Lumped Mass Model Research Articles

Seismic fragility analysis of traditional Chinese timber structures based on a simplified lumped mass model considering joint damage

To evaluate the dynamic performance of seismic-damaged ancient timber structure, a spring-rigid rod model considering column rocking (C-R), mortise-tenon (M-T) joints, and bracket set (B-S) joint was initially developed. Subsequently, based on the centroid method and stiffness equivalent method, a simplified lumped mass model (LMM) was proposed, and the accuracy was verified through shaking table tests. PGA and maximum story drift were utilized as indicators of seismic intensity and response parameters for the incremental dynamic analysis (IDA) of models, the influence of varying degrees of M-T joint damage on structural fragility was investigated. The results revealed that M-T joint damage significantly influence the structural performance level compared to B-S joint damage. Under 0.018 g, the probability of slight damage to the model is 27.04 %, while between 0.2 g and 0.4 g, the probability of moderate and severe damage reaches 70.00 %. The structures exhibit a pattern of low fragility at low intensities and a propensity for collapse at high intensities. For seismic action of Intensity 6, when the joint damage level reaches 13.30 %, and under the design for Intensity 8 seismic action, when the joint damage level is at 6.70 %, and under the seismic action of Intensity 9, the models should be repaired and reinforced.

Coupled Electro-Thermal-Aging Battery Pack Modeling—Part 1: Cell Level

This paper presents a modeling approach to capture the coupled effects of electrical–thermal aging in Li-ion batteries at the cell level. The proposed semi-empirical method allows for a relatively high accuracy and low computational cost compared to expensive computer simulations. This is something current models often lack but is essential for system level simulations, relevant for electric vehicle manufacturers. The aging analysis includes both cycling and calendar effects across the lifetime of the cell and reversible and irreversible heat in a lumped-mass model to capture the temperature evolution of the cell in operation. The Thévenin equivalent circuit model with capacitance used to simulate the electrical behavior of the cell was experimentally validated, showing a high correlation with the proposed model during the charging and discharging phases. A maximum error of 3% on the voltage reading was identified during discharge with the complete model. This model was also designed to be used as a stepping stone for a comprehensive model at the module and vehicle levels that can later be used by designers.

Design of an Active Axis Wind Turbine (AAWT) That Can Balance Centrifugal and Aerodynamic Forces to Reduce Support Infrastructure While Maintaining a Stable Flight Path

This study introduces a novel approach to wind energy by investigating a novel Active Axis Wind Turbine design. The turbine is neither a horizontal nor vertical axis wind turbine but has an axis of operation that can actively change during operation. The design features a rotor with a single blade capable of dynamic pitch and tilt control during a single rotor rotation. This study examines the potential to balance the centrifugal and aerodynamic lift forces acting on the rotor blade assembly, significantly reducing blade, tower, foundation and infrastructure costs in larger-scale devices and decreasing the levelised cost of energy for wind energy. The design of a laboratory prototype rotor assembly is optimised by varying the masses and lengths in a lumped mass model to achieve equilibrium between centrifugal and lift forces acting on the turbine’s rotor assembly. The method involves an investigation of the variation of blade pitch angle to provide a balance between centrifugal and aerodynamic forces, thereby facilitating the cost advantages and opening the opportunity to improve the turbine efficiency across a range of operation conditions. The implication of this study extends to different applications of wind turbines, both onshore and offshore, introducing insight into innovation for sustainable energy and cost-effective solutions.

Smart whole-body vibration attenuation, cushion for heavy equipment seating: Model and simulation

Off-road mobile machine operators are exposed to whole-body vibration (WBV) which can result in adverse health effects. Seat suspensions are used to reduce WBV exposure, but typical passive seats cannot attenuate frequencies below 1.13 Hz. The proposed device is designed to minimize transmissibility from 0 to 20 Hz because this bandwidth contains the dominant frequency for most off-road vehicles. The semi-active smart device uses bang-bang control and is designed to be installed in place of the seat-pan cushion in OEM passive seats. Modelled as a two degree of freedom system, simulations were performed using a lumped mass model (ωn = 3 Hz; sinusoidal base excitation 0-20 Hz). Using a hexapod robot, a prototype reduced transmissibility compared to a passive OEM seat. The device was up to 5 times more effective than a passive seat in reducing vibration transmissibility. Simulations revealed that operator mass and seat stiffness variations have little effect on device WBV attenuation performance.

