Lumped Element Method Research Articles

Total harmonic distortion estimation in piezoelectric micro-electro-mechanical-system loudspeakers via a lumped elements approach

In the context of the increasing trend towards miniaturization required by new wireless audio devices, piezoelectric micro-electro-mechanical-system (MEMS) loudspeakers are getting extensive attention. Finite Element Methods (FEM) and Lumped Element Methods (LEM) models able to accurately predict their linear response have been recently proposed in the literature. However, a nonlinear model able to predict the Total Harmonic Distortion (THD) of theses types of devices is to date not available. In this paper we present a FEM- assisted lumped-parameters equivalent circuit accounting for piezoelectric hysteresis which demonstrates good agreement with experimental THD results carried out on piezoelectric MEMS loudspeakers prototypes fabricated by STMicroelectronics. The nonlinear electro-mechanical domain is simulated through a Reduced Order Model (ROM) which considers as basis function the pre-stressed undamped actuated mode of the device computed via FEM, to simulate loudspeaker diaphragms of arbitrarily complex geometry. The parameters of the acoustical circuit are instead derived through analytical formulas.

The Application of the Particle Element Method in Tubular Propellant Charge Structure: Lumped Element Method and Multiple-Element Method

Due to the orderly arrangement of tubular propellant, the permeability of combustion gases is improved, which is beneficial for enhancing the safety of the combustion system. However, current internal ballistic gas-solid flow calculation methods adopt a quasi-fluid assumption, which cannot accurately account for the characteristics of long tube shapes. Additionally, tubular propellants exhibit both overall movement and parameter distribution characteristics, necessitating the decoupling of gas and solid phases. These two deficiencies in previous studies have limited the effectiveness of gas-solid flow simulations for tubular propellant. This paper proposes a numerical calculation model suitable for tubular propellant charging based on the particle element method for internal ballistic two-phase flow. Firstly, considering the overall movement characteristics of tubular propellants, the concept of blank particle elements is introduced to represent pure gas phase regions. Then, based on computational requirements, the tubular propellants are divided to form the lumped element method and the multiple-element method. The moving boundary method is used to calculate the movement process of the propellant bed particle group and is compared with experimental results to verify the applicability of the two methods in tubular propellant beds. Analysis results show that the particle element method can effectively capture changes in the flow field inside the chamber and the position of tubular propellants. The lumped element method can quickly obtain the flow field distribution characteristics inside the chamber, while the multiple-element method can capture parameter distribution characteristics at different positions of the tubular propellants while ensuring overall movement.

Lumped Element Method Based Conductivity Reconstruction Algorithm for Localization Using Symmetric Discrete Operators on Coarse Meshes

The inverse conductivity problem in electrical impedance tomography involves the solving of a nonlinear and under-determined system of equations. This paper presents a new approach, which leads to a quadratic and overdetermined system of equations. The aim of the paper is to establish new research directions in handling of the inverse conductivity problem. The basis of the proposed method is that the material, which can be considered as an isotropic continuum, is modeled as a linear network with concentrated parameters. The weights of the obtained graph represent the properties of the discretized continuum. Further, the application of the developed procedure allows for the dielectric constant to be used in the multi-frequency approach, as a result of which the optimized system of equations always remains overdetermined. Through case studies, the efficacy of the reconstruction method by changing the mesh resolution applied for discretizing is presented and evaluated. The presented results show, that, due to the application of discrete, symmetric mathematical structures, the new approach even at coarse mesh resolution is capable of localizing the inhomogeneities of the material.

Waveguide Analysis of Radiofrequency Transmission in Well Tubulars for Electromagnetic Heating of Heavy Oil

This paper presents the numerical modelling and simulation of a 2D vertical well tubular model excited by a coaxial radiofrequency transmission line placed in its annular space for the purpose of downhole RF energy transmission. The study identifies the mechanism of energy losses due to coupling between the transmission line and steel tubing and casing using resonance mode analysis. The design of a left-handed artificial power line is proposed to minimize the losses due to the right-handed properties of the coaxial transmission line. The design utilizes ideal lumped element method to determine the left-handedness of the right-handed coaxial transmission line over the industrial heating radio-frequency band. The model is developed and simulated using COMSOL multi-physics commercial simulation software. The effect of transmission line position within the annular space on the tangential magnetic field and resulting power losses along the tubing is discussed. It is observed that the resulting artificial power line improves RF power transmission over 60 m depths of the vertical oil well within the industrial heating radiofrequency band.

