to be separate from the structure. This paper presents two numerical methods to control the responses of the frame under the dynamic loadings: (1) the lumped mass method for quickly designing the TLDs, and (2) the finite volume method/finite element method (FVM/FEM) for analyzing the fluid and solid domains of the TLDs in a single computational 3D model. In addition, the multi-field interaction between the structure-fluid-tank walls is considered by solving the coupling equations at the interfaces. A steel frame is fitted with an MTLD and tested experimentally on a shaking table to investigate its dynamic response. Numerical results are verified with the experimental ones, which show good agreement.

Investigations on Linear Manoeuvres of Underwater Towed Cable in Current

In this paper, a numerical method for dynamic characteristics of cable in marine linear towage is proposed. The governing equation of the towing system is established based on the lumped mass method. The continuous dynamic characteristic partial differential equation is obtained by the discretization of cascade nodes. The equation is solved by the finite difference time domain method. Through numerical simulation, the tension variation curves and cable response configuration under three different operating conditions-when there is no current, along with and against sea current directions-are given respectively, which can be used for dynamic load estimation and motion trajectory prediction in towed-array systems. The comparison between the numerical example results and the experimental demonstrates the validity of the method and is of practical significance for improving maritime safety and operational efficiency.

Hydrodynamic model of Daya Bay based on finite element method

The current problems are hot spots in recent years. With the rapid development of modern computer technology, numerical simulation technology has become an important means of scientific research, and the correlation numerical solution of two-dimensional shallow water equation is endless. In this paper, the two-dimensional shallow water equation was discretized by the finite element weighted lumped mass method, and the time is discretized by the forward Euler scheme, then the planar two-dimensional hydrodynamic model was established. The water boundary condition was defined by harmonic analysis method. The two-dimensional hydrodynamic model was applied to Daya Bay area and verified according to the measured meteorological data. Therefore, the hydrodynamic model established in this paper can be used to study the actual water flow in Daya Bay area.

Feasibility of reducing dynamic response of a fixed offshore platform using tuned liquid dampers

ABSTRACT Fixed offshore platforms are always subjected to dynamic loading. A potentially economical method to improve the dynamic behaviour of these platforms is using passive control devices. In this paper, the application of tuned liquid damper, TLD, in controlling the response of a fixed offshore platform located in the Persian Gulf against earthquake and wave loading was studied. Analysis of a 3D model of the structure equipped with TLDs was carried out using the finite element method, and the efficiency of TLDs was investigated. Also, the equivalent models of TLDs were constructed based on the lumped mass method, and linear wave theory and the results were compared to finite element modelling of TLD. Results showed good agreement between the finite element model of TLD and equivalent lumped mass model. Results also indicated that adding TLDs can mitigate jacket deck vibrations and their efficiency increases as wave height or ground motion increase.

A Dynamic Model for Continuous Lowering Analysis of Deep-Sea Equipment, Based on the Lumped-Mass Method

The installation of subsea equipment is a critical step in offshore oil and gas development. A dynamic model to evaluate the lowering process is proposed. The cable–payload system is discretized as a series of spring dampers with the lumped-mass method. For the first time, not only the lowering velocity but also the rope’s structural damping and the nonlinear loads, such as drag force and snap load, are considered. The lowering velocity of the cable is considered through a variable-domain technique. Snap loads are considered by setting the internal forces in the elements to be zero when the cable slacks. A series of simulations reveals that the lowering velocity has great effects on the dynamic force in the cable. However, the structural damping of the cable has little effect on the system response. The snap load may occur in the cable when subjected to rapid downward heave motion, and decreases with the lowered depth increasing. The cable stiffness affects the system’s resonance depth, but has little effect on the peak dynamic force. The present work should be a valuable reference for future subsea equipment installation analysis.