Numerical Simulation and On-Site Measurement of Dynamic Response of Flexible Marine Aquaculture Cages

Flexible cages are widely used in marine aquaculture, yet their mechanical features in extreme seas are still unclear. This study proposes a numerical algorithm to solve the coupled response of the multiple cage systems. The net and mooring lines are modeled using the lumped-mass model, while the flexible floating collar system is assessed with the large-deformation FEM model, and the two models are coupled through an iterative scheme. Sea trials are conducted, and the motion of the cage is obtained using an image processing technique, which validates the numerical algorithm. Using the proposed numerical algorithm, a series of simulations are performed to investigate the response of flexible cages in extreme seas. Motions, line tensions, and structural sectional forces are studied, and the effects of factors such as the wavelength of incident waves and the diameter of collar pipes are investigated.

Optimization and evaluation of tuned inerter-based dampers for mitigating coupled responses of offshore wind turbines

To achieve lightweight vibration control in offshore wind turbines (OWTs), this study proposes the utilization of two types of tuned inerter-based dampers (TIBDs), namely, the tuned viscous mass damper (TVMD) and tuned inerter damper (TID), to mitigate the coupled responses of an OWT induced by wind and wave loads. First, a multi-degree-of-freedom (MDOF) lumped mass model is established to represent an OWT equipped with a TIBD. Then, a novel structural control module for TIBDs is developed and seamlessly integrated into the modular numerical analysis code OpenFAST. This enables fully coupled aero-hydro-servo-elastic simulations of the OWT-TIBD system. Using the established MDOF model, a TIBD parameter optimization design method is proposed to minimize the peak of the non-dimensional displacement frequency response function. Additionally, a parametric study is performed to investigate the effect of inertance and span height on the control performance. Finally, the performance of the TIBD in attenuating both fatigue and extreme loads is evaluated through nonlinear fully coupled time-domain simulations using OpenFAST and compared to traditional tuned mass dampers (TMDs). The results showed that a lightweight and small damper displacement TIBD is capable of effectively dampening OWT vibrations, yielding a better mitigation effect than that provided by a bulky TMD. Overall, the reduced installation requirements and the commendable control efficiency of a TIBD highlight its potential as a promising candidate for passive control devices in OWT applications.

Speech intelligibility prediction based on a physiological model of the human ear and a hierarchical spiking neural network.

A speech intelligibility (SI) prediction model is proposed that includes an auditory preprocessing component based on the physiological anatomy and activity of the human ear, a hierarchical spiking neural network, and a decision back-end processing based on correlation analysis. The auditory preprocessing component effectively captures advanced physiological details of the auditory system, such as retrograde traveling waves, longitudinal coupling, and cochlear nonlinearity. The ability of the model to predict data from normal-hearing listeners under various additive noise conditions was considered. The predictions closely matched the experimental test data under all conditions. Furthermore, we developed a lumped mass model of a McGee stainless-steel piston with the middle-ear to study the recovery of individuals with otosclerosis. We show that the proposed SI model accurately simulates the effect of middle-ear intervention on SI. Consequently, the model establishes a model-based relationship between objective measures of human ear damage, like distortion product otoacoustic emissions, and speech perception. Moreover, the SI model can serve as a robust tool for optimizing parameters and for preoperative assessment of artificial stimuli, providing a valuable reference for clinical treatments of conductive hearing loss.