Nonlinear dynamic model for the free rotor of the swash plate-rotating hydraulic transformer

Hydraulic transformer (HT) is an energy conservation component used in the common pressure rail system and achieves an excellent energy-saving effect in construction machinery and vehicle transmission. This paper reports a complete nonlinear dynamic model and validation for the free rotor in a swash plate-rotating hydraulic transformer (SPRHT), accounting for various time-varying effects. A parameter characterization model for the oil properties considering gas-liquid phase and pressure is described. Based on the lumped element method, the fluid dynamic model for the working chambers is established, taking account of the variation of the control volume/flow area in the working chambers and leakage. The dynamic model for the free rotor is constructed, accounting for the piston distribution and nonlinear friction. Combining the above models, the speed of the free rotor is solved by the Runge-Kutta method. The SPRHT is simulated in the AMESim. Particularly, a prototype is developed, and the dynamic test is carried out. Then the potential of the nonlinear model for the free rotor is verified. The proposed nonlinear dynamic model of the free rotor can be used for the dynamic behavior analysis and energy efficiency optimization of the HT.

Three-Dimensional Simulation Platform for Optimal Designs of the MEMS Microphone

MEMS microphone has a wide range of application prospects in electronic devices such as mobile phones, headphones, and hearing aids due to its small size, low cost, and reliable performance. Research and development of MEMS microphones involves multiple thermo-electro-mechanical couplings among various physical and electrical fields. Unfortunately, there is not an accurate three-dimensional (3D) MEMS microphone simulation platform, which can be applied for the design of chip parameters and packaging characteristics. Herein, based on commercial COMSOL software, we have established a 3D simulation platform for MEMS microphones, which is used to systematically study the influences of geometric structure and physics parameters on the sensitivity and frequency responses of the microphone and consider the influences of packaging characteristics on the performance of the microphone. The simulation results are consistent with those obtained using a lumped element method, which proves the accuracy of the simulation platform. The platform can be used to design and explore new principles or mechanisms of MEMS microphone devices.

A lumped mass Chebyshev spectral element method and its application to structural dynamic problems

A lumped mass Chebyshev spectral element method and its application to structural dynamic problems

Stochastic model of the human middle ear using a nonparametric probabilistic approach.

Several mathematical models of the human middle ear dynamics have been studied since the mid-twentieth century. Despite different methods applied, all of these models are based on deterministic approaches. Experimental data have shown that the middle ear behaves as an uncertain system due to the variability among individuals. In this context, stochastic models are useful because they can represent a population of middle ears with its intrinsic uncertainties. In this work, a nonparametric probabilistic approach is used to model the human middle ear dynamics. The lumped-element method is adopted to develop deterministic baseline models, and three different optimization processes are proposed and applied to the adjustment of the stochastic models. Results show that the stochastic models proposed can reproduce the experimental data in terms of mean and coefficient of variation. In addition, this study shows the importance of properly defining the acceptable range of each input parameter in order to obtain a reliable stochastic model.

Lumped Element Method ? A Discrete Calculus Approach for Solving Elliptic and Parabolic PDEs

Lumped Element Method ? A Discrete Calculus Approach for Solving Elliptic and Parabolic PDEs

Lumped Mass Finite Element Method of the Nonlinear BBM Equation

In this paper, the full-discrete approximation scheme of the lumped mass nonconforming finite element method for BBM equation is discussed. Without the Riesz projection used in the traditional finite element analysis, the optimal error estimations are derived based on interpolation technique and special properties of element.

Longitudinal vibration compensation model of stepped-pipe strings in deep-sea mining.

In this paper, the dynamic model of the rigid space stepped-pipe strings system is derived with Lagrangian method to represent the system dynamic behaviors which enriches the analysis method of longitudinal vibration of stepped-pipe strings. The stepped-pipe strings is constructed of pipes with different diameters and lengths, the physical properties of which mainly depends on the axial force and the depth of deep-sea mining. Based on lumped element method, the heave compensation system with dynamic vibration absorber is designed for longitudinal vibration suppression of the stepped-pipe strings. The analytical solution is obtained by modal analysis method when the mining ship is subjected to sea breeze excitation. The proposed method is easily implementable for rigid space stepped-pipe strings system with complex multi-degree-of-free deep-sea mining dynamic model. Furthermore, the optimal combination of mass ratio, spring coefficient and damping ratio is shown to have a better vibration suppression performance. Finally, numerical simulations on the stepped-pipe strings system with or without dynamic vibration absorbers are provided to demonstrate the effectiveness of the proposed method.

