Simple Lumped Parameter Model Research Articles

On the resonance frequency of the irregular shaped visco-acoustic Helmholtz cavity problem

In this paper we develop a closed-form mathematical solution for the resonance frequency of the axisymmetric irregular shaped visco-acoustic Helmholtz cavity problem. The solution is based on a conformal mapping that transforms the governing visco-acoustic equations of motion for the irregular cavity geometry into a new domain described by a set of orthogonal curvilinear coordinates. These orthogonal curvilinear coordinates have an important characteristic relative to the transformation of the physical boundary: the mapped domain is constructed such that the locus of all points for the length-wise profile of the physical boundary coincides with a constant value for a (quasi radial) coordinate in the new mapped domain. In these orthogonal curvilinear coordinates we obtain an analytical solution for the visco-acoustic equations of motion and exactly satisfy the no-slip fluid boundary conditions over the irregular shaped cavity walls by matching the coefficients of an orthogonal Legendre polynomial series representation for the non-uniform velocity on the cavity walls. The mathematical solution is an approximation to the extent that the scale factors chosen for the mapping consist of strictly the mutual-coupling terms of the true scale factors. Thus we analyze some results to understand the correlation of the analytical solution frequency response spectra with numerical finite element analyses of the idealized boundary conditions with various irregular shaped cavity geometries. The results for fundamental resonance frequency were found to exhibit good correlation with the results of finite element analyses over a significant range of fluid properties with different irregular cavity geometries. As the primary motivation for the derivation stems from the lack of a rapid yet accurate alternative to computationally intensive MultiPhysics FEA in the formulation of acoustic trendlines for sensor development, the solution’s acoustic impedance was applied as dispersive loading in a simple lumped parameter model of a fluid identification sensor for comparison. The resulting acoustic trendlines of the reduced (5 DOF) model were found to exhibit good correlation with the results of the MultiPhysics FEA (>105 DOF). Thus the solution was found to enable a closed-form analytical method for rapid construction of parametric studies in the practical design of fluid analysis sensors based on complex resonant cavity geometries.

Hand Vibration Reduction Using Nonlinear Vibration Absorber for the Vibro-Impact Hammer Model

Abstract This work investigates the effectiveness of a passive vibration control device to minimize the amplitude of vibrations from a hand-held impact machine (HHIM) transmitted to a hand-arm system (HAS). For this purpose, we employ a simplified lumped parameter model of an HHIM and the hand-arm system consisting of lumped masses, springs, and viscous dampers. For a better understanding of the system dynamics, we use a vibro-impact model for a more accurate representation of HHIM–ground interactions. We then examine the effectiveness of a cubic nonlinear vibration absorber in minimizing these undesirable vibrations via a nonlinear bifurcation analysis of the system. A parametric study on the numerical bifurcation analysis of the system reveals the criticality of different design parameters of the proposed nonlinear vibration absorber on the system dynamics. Our findings demonstrate that an appropriate selection of absorber parameters could significantly change the amplitude and the periodicity of vibrations transmitted to the hand. Furthermore, we observe the existence of complex motions such as period-2, period-4, and chaotic attractors in the system for the given values of the absorber and operating parameters.

Analytical solutions for single and multiple scattering from rib-stiffened plates in water.

The interaction of an acoustic plane wave with a pair of plates connected by periodically spaced stiffeners in water is considered. The rib-stiffened structure is called a "flex-layer" because its low frequency response is dominated by bending stiffness. The quasi-static behavior is equivalent to a homogeneous layer of compressible fluid, which we identify as air for the purposes of comparison. In this way, an air layer is acoustically the same as a pair of thin elastic plates connected by a periodic spacing of ribs. At discrete higher frequencies, the flex-layer exhibits perfect acoustic transmission, the cause of which is identified as fluid-loaded plate waves propagating back and forth between the ribs. Both the low and finite frequency behavior of the flex-layer are fully explained by closed-form solutions for reflection and transmission. The analytical model is extended to two flex-layers in series, introducing new low and high frequency phenomena that are explained in terms of simple lumped parameter models.