Seismic assessment of cylindrical storage tanks to records with different frequency contents considering fluid–structure–soil/foundation interaction

This study aims to primarily assess the dynamic behavior of ground-supported cylindrical tanks to real near-fault earthquake records with different frequency contents including soil-structure interaction effects. A cylindrical tank’s fluid-tank-soil interaction is modeled using a three-degree-of-freedom lumped mass model for the fluid. A mass-spring-dashpot model with frequency independence is used to model the soil/foundation system. Broad, medium, and slender tank models are developed considering and ignoring the soil flexibility effect. An algorithm based on discrete-time state-space approaches is developed for performing numerical simulations of the modeled tanks excited by the low-, medium-, and high-frequency contents. The obtained results for the modeled tanks in terms of base shear, overturning moment, and connective and impulsive mass displacements incorporating the influence of supporting soils as well as the frequency contents of excitation records are evaluated and compared with the corresponding results for modeled tanks with a fixed base. In addition, the liquid sloshing height for all aspect ratios is also evaluated and compared. The study’s findings clearly indicate that records with low-frequency contents require significantly more seismically demanding than other records for the considered soil types. Remarkably, soil-tank interaction under earthquake motions substantially amplifies the induced response.

Seismic Fragility Assessment of Equipment in Nuclear Power Plant Structures Considering Nonlinear Hysteretic Behavior of Squat Walls

Accurate seismic risk assessment of structures necessitates precise fragility analysis. This study focuses on the seismic fragility assessment of equipment in nuclear power plant structures, particularly emphasizing the influence of nonlinear hysteretic behavior exhibited by squat walls. By developing and comparing linear and nonlinear models of reactor containment and auxiliary buildings within a nuclear power plant, this research elucidates the significant impact of nonlinear behaviors on the seismic response and subsequent fragility curves of associated equipment and systems. Utilizing a lumped-mass stick model, the study efficiently captures the characteristics of squat shear walls, facilitating the calculation of floor response spectra and fragility for nuclear facility structures. The impacts of pinching and degradation, inherent characteristics of a squat wall’s hysteresis under cyclic loading, were identified as significant. These include the shift and change in amplitude of the floor response’s peak, along with amplification in high-frequency domains. Fragility assessments, informed by seismic response analysis, indicate significant variations in fragility curve parameters based on equipment location and frequency. The findings question the effectiveness of traditional response factor methods and general regression techniques in accurately addressing the complex probabilistic seismic demands of equipment, thus highlighting the importance of using direct analysis for calculating fragility in situations with significant nonlinearity.

Seismic vulnerability and performance-based assessment of monopile offshore wind turbine considering turbine blades

This paper investigated the seismic vulnerability and performance-based assessment of offshore monopile wind turbine (OWT) considering turbine blades. A three-dimensional finite-element model of NREL 5-MW OWT was established with detailed consideration of the nonlinear-behavior of turbine, monopile, blades, pile-soil interactions and pile-water interaction etc. Subsequently, incremental dynamic analysis and fragility evaluation were conducted via a great number of nonlinear time history analysis involving far-field and near-fault records with and without pulse characteristics. It is found that the ignorance of turbine blades in conventional lumped mass (LM) model would significantly underestimate the vulnerability of OWT's acceleration responses, and more importantly, underestimates the stress level at turbine top, misleading the failure pattern of OWT which may be probably damaged at both top and middle part of OWT rather than solely the middle part as estimated by the LM model ignoring the effect of turbine blades. Finally, it can be concluded that the modeling of turbine blades should be consider in the numerical studies.

A Survey of Aero-Engine Blade Modeling and Dynamic Characteristics Analyses

The rotating blade is a key component of an aero-engine, and its vibration characteristics have an important impact on the performance of the engine and are vital for condition monitoring. This paper reviews the research progress of blade dynamics, including three main aspects: modeling of blades, solution methods, and vibration characteristics. Firstly, three popular structural dynamics models for blades are reviewed, namely lumped-mass model, finite element model, and semi-analytical model. Then, the solution methods for the blade dynamics are comprehensively described. The advantages and limitations of these methods are summarized. In the third part, this review summarizes the properties of the modal and vibration responses of aero-engine blades and discusses the typical forms and mechanisms of blade vibration. Finally, the deficiencies and limitations in the current research on blade modeling and vibration analysis are summarized, and the directions for future efforts are pointed out. The purpose of this review is to provide meaningful insights to researchers and engineers in the field of aero-engine blade modeling and dynamic characteristics analysis.