Dynamics Modeling and Motion Simulation of USV/UUV with Linked Underwater Cable

This paper describes a study on the dynamic modeling and the motion simulation of an unmanned ocean platform to overcome the limitations of existing unmanned ocean platforms for ocean exploration. The proposed unmanned ocean vehicle combines an unmanned surface vehicle and unmanned underwater vehicle with an underwater cable. This platform is connected by underwater cable, and the forces generated in each platform can influence each other’s dynamic motion. Therefore, before developing and operating an unmanned ocean platform, it is necessary to derive a dynamic equation and analyze dynamic behavior using it. In this paper, Newton’s second law and lumped-mass method are used to derive the equations of motion of unmanned surface vehicle, unmanned underwater vehicle, and underwater cable. As the underwater cable among the components of the unmanned ocean platform is expected to affect the motion of unmanned surface vehicle and unmanned underwater vehicle, the similarity of modeling is described by comparing with the cable modeling results and the experimental data. Finally, we constructed a dynamic simulator using Matlab and Simulink, and analyzed the dynamic behavior of the unmanned ocean platform through open-loop simulation.

Dynamics of an ultra-deepwater mooring line with embedded chain segment

A code is developed to study the mooring tensions on a line with an embedded segment considered, based on lumped mass method. The accuracy of this code is validated by published results. The influence of soil-chain interaction on the static and dynamic behaviour of a 1500 m mooring line is studied under two operational situations: shallow embedded taut mooring line and deep embedded semi-taut mooring line. The shallow case has an embedded depth setting as 10 m under seafloor, while the embedded depth is 20 m for deep water. To study the influence of soil on mooring dynamics, three simplified cases without soil force considered are investigated and the results are compared with the dynamics of embedded mooring. These three cases include: i) Case MA has the same spread distance to embedded mooring anchored on seafloor; ii) Case MB is anchored on seafloor and it has the same pretension with embedded mooring; iii) Case MC is anchored to the same point to the embedded mooring but the soil force is not considered. Furthermore, the effects of effective width parameters of tangential and bearing soil resistance on mooring dynamics are also discussed. In this work, three different oscillations are forced on fairlead to study the mooring dynamics, which are low frequency oscillation, hybrid oscillation (low frequency and wave frequency) and wave frequency oscillation.

Coupled three-dimensional dynamics model of multi-component mooring line for motion analysis of floating offshore structure

A coupled dynamics model of multi-component mooring line is proposed to analyze the motion of a floating offshore structure. The model is developed by extending three-dimensional lumped mass method allowing the motion of segment connection points and including an anchor and clump weights. It offers analysis on simultaneous interlocking-segment line motions to solve three-dimensional dynamic responses of a multi-component mooring line. The model integrates hydrodynamic loads, line-seabed interaction, elasticity, current effect, and dragging anchor motions. It is then coupled with a ship-type floating offshore structure and validated by comparing with equivalent model based on a conventional numerical method. Comparison against two-dimensional model is also established. Finally, coupled motion analysis of the floating structure moored by multi-leg with multi-component mooring lines in realistic operations are conducted by considering actual environmental loads. The impact of the presented dynamics model on the evaluation of the response of the floating structure and mooring line tension are investigated. The results conclude that the model can successfully provide the realistic prediction of the motion of the floating structure. Farther, this paper found out that three-dimensional mooring line treatment needs to be considered since lateral mooring line motion has considerable impact on mooring line tension.