A novel framework for effective structural vulnerability assessment of tubular structures using machine learning algorithms (GA and ANN) for hybrid simulations

Abstract Seismic vulnerability assessments are conventionally conducted by using sophisticated nonlinear analytical models, leading to aggressive computational demands. Previous attempts were made to reduce computational efforts for establishing vulnerability assessment of structures; however, the area of super tall and tubular structures still faces considerable lack. Advent of efficient machine learning (ML) has enabled engineering practitioners to automate the processes for fragility analysis; however, its application for high-rise tubular structures is not yet exploited, and most implementations are limited to basic ML. In this work, an attempt was made to reduce computational demand for the fragility assessment process for tubular structures by employing genetic algorithms (GAs) for nonlinear structural modeling, and development of artificial neural network (ANN) using deep learning for fragility development. Consequently, a simple lumped parameter model had been developed using open-source code of ZEUS-NL, containing parameters selected by GA to acutely account for convoluted interactive behavior of structural systems and dynamic demands. Subsequently, incremental dynamic analysis (IDA) was performed on the optimized model. A new framework has been established to develop and train ANN architecture by amalgamating Weka’s capability of data preprocessing with deep learning. The established ANN model resulted in correlation coefficient of 0.9972 and R 2 of 0.95, demonstrating adequate performance.

Understanding the Impact of Active-to-Passive Area Ratio on Deformation in One-Dimensional Dielectric Elastomer Actuators with Uniaxial Strain State.

There is increasing interest in the use of novel elastomers with inherent or modified advanced dielectric and mechanical properties, as components of dielectric elastomer actuators (DEA). This requires corresponding techniques to assess their electro-mechanical performance. A common way to test dielectric materials is the fabrication of actuators with pre-stretch fixed by a stiff frame. This results in the problem that the electrode size has an influence on the achievable actuator displacement and strain, which is detrimental to the comparability of experiments. This paper presents an in-depth study of the active-to-passive ratio with the aim of investigating the influence of the coverage ratio on uniaxial actuator displacement and strain. To model the effect, a simple lumped-parameter model is proposed. The model shows that the coverage ratio for maximal displacement is 50%. To validate the model results, experiments are carried out. For this, a rectangular, fiber-reinforced DEA is used to assess the relation of the coverage ratio and deformation. Due to the stiffness of the fibers, highly anisotropic mechanical properties are achieved, leading to the uniaxial strain behavior of the actuator, which allows the validation of the one-dimensional model. To consider the influence of the simplifications in the lumped-parameter model, the results are compared to a hyperelastic model. In summary, it is shown that the ratio of the active-to-passive area has a significant influence on the actuator deformation. Both the model and experiments confirm that an active-to-passive ratio of 50% is particularly advantageous in most cases.

Experimental modal analysis of a single-link flexible robotic manipulator with curved geometry using applied system identification methods

In this paper, the principal time-domain system identification methods are studied and used to carry out the experimental modal analysis of a single-link flexible manipulator with curved geometry in a comparative fashion. The identification process carried out in this study is aimed at deriving first-order state-space dynamical models and second-order configuration-space dynamical models of the single-link flexible manipulator by using an array of fundamental system identification procedures, which includes the ARX (AutoRegressive eXogenous method), SSEST (State-Space ESTimation method), N4SID (Numerical Algorithm for Subspace State-Space System Identification), ERA/OKID (Eigensystem Realization Algorithm combined with the Observer/Kalman Filter Identification method), and TFEST (Transfer Function ESTimation method) methods. The main goal of this paper is, therefore, to perform a comparative study between the most fundamental system identification procedures applied to the numerical and experimental analysis of the structural vibrations of a flexible manipulator having a curved geometric shape. First, this paper poses the theoretical foundations for the development of the numerical study and the experimental testing to be performed for the case study. Subsequently, the flexible manipulator analyzed in this work is modeled with various levels of complexity, which range from a simple lumped parameter model to a linear finite element model developed by integrating the interconnections between the SOLIDWORKS and ANSYS software. By doing so, the computational procedures applied to the time-domain experimental measurements of the dynamic behavior of the flexible manipulator allow for reconstructing first-order and second-order mechanical models of the structural system of interest in the MATLAB simulation environment. The numerical results and the experimental tests reported in this investigation demonstrate the effectiveness of all the time-domain system identification approaches considered in the paper.