Thermodynamic modelling of low fill levels in cryogenic storage tanks for application to liquid hydrogen maritime transport

One of the key challenges in transporting liquid hydrogen (LH2) in bulk onboard carriers is the requirement for high performance insulation to reduce the heat transfer and cargo boil-off losses. After unloading their cargo, carriers on the return voyage may retain a small amount of liquid (heel) to keep tanks relatively cold, as well as to chill down to the tanks prior to cargo loading. Therefore, there is an aim to reduce net heat transfer into the tank while minimising the required volume of heel. While practices are relatively mature in the liquefied natural gas (LNG) industry, it is not clear how this may differ for future LH2 carriage. In this study, a new analytical, lumped-mass model was proposed to predict vapour stratification and tank warm-up. A 40,000 m3 double-walled LH2 spherical tank was considered with vacuum perlite and polyurethane foam (PUF) insulation, and the effects of tank pressurisation and fill level on cumulative heat gain were investigated. The model pointed to key differences between the two insulation types. Heat gain in the vacuum perlite tank was not predicted to be sensitive to changes in fill level, while heat gain in PUF tank was predicted to be less sensitive to pressurisation. In each case, pressurisation was predicted to enable reductions in heel boil-off which offset any associated increase in cumulative heat gain. In comparing LNG and LH2, the model pointed to a slower thermal response of the LH2 tanks. Consequently, the increase in inner shell temperature was not expected to lead to significant reductions in environmental heat transfer into the tank. The findings of this study point to potential operational differences in the management of LNG and LH2 heel during the ballast voyage as well as considerations for vacuum insulated tanks.

An adaptive lumped-mass dynamic model and its control application for continuum robots

Dynamic modeling for continuum robots remains challenging due to their large nonlinear deformation and the variation of dynamic parameters during movement. In this paper, a lumped-mass dynamic model (LMD) for a continuum robot is constructed including elastic and viscous parameters in the robotic joints. Then the appropriate dynamic parameters (e.g. spring and damping coefficients of the LMD) with respect to the motion status (e.g. position and velocity of the robot) are estimated using a Genetic Algorithm (GA). Based on the obtained data set, a Multi-Layer Perception (MLP) is trained to establish a direct mapping from the motion status to the dynamic parameters, so the LMD can tune its parameters in real-time when moving within the workspace, resulting an adaptive lumped-mass dynamic model (ALMD). Compared to the fixed-parameter LMD, the modeling error of the ALMD is reduced by up to 60.2 %. Finally, a feedforward controller is implemented to control a continuum robotic prototype using the presented ALMD, reducing the maximum tracking error by 67.5 %.

Seismic vulnerability analysis of palace-style timber structures base on lumped mass model considering column rocking effect

To investigate the influence of joint reinforcement on the vulnerability of palace-style ancient timber structures, a spring-rigid rod analysis model was established, considering the mechanical behavior of tenon-mortise joints, column base joints, and bracket set joints. A lumped mass model was proposed using the centroid method and stiffness equivalent method and the accuracy of the simplified model is verified through shake table tests. Additionally, the influence of reinforcement on tenon-mortise joints and bracket set joint on the seismic displacement response was investigated, the optimal reinforcement range for joints was determined. Finally, incremental dynamic analysis was conducted on the model considering joint reinforcement, and the influence of optimal joint reinforcement on the seismic vulnerability of timber structures was researched. The study found that the optimal stiffness enhancement of column frame mortise-tenon joints range from 4 to 6 times and the stiffness of bracket set joints by 2.9 times. The probability of structural collapse of reinforced both mortise-tenon joints and bracket set joints was reduced by 15.56 %. However, individually reinforcing either tenon-mortise joints or bracket set joints only slightly decreases the probability of collapse.