Coupling Effects of A Deep-Water Drilling Riser and the Platform and the Discharging Fluid Column in An Emergency Disconnect Scenario

As drilling operations move into remote locations and extreme water depths, recoil analysis requires more careful considerations and the incidence of emergency disconnect is increased inevitably. To accurately capture the recoil dynamics of a deep-water riser in an emergency disconnect scenario, researchers typically focus on modelling the influential subsystems (e.g., the tensioner, the mud discharge and seawater refilling process) which can be solved in the preprocessing, and then the determined parameters are transmitted into an existing global riser analysis software. Distinctively, the current study devotes efforts into the coupling effects resulting from that the suspended riser reacts the platform heave motion via the tensioner system in the course of recoil and the discharging fluid column follows the oscillation of the riser in the mud discharge process. Four simulation models are established based on lumped mass method employing different formulas for the top boundary condition of the riser and the discharging flow acceleration. It demonstrates that the coupling effects discussed above can significantly affect the recoil behavior during the transition phase from initial disconnect to the final hang-off state. It is recommended to develop a fully-coupled integrated model for recoil analysis and anti-recoil control system design before extreme deep-water applications.

Numerical Study on Hydrodynamic Responses of Floating Rope Enclosure in Waves and Currents

Enclosure aquaculture is a healthy and ecological aquaculture pattern developed in recent years to relieve the pressure due to the wild fish stock decline and water pollution. The object of this paper was a floating rope enclosure, which mainly consisted of floaters, mooring lines, sinkers and a net. In order to optimize mooring design factors, the hydrodynamic responses of the floating rope enclosure with different mooring systems in combined wave-current were investigated by experimental and numerical methods. Physical model experiments with a model scale of 1:50 were performed to investigate the hydrodynamic characteristics of a floating rope enclosure with 12 mooring lines. Based on the lumped mass method, the numerical model was established to investigate the effects of mooring design factors on the mooring line tension, force acting on the bottom, and the volume retention of the floating rope enclosure. Through the analysis of numerical and experimental results, it was found that the maximum mooring line tension of the floating rope enclosure occurs on both sides of the windward. Increasing the number of mooring lines on the windward side is helpful to reduce the maximum mooring line tension. Waves and current both have an influence on the mooring line tension; in contrast, currents have a more obvious effect on the mooring line tension than waves. However, the influence of the wave period on the maximum mooring line tension is small. The force endured by the bottom of the floating rope enclosure also changes periodically with the wave period. Yet, the maximum force endured by the bottom of floating rope enclosure occurred at the windward and leeward of the structure. The volume retention of the floating rope enclosure increased with the increasing amount of mooring lines.

Nonlinear dynamics analysis of high contact ratio gears system with multiple clearances

A brief research status on high contact ratio gears (HCRG) is first conducted to obtain a basic understanding. Subsequently, a nonlinear dynamic model of HCRG with multiple clearances is established by the lumped mass method, in which time-varying mesh stiffness (TVMS), static transmission error, gear backlash, and bearing radial clearance are taken into consideration as well. The TVMS of HCRG is calculated based on an improved potential energy model and then fitted into a Fourier series form. After the dimensionless treatment, the system differential equations of motion are solved using Runge–Kutta numerical integration method. With the help of bifurcation diagrams, largest Lyapunov exponent charts, time-domain waveforms, FFT spectra, Poincare maps, and phase diagrams, the influence of excitation frequency, gear backlash, mesh damping ratio, error fluctuation, and bearing radial clearance on the nonlinear dynamic characteristics of the system is investigated in detail. The results show that with the changes of these analysis parameters, the system exhibits different types of nonlinear behaviors and dynamic evolution mechanism, including period-one, multi-periodic, quasi-periodic, chaotic motions, and jump discontinuity phenomenon. Meanwhile, three typical routes to chaos, namely period-doubling bifurcation to chaos, quasi-period to chaos, and crisis to chaos, are also demonstrated. Additionally, it is found that the bearing radial clearance produces a weaker nonlinear coupling effect when compared to gear backlash. The research results can provide a certain theoretical support for the dynamic design and vibration control of the HCRG.