Simplified Lumped Parameter Model for Oscillatory Flow in an Elastic Tube: A Hierarchical Approach

Abstract In this article, the significant characteristics of wave transmission and boundary layer influence are studied for an incompressible fluid flowing through a long elastic tube using lumped parameter model. An ameliorated version of the lumped parameter model is derived, where the flow impedance is linked with Womersley number to understand the phenomena of fluid wall interaction, especially in human airways. To analyze the flow phenomena through tubes, the flow governing equations are transformed through the Bessel series. We have observed that for the low value of Womersley number, there is a phase difference between pressure and flowrate, which produces a frequency-dependent flow impedance. The physiological relevance of this result is especially shown in the nasal-pharynx during breathing. The results are validated by ansys-based numerical simulation as well as by experimental results.

Experimental analysis of natural ventilation of an office building in Mexico city

An experiment is described to evaluate natural ventilation in a ten-story office building in Mexico City. The airflow results from the flotation of the internal hot air when the outside environment is colder. The objective of this work is to establish basic design considerations for effective ventilation of similar buildings. The experience is based on temperature measurements. These were taken at different levels in the building during several years and appear to be mutually consistent. A simple lumped-parameter mathematical model, which simulates the variation of temperature over time, fits well with the observed data. Some selected samples illustrate specific characteristics of the ventilation phenomenon. Thus, natural ventilation in other buildings can be designed to promote ventilation and improve comfort if there are some temperature measurements available for the calibration of the proposed model. The study validates the use of natural ventilation to provide passive thermal comfort throughout the year in Mexico City, although on some days slightly uncomfortable temperatures occur.

Theoretical band-gap bounds and coupling sensitivity for a waveguide with periodically attached resonating branches

Elastic metamaterials may exhibit band gaps at wavelengths far exceeding feature sizes. This is attributed to local resonances of embedded or attached substructures. In configurations with attached substructures, such as a pillared plate, waves propagating in the base medium–e.g., the plate portion–experience attenuation at band-gap frequencies. Considering a simplified lumped-parameter model for a waveguide with attached resonating branches, we present a theoretical treatment for a periodic unit cell comprising a base mass-spring chain with a multi-degree-of-freedom, mono-coupled branch. Bloch’s theorem is applied, combined with a sub-structuring approach where the resonating branch is modeled separately and condensed into its effective dynamic stiffness. Thus, the treatment is generally applicable to an arbitrary branch regardless of its size and properties. We provide an analysis–supported by guiding graphical illustrations–that yields an identification of fundamental bounds for the band-gap edges as dictated by the dynamical characteristics of the resonating branch. Analytical sensitivity functions are also derived for the dependence of these bounds on the degree of coupling between the base and the branch. The sensitivity analysis reveals further novel findings including the role of the frequency derivative of the branch dynamic stiffness in providing a direct relation between the band-gap edge locations and variation in the coupling parameters—the mass and stiffness ratios between the base chain and the branch root. In additional analysis, sub-Bragg bounds of an exact model comprising a one-dimensional continuous base–modeled as a rod–and a discrete resonating branch are derived and shown to be tighter than those of the all-discrete model. Finally, the applicability of the derived bounds and sensitivity functions are shown to be valid for a corresponding full two-dimensional finite-element model of a pillared waveguide admitting out-of-plane shear waves.

An appropriate biomechanical model of seated human subjects exposed to whole-body vibration

Long duration automobile-induced vibration is the cause of many ailments to humans. Predicting and mitigating these vibrations through seat requires a good model of seated human body. A good model is the one that strikes the right balance between modelling difficulty and simulation results accuracy. Increasing the number of body parts which have been separately modelled and increasing the number of ways these parts are connected to each other increase the number of degrees of freedom of the entire model. A number of such models have been reported in the literature. These range from simple lumped parameter models with limited accuracy to advanced models with high computational cost. However, a systematic comparison of these models has not been reported till date. This work creates eight such models ranging from 8 to 26 degrees of freedom and tries to identify the model which strikes the right balance between modelling complexity and results accuracy. A comparison of the models’ prediction with experimental data published in the literature allows the identification of a 12 degree of freedom backrest supported model as optimum for modelling complexity and prediction accuracy.