Force Control of a Haptic Flexible-Link Antenna Based on a Lumped-Mass Model.

Haptic organs are common in nature and help animals to navigate environments where vision is not possible. Insects often use slender, lightweight, and flexible links as sensing antennae. These antennae have a muscle-endowed base that changes their orientation and an organ that senses the applied force and moment, enabling active sensing. Sensing antennae detect obstacles through contact during motion and even recognize objects. They can also push obstacles. In all these tasks, force control of the antenna is crucial. The objective of our research is to develop a haptic robotic system based on a sensing antenna, consisting of a very lightweight and slender flexible rod. In this context, the work presented here focuses on the force control of this device. To achieve this, (a) we develop a dynamic model of the antenna that moves under gravity and maintains point contact with an object, based on lumped-mass discretization of the rod; (b) we prove the robust stability property of the closed-loop system using the Routh stability criterion; and (c) based on this property, we design a robust force control system that performs efficiently regardless of the contact point with the object. We built a mechanical device replicating this sensing organ. It is a flexible link connected at one end to a 3D force-torque sensor, which is attached to a mechanical structure with two DC motors, providing azimuthal and elevation movements to the antenna. Our experiments in contact situations demonstrate the effectiveness of our control method.

Generalized Quasi-Static Mooring System Modeling with Analytic Jacobians

This paper presents a generalized and efficient method for quasi-static analysis of mooring systems, including complex scenarios such as when shared mooring lines interconnect multiple floating wind or wave energy devices. While quasi-static mooring models are well established, most published formulations are focused on specific applications, and no publicly available implementations provide efficient handling of large mooring system networks. The present formulation addresses these gaps by: (1) formulating solutions for edge cases not typically supported by quasi-static models; (2) creating a fully generalized model structure such that any combination of mooring lines, point masses, and floating bodies can be assembled; and (3) deriving analytic expressions for the system Jacobians (stiffness matrices) so that systems with many degrees of freedom can be solved efficiently. These techniques form the theory basis of MoorPy, an open-source mooring analysis library. The model is demonstrated on nine scenarios of increasing complexity with features of interest for offshore renewable energy applications. When compared with steady-state results from a lumped-mass dynamic model, the results show that the quasi-static formulation accurately calculates profiles and tensions and that its analytic approach provides more efficient and reliable computation of system stiffness matrices than finite-differencing methods. These results verify the accuracy of the MoorPy model.

Bayesian structural model updating with multimodal variational autoencoder

A novel framework for Bayesian structural model updating is presented in this study. The proposed method utilizes the surrogate unimodal encoders of a multimodal variational autoencoder (VAE). The method facilitates an approximation of the likelihood when dealing with a small number of observations. It is particularly suitable for high-dimensional correlated simultaneous observations applicable to various dynamic analysis models. The proposed approach was benchmarked using a numerical model of a single-story frame building with acceleration and dynamic strain measurements. Additionally, an example involving a Bayesian update of nonlinear model parameters for a three-degree-of-freedom lumped mass model demonstrates computational efficiency when compared to using the original VAE, while maintaining adequate accuracy for practical applications.

Heavy fuel oil pyrolysis: A family of practical kinetic reaction models supported by TGA

The intricate nature and diverse composition of heavy fuel oil (HFO) pose significant challenges in constructing chemical kinetic models for its pyrolysis, gasification, and combustion processes. This study aims to introduce a model incorporating the kinetic impact of thermal decomposition reactions on pyrolysis. A novel methodology is proposed for formulating kinetic reaction models to forecast the mass transfer dynamics during the thermal decomposition of heavy fuel oil, as observed through thermogravimetric analysis. The principal objective is to predict the influence of heat on reaction kinetics, mass transfer phenomena, and the transformation of constituents. This investigation presents three distinct kinetic models: two focused on single-component representations, four structured as lumped mass models and an encompassing multi-pseudo-component model. Each model serves specific purposes tailored to its distinct applications. The lumped mass model accurately predicts the rates of light oil, middle oil, heavy oil, coke, and gas production. Conversely, the eleven pseudo-component model achieves superior precision by adjusting constituent counts based on fuel characteristics. Validation of the most effective lump model and the eleven pseudo-components confirms their reliability and validity in predicting system behavior.