Dynamic analysis of a helical gear reduction by experimental and numerical methods

Presented in this study is investigation of dynamic behavior of a helical gear reduction by experimental and numerical methods. A closed-loop test rig is designed to measure vibrations of the example system, and the basic principle as well as relevant signal processing method is introduced. A hybrid user-defined element model is established to predict relative vibration acceleration at the gear mesh in a direction normal to contact surfaces. The other two numerical models are also constructed by lumped mass method and contact FEM to compare with the previous model in terms of dynamic responses of the system. First, the experiment data demonstrate that the loaded transmission error calculated by LTCA method is generally acceptable and that the assumption ignoring the tooth backlash is valid under the conditions of large loads. Second, under the common operating conditions, the system vibrations obtained by the experimental and numerical methods primarily occur at the first fourth-order meshing frequencies and that the maximum vibration amplitude, for each method, appears on the fourth-order meshing frequency. Moreover, root-mean-square (RMS) value of the acceleration increases with the increasing loads. Finally, according to the comparison of the simulation results, the variation tendencies of the RMS value along with input rotational speed agree well and that the frequencies where the resonances occur keep coincident generally. With summaries of merit and demerit, application of each numerical method is suggested for dynamic analysis of cylindrical gear system, which aids designers for desirable dynamic behavior of the system and better solutions to engineering problems.

Numerical simulations for the predator-prey model on surfaces with lumped mass method

The predator-prey model is powerful mathematical tool to describe the dynamics of biological systems and promote research on biological populations. In this paper, we present a lumped mass finite element method for solving the predator-prey models on surfaces. The main purpose of the proposed method is to overcome the difficulty of the positivity preservation of the solutions. Based on positivity preservation results, we investigate the stabilities of semi-discrete and fully discrete approximations. Besides, numerical simulations are considered to illustrate the feasibility of the numerical method by convergence tests. Two classical phenomena of the predator-prey model are simulated on three different implicit surfaces.

Study on vibration suppression performance of a flexible fixture for a thin-walled casing

Because of its poor rigidity, a thin-walled casing can easily cause chatter during the cutting process, which seriously affects the efficient processing of the casing, so some measures are needed to suppress the flutter. In this paper, a dynamic model of flexible fixtures for thin-walled casings is presented. This model differs from the analysis of casings with rigid fixtures. A new flexible fixture has been designed based on the principle of multiple dynamic vibration absorbers. A hybrid dynamic model of the lumped mass method and the finite element method for thin-walled casings and flexible fixtures has been developed, and the effect of flexible fixtures on the vibration suppression of thin-walled casings is analyzed. To verify the model, a typical thin-walled casing is taken as an example, and the accuracy of the dynamic model is verified by the comparison between the modal test results and the simulation results. The simulation and experimental results show that the model can effectively reflect the dynamic response of thin-walled casings under the flexible fixture. With a flexible fixture, the corresponding amplitude of the frequency response of the casing is reduced, and the frequency is shifted to the right. Through cutting experiments, it is found that the low-order vibration amplitude of the system is reduced by nearly 20 times and the coupling vibration amplitude of the cutter and the workpiece is reduced by nearly 5 times with a flexible fixture. Finally, it is also noted that flexible fixtures are an effective measure to suppress casing flutter.

基于等效梁模型的运载火箭动力学特性仿真预示研究

An efficient and accurate method was proposed for dynamic characteristics prediction of launch vehicles based on the equivalent beam model, with which the influence of liquid propellants can be considered. The equivalent beam model for the launch vehicle was established based on the cross-sectional area equivalence principle, and improved through model updating against the natural frequencies and mode shapes of the fine finite element model. The present method was validated through computation of a certain type of launch vehicles. A highly representative equivalent beam model for the launch vehicle was established. The dynamic characteristics of the launch vehicle were predicted based on the equivalent beam model under the influence of liquid propellants in 2 ways of the lumped mass method and the coupled mass method, and the results were compared.