The dynamic response of infinitely long constrained bars and its application for modelling SSI

In dynamic analysis of complex systems usually simplified models are used. In case of floor vibration, an SDOF model is used to calculate the acceleration of the structure, in the seismic design of structures lumped parameter models are recommended to include the effect of the soil-structure interaction (SSI) in the analysis. Nonetheless, for rib stiffened floors, and for finite depth soil layers under the structure these models can be very inaccurate. In these cases (infinitely) long constrained bars (or beams) are recommended as simplified models. In this article an infinitely long, axially constrained bar connected parallelly to a mass-spring system is analysed. An analytical solution is derived, and the impedance functions are determined, which are significantly different from those of simple lumped parameter models. It is shown that this simple model, which depends only on three parameters, is an excellent tool for determining the response of structures excited by horizontal harmonic or earthquake loads, where SSI plays an important role.

Lumped-Parameter and Finite Element Modeling of Heart Failure with Preserved Ejection Fraction.

Scientific efforts in the field of computational modeling of cardiovascular diseases have largely focused on heart failure with reduced ejection fraction (HFrEF), broadly overlooking heart failure with preserved ejection fraction (HFpEF), which has more recently become a dominant form of heart failure worldwide. Motivated by the paucity of HFpEF in silico representations, two distinct computational models are presented in this paper to simulate the hemodynamics of HFpEF resulting from left ventricular pressure overload. First, an object-oriented lumped-parameter model was developed using a numerical solver. This model is based on a zero-dimensional (0D) Windkessel-like network, which depends on the geometrical and mechanical properties of the constitutive elements and offers the advantage of low computational costs. Second, a finite element analysis (FEA) software package was utilized for the implementation of a multidimensional simulation. The FEA model combines three-dimensional (3D) multiphysics models of the electro-mechanical cardiac response, structural deformations, and fluid cavity-based hemodynamics and utilizes a simplified lumped-parameter model to define the flow exchange profiles among different fluid cavities. Through each approach, both the acute and chronic hemodynamic changes in the left ventricle and proximal vasculature resulting from pressure overload were successfully simulated. Specifically, pressure overload was modeled by reducing the orifice area of the aortic valve, while chronic remodeling was simulated by reducing the compliance of the left ventricular wall. Consistent with the scientific and clinical literature of HFpEF, results from both models show (i) an acute elevation of transaortic pressure gradient between the left ventricle and the aorta and a reduction in the stroke volume and (ii) a chronic decrease in the end-diastolic left ventricular volume, indicative of diastolic dysfunction. Finally, the FEA model demonstrates that stress in the HFpEF myocardium is remarkably higher than in the healthy heart tissue throughout the cardiac cycle.

A new perspective on static bifurcations in the presence of viscoelasticity

This manuscript explores the effect of viscoelasticity on static bifurcations: such as pitchfork, saddle-node, and transcritical bifurcations, of a single-degree-of-freedom mechanical oscillator. The viscoelastic behavior is modeled via a differential form, where the extra degree of freedom represents the internal force provided by the viscoelastic element. The governing equations are derived from a simplified lumped parameter model consisting of a rigid rod incorporating a viscoelastic element and subjected to axial and transverse forces at the free end, in addition to an external time-varying moment applied to the rod. In order to study the effect of viscoelasticity on bifurcation diagrams, the equations of motion are non-dimensionalized. Next, a review of static bifurcations in the absence of viscoelasticity is conducted, followed by an examination of the effect of viscoelasticity on the bifurcation diagrams. Finally, this paper investigates the effects of viscoelasticity on the transient behavior of the oscillator. Results show that the Deborah number, which measures the ratio of the viscoelastic time constant to the natural periodic time of the system, controls the duration of time needed to maintain oscillations around an unstable point before jumping to a stable equilibrium point.

Grid Scale Energy Storage: Modeling of Electrolyzer-Fuel Cell Combination and Comparison with Flow Batteries