Feasibility investigation of tuned mass damper for vibration control of curved floating bridge in winds and waves

This paper investigates the feasibility and operability of a tuned mass damper (TMD) to control the lateral vibrations of a curved floating bridge. A curved floating bridge was designed with a bridge girder, 38 columns, and 19 pontoons, which was the same concept proposed for crossing Bjørnafjorden in Norway, except that the cable-stayed bridge was excluded in the present model. TMD was then attached to the mid-length of the bridge girder. Time-domain model was built to consider the girder-column-pontoon interaction based on the Cummins equation for pontoons and the lumped-mass line model for the bridge girder and columns, while TMD was modeled by the mass-spring-damper system. First, the genetic algorithm was employed to optimize the spring and damping coefficients of TMD at a fixed TMD mass under white noise wave excitations, and the fitness function was a summation of the standard deviation of the sway motion of 19 pontoons. Then, its feasibility was evaluated by comparing lateral vibrations and vertical bending moments with and without TMD under various combinations of wind/wave/current loads. Results demonstrate that TMD contributes to a reduction in the lateral vibration when resonance at the second wet natural frequency occurs, which can improve passenger comfort. Wind-induced lateral motions are significantly reduced at the second wet natural frequency while TMD has limited effects under other environmental loads. Moreover, bending moments are governed by higher modes mostly induced by storm waves, which cannot be controlled by TMD effectively.

Analytical identification of dynamic structural models: Mass matrix of an isospectral lumped mass model

AbstractCombining the accurate physical description of high‐fidelity mechanical formulations with the practical versatility of low‐order discrete models is a fundamental and open‐ended topic in structural dynamics. Finding a well‐balanced compromise between the opposite requirements of representativeness and synthesis is a delicate and challenging task. The paper systematizes a consistent methodological strategy to identify a physics‐based reduced‐order model (ROM) preserving the physical accuracy of large‐sized models with distributed parameters (REM), without resorting to classical techniques of dimensionality reduction. The leading idea is, first, to select a limited configurational set of representative degrees of freedom contributing significantly to the dynamic response (model reduction) and, second, to address an inverse indeterminate eigenproblem to identify the matrices governing the linear equations of undamped motion (structural identification). The physical representativeness of the identified model is guaranteed by imposing the exact coincidence of a selectable subset of natural frequencies and modes (partial isospectrality). The inverse eigenproblem is solved analytically and parametrically, since its indeterminacy can be circumvented by selecting the lumped mass matrix as the primary unknown and the stiffness matrix as a parameter (or vice versa). Therefore, explicit formulas are provided for the mass matrix of the ROM having the desired low dimension and possessing the selected partial isospectrality with the REM. Minor adjustments are also outlined to remove a posteriori unphysical effects, such as defects in the matrix symmetry, which are intrinsic consequences of the algebraic identification procedure. The direct and inverse eigenproblem solutions are explored through parametric analyses concerning a multistory frame, by adopting a high‐fidelity Finite Element model as REM and an Equivalent Frame model as ROM. Before mass matrix identification, modal analysis results indicate a general tendency of ROM to underestimate natural frequencies, with the underestimation strongly depending on the actual mass distribution of the structure. After the identification of the mass matrix and the elimination of unphysical defects, isospectrality is successfully achieved. Finally, extensions to prototypical highly massive masonry buildings are presented. The qualitative and quantitative discussion of the results under variation of the significant mechanical parameters provides useful insights to recognize the validity limits of the approximations affecting low‐order models with lumped parameters.