Dynamics analysis of deep-sea mining pipeline system considering both internal and external flow

The transportation pipeline subsystem is an essential part of the deep-sea mining system. In order to explore the internal flow field of the pipeline, the internal flow simulation is carried out by CFD-DEM coupling method. The pressure and wall shear stress of the pipe are computed to show the influence of internal flow on the pipelines. Moreover, a novel multi-body dynamic model of the pipeline system is established by the lumped-mass finite element method (LM_FEM) considering both internal and external flow to investigate its dynamic performance. The model includes a 900 m lifting rigid pipe, a 400 m conveying flexible hose and a simplified buffer. The results show that the dynamic performance of pipeline system is greatly affected by ocean current angle, sea depth and buoyancy module distribution. As the ocean current angle increases, the maximum bending moment of rigid pipe is significantly reduced, and the value of flexible hose is gradually increased. This study provides an important theoretical basis and technical references for the pipeline design, performance evaluation and coordinated motion control of the practical deep-sea mining system.

Influence of ocean currents on the stability of underwater glider self-mooring motion with a cable

The underwater glider mooring motion with a cable has its unique advantages and is gradually gaining attention. The influence of ocean currents on its residence stability cannot be ignored. To analyze the impact of ocean currents on the stability of the underwater glider self-mooring motion, the multi-body dynamics is solved. In this paper, the lumped mass method is utilized to discretize the cable into a series of lumped mass points and massless springs, which considers the nonlinear forces acting on the cable. The kinematic and dynamic models of the underwater glider resident process are established by the KANE method and the generalized force method, respectively, which fully considers the interactions of the underwater glider, cable and anchor. The simulations are conducted by applying fourth Runge–Kutta method in the time domain. The results show that the numerical method proposed is reasonable, and it is observed that the ocean currents with different speeds and directions affect the stability of the underwater glider in the self-mooring motion with a cable. In addition, the length of the cable in the same ocean current environment will also have a certain impact on the stability of the underwater glider.

Theoretical analysis of the vibration modes of the star herringbone gear transmission system

The star herringbone gear transmission system has a high load-carrying capacity, and is widely used in aviation, marine power drives, off-road vehicles, and hybrid electric-drive vehicles. Vibration and noise are the key concerns with this transmission system. The lumped mass method was adopted to establish the dynamic model and equations of this system. The modes of the system were analyzed and classified, and the eigenvalues and their multiplicities were determined. The results showed that the system has four typical vibration modes: (1) a lateral-rotational coupled vibration mode (multiplicity m = 1), (2) star gear compound mode (multiplicity m = N-3, N > 3), (3) center component lateral vibration mode (multiplicity m = 2), and (4) star gear and center gear-coupled mode (multiplicity m = 2). The contribution of this paper lies in the discovery of the coupling vibration modes in the star herringbone gear transmission system and the multiplicities of these modes. This work provides the foundation for further research on vibration suppression for the star herringbone gear transmission system and the theory of planet phasing.

Dynamic Characteristics Analysis with Multi-Directional Coupling in a TBM Mainframe

The cutterhead of a full-face rock tunnel boring machine (TBM) is constantly subjected to varying impact and dynamic loads during tunneling processes, resulting in relatively large vibrations that could easily lead to fatigue cracking of the entire machine and affect the tunneling performance and efficiency. To explore the dynamic characteristics of the TBM mainframe, a TBM from a water-diversion project is investigated in this research. According to the TBM vibration transmission route, an equivalent dynamic model of the TBM mainframe is established using the lumped-mass method in which the relevant dynamic parameters are solved. Additionally, the dynamic response characteristics of the TBM mainframe are analyzed. The results indicate that the vibration levels in three directions are approximately the same, the multi-directional vibration of the cutterhead is more intense than that of other components, and the vibration and external excitation exhibit identical change trends. A set of vibration field tests is performed to analyze the in situ dynamic responses of the mainframe and verify the correctness of the dynamic model. The theoretical and measured acceleration values of the TBM mainframe have the same magnitude, which proves the validity of the dynamic model and its solution. The aforementioned results provide an important theoretical value and practical significance for the design and assessment of the TBM mainframe.