: Grid-scale renewable energy installations are gaining traction around the world. The addition of these intermittent resources onto the energy grids is resulting in challenges that need to be addressed [1]. The challenge with the mismatch between supply and demand has accelerated the need for grid-scale energy storage technologies. The viability of some of these technologies from a future technical and economic requirements standpoint is being studied widely [2].Though today over 95% of the energy stored is in the form of pumped hydro, many other technologies spanning the broad areas of Mechanical (flywheel, compressed air, etc.), Thermal (molten salt, thermal dams, etc.), Batteries (lithium-based, flow batteries, etc.) and Hydrogen (electrolysis, fuel cells, etc.) are actively under development with a focus on future requirements [1-5].In this paper, we will investigate the viability of Hydrogen electrolyzer and fuel cell technologies for long duty cycle and steep ramp frequency regulation applications. We will compare the characteristics of Polymer Electrolyte Membrane (PEM) and Solid Oxide (SO) Electrolyzer Fuel Cell (EFC) combinations with Flow Batteries. The techno-economic comparison will be in the areas of (a) Levelized Cost of Energy (LCOE) and (b) Transient Capability.The LCOE models will consider round trip efficiency, equipment capital costs, storage costs, operating costs, and system durability/reliability. The key input data/parameter set for the LCOE calculations will be obtained by extrapolating real-life performance information from key Electrolyzer, Fuel Cell, and Flow Battery suppliers [3-5]. Whereas the transient capability models will be based on applicable charge and discharge duty cycle regimes as well as the transient response to a full range of variation in loads. The transient modeling will be obtained by fitting real-life electrochemical data to simple lumped parameter models [2,5].

Harmonic tremor model during the 2011 Shinmoe-dake eruption, Japan

Summary The Shinmoe-dake volcano started with three sub-Plinian eruptions from 26 to 27 January 2011, followed by a magma effusive stage from 28 to 31 January 2011, and Vulcanian eruptions occurred frequently during 1 to 10 February 2011. During the magma effusive and Vulcanian stages, multiple episodes of harmonic tremors were observed at stations near the summit crater. Although harmonic tremors have been observed at various volcanoes worldwide, the source mechanism remains poorly understood. This paper proposes a source model for harmonic tremors, which is composed of a nonlinear viscous fluid flow in a flexible channel. A simple lumped parameter model is used to consider the process. The dynamics are described by a third-order system of ordinary differential equations using model variables for a cross-sectional area of the constricted segment and the fluid velocities in the upstream and downstream tubes. This model produces various kinds of trajectories for self-sustained oscillations that change the reservoir pressure connected on the upstream channel of the model. Linearization analysis around the stationary point and global analysis employing nullcline planes reveal the mechanism of self-sustained oscillations of the system qualitatively. To consider both the frequency peaks of the harmonic tremor and the characteristics of observed phase spectra, the qualitative characteristics of an observed phase portrait are compared to those of a simulated one. This tremor model simulates the frequency peaks and the phase portraits of typical harmonic tremors observed during the 2011 Shinmoe-dake eruption. Because this model involves several geometrical configuration parameters, it has the potential to reveal the source mechanism of various kinds of harmonic tremors.

Visco-elastic response of combined footings on earth beds with geocell-geomembrane inclusions

Visco-elastic response of combined footings lying on earth beds with geocell-geomembrane inclusions has been studied using a simple lumped parameter model. The earth bed has been simulated with the help of series of Burgers model, i.e., Maxwell and Kelvin models coupled in series, connected by an elastic member. Overlying the soft visco-elastic bed, there exists a geocell layer with soil infill idealized by a beam having finite flexural rigidity. On top of this, granular mat has been laid and idealized as Pasternak shear layer underlying the combined footing considered as a beam. The footing has been subjected to equi-spaced columnar loads. The weight of granular mat has been considered on top of reinforcing beam. A lumped-parameter model has been used for idealizing the physical problem. Thereafter the governing differential equations have been developed and solved numerically with the help of suitable boundary conditions. Validation of the proposed model has been done before taking up the detailed study to exhibit the influence of various model parameters on the response of footing-soil system. Magnitude of columnar loads, location of geocell layer, relative elastic and viscous coefficients of Burgers model, and tension in elastic membrane have been found to have significant impact on deflection and bending moment in both footing and the geocell. All the analyses and results have been presented in terms of non-dimensional parameters. Many parameters combining together forms a number (non-dimensional) and the same number can be used in designing a typical case of combined footings using the charts developed.

Application of a physics-based lumped parameter model to evaluate reservoir parameters during CO2 storage

Evaluating reservoir performance could be challenging, especially when available data are only limited to pressures and rates from oil field production and/or injection wells. Numerical simulation is a typical approach to estimate reservoir properties using the history match process by reconciling field observations and model predictions. Performing numerical simulations can be computationally expensive by considering a large number of grids required to capture the spatial variation in geological properties, detailed structural complexity of the reservoir, and numerical time steps to cover different periods of oil recovery. In this work, a simplified physics-based model is used to estimate specific reservoir parameters during CO2 storage into a depleted oil reservoir. The governing equation is based on the integrated capacitance resistance model algorithm. A multivariate linear regression method is used for estimating reservoir parameters (injectivity index and compressibility). Synthetic scenarios were generated using a multiphase flow numerical simulator. Then, the results of the simplified physics-based model in terms of the estimated fluid compressibility were compared against the simulation results. CO2 injection data including bottom hole pressure and injection rate were also gathered from a depleted oil reef in Michigan Basin. A field application of the simplified physics-based model was presented to estimate above-mentioned parameters for the case of CO2 storage in a depleted oil reservoir in Michigan Basin. The results of this work show that this simple lumped parameter model can be used for a quick estimation of the specific reservoir parameters and its changes over the CO2 injection period.

An AlN Micromachined Mass Sensor: Modeling and Characterization

This article presents a mass sensor based on a low-frequency MEMS resonator. Its mechanical structure grants a linear relationship between the measured mass and resonance frequency. The presence of an embedded AlN layer allows for exploiting piezoelectric actuation and sensing and for using a simple and low-cost read-out electronics. In this article, the linear behavior of the sensor is demonstrated by finite-element method (FEM) modal analysis, by developing a simple lumped parameter model and by experimental campaigns. Moreover, in this article, the device performance in terms of piezoelectric transduction is theoretically analyzed and demonstrated using both FEM analysis and experiments, showing that the proposed MEMS device is suitable also for applications in the low-power electronics scenario.

Characterization of flow dynamics around highly-utilized agricultural wells in a fractured-rock aquifer: Assessment of uncertainties lying on groundwater age-dating

When environmental tracers are used to determine groundwater age distributions, various factors including measurement error, model structural error, and sample contamination can affect the outcome. In this study, we tried to untangle and explain the uncertainties associated with the inference of age distribution for a set of highly-utilized production wells in a fractured-rock aquifer system. A total of 17 samples were collected at various depths (22–150 m) from production wells. These samples were analyzed for six age tracers, including 3H, tritiogenic 3He, radiogenic 4He, CFC-11, CFC-12, and CFC-113. A Bayesian approach was used for evaluating age distribution for the samples based on several presumed lumped parameter models (LPM)s and shape free models. It was found that the measured data in most wells could be explained by traditional LPMs reasonably well. However, for five of the 17 wells it was found that the simple LPMs were not adequate and the more complex shape-free approaches resulted better based on the Deviance Information Criteria (DIC) measure. This looked attributed to 1) competition between densely located wells, 2) a thick vadose zone layer possibly causing preferential flows 3) fractures allowing a localized production. Furthermore, it was shown that three other factors including tracer contamination, non-uniform 4He production, and the heterogeneity in the travel time in vadose zone added uncertainties to groundwater age-dating. Overall results showed that the combination of Bayesian approach with DIC criterion can help to identify uncertainties associated with the age distribution for hydrologically complicated systems.

A fast prediction method for maximum APF of heat pump type air conditioners based on a single group of experimental data

The annual performance factor (APF) is a new performance index of heat pump type air conditioners (HPACs) based on multiple testing conditions which may result in orders of magnitude larger workload in the product development for enhancing the APF to be close to the maximal value. The development process can be accelerated if the maximum APF can be predicted. The purpose of this study is to present a fast prediction method with a high precision for the maximum APF of HPACs based on a single group of experimental data. The idea of achieving fast prediction is to establish a simplified lumped parameter model for the calculation of capacities and efficiencies of HPACs, and to present a simplified approximate APF correlation by eliminating all the intermediate parameters from the complicated APF equations defined in standards of HPACs. A group of experimental data is applied in the prediction model to improve the precision of the fast prediction method. Application of this method for a typical HPAC shows that the predicted maximum APF of the HPAC agrees well with the tested maximum APF, the maximum deviation of predicted capacities and efficiencies from the experimental data is within ±1.4%; and the duration of prediction for maximum APF is within 12 s on a typical personal computer, significantly saving the time of HPAC development.