A Semi-Analytical and Computationally Efficient Method to Calculate the Touch-Point Pressure and Pull-In Voltage of a MEMS Pressure Sensor With a Circular Diaphragm

Micro-Electromechanical Systems (MEMS) based capacitive pressure transducers have a pivotal role in transducer devices for real-world applications. Thus, the efficient analysis for modelling these transducers is increasingly becoming important. These transducers use diaphragms of various geometries, however for the same active area, circular diaphragms are more sensitive as compared to square diaphragms. Pull-in voltage and touch-point pressure are two parameters which determine the performance of a micro- electromechanical systems device. In this work a complete analysis is presented for evaluating these parameters along with the mechanical and capacitive sensitivity for a circular diaphragm based capacitive pressure transducer. The effect of thickness and radius of the diaphragm has been illustrated, as they form the essential design parameters for fabricating the micro-electromechanical systems devices. Literature review suggests that relatively less work has been reported for this analysis and more complicated and computationally complex methods have been used. The semi-analytical approach presented in this research is less complex and computationally efficient, in comparison to finite element method (FEM). Critical differentiator of this formulation is related to its applicability for analysing sensor parameters with or without considering the effect of electrostatic pressure on diaphragm deflection. Furthermore, this analysis eliminates the need for determining spring constant k which is used in lumped element methods. MATLAB has been used to compute and simulate the results. The mathematical model developed is verified with a standard Finite Element Analysis (FEM) using COMSOL v5.5.

Electrical analogies applied on MMR micropump

Micropumps are among useful equipment in microsystems. The magnetically actuated mercury micropump, which has been introduced for less than a decade, is an innovative kind of micropumps which uses mercury droplets motion as a pumping agent. The equations governing this micropump are complex and their numerical solution is a time-consuming process, due to electromagnetic, hydrodynamic, and unsteady effects. In the present study, for the first time, using simplifying assumptions, the performance of a Magneto Mercury Reciprocating (MMR) micropump with electromagnetic actuation is studied through electrical analogy and then, the components and operational stages of the micropump are simulated using a lumped element method with an equivalent electric circuit, while calculating its currents and potentials. Then, the characteristic curves of this micropump are extracted as a function of head and the flow rate and the results of the proposed modeling are verified by laboratory results. Finally, the effect of geometric parameters and the actuation frequency on the micropump performance is studied. The results of modeling indicate that an increase in the volume of the liquid droplet chamber, as well the actuation frequency could improve the performance of this micropump.

An acoustic model of a Helmholtz resonator under a grazing turbulent boundary layer

Acoustic models of resonant duct systems with turbulent flow depend on fitted constants based on expensive experimental test series. We introduce a new model of a resonant cavity, flush mounted in a duct or flat plate, under grazing turbulent flow. Based on previous work by Goody, Howe and Golliard, we present a more universal model where the constants are replaced by physically significant parameters. This enables the user to understand and to trace back how a modification of design parameters (geometry, fluid condition) will affect acoustic properties. The derivation of the model is supported by a detailed three-dimensional direct numerical simulation as well as an experimental test series. We show that the model is valid for low Mach number flows (M = 0.01-0.14) and for low frequencies (below higher transverse cavity modes). Hence, within this range, no expensive simulation or experiment is needed any longer to predict the sound spectrum. In principle, the model is applicable to arbitrary geometries: Just the provided definitions need to be applied to update the significant parameters. Utilizing the lumped-element method, the model consists of exchangeable elements and guarantees a flexible use. Even though the model is linear, resonance conditions between acoustic cavity modes and fluid dynamic unstable modes are correctly predicted.

The lumped mass FEM for a time-fractional cable equation

We consider the numerical approximation of a time-fractional cable equation involving two Riemann–Liouville fractional derivatives. We investigate a semidiscrete scheme based on the lumped mass Galerkin finite element method (FEM), using piecewise linear functions. We establish optimal error estimates for smooth and middly smooth initial data, i.e., v∈Hq(Ω)∩H01(Ω), q=1,2. For nonsmooth initial data, i.e., v∈L2(Ω), the optimal L2(Ω)-norm error estimate requires an additional assumption on mesh, which is known to be satisfied for symmetric meshes. A quasi-optimal L∞(Ω)-norm error estimate is also obtained. Further, we analyze two fully discrete schemes using convolution quadrature in time based on the backward Euler and the second-order backward difference methods, and derive error estimates for smooth and nonsmooth data. Finally, we present several numerical examples to confirm our theoretical results.

Use of a Simple Mechanical Analogy to Analytically Tune the PD Controller of a Flexible Manipulator System

A study is presented in this paper that uses a simple mechanical analogy to analytically tune the PD (proportional‐derivative) controller of a linear flexible manipulator system. More specifically, the aim is to give simple closed‐form solutions of the optimal P and D gains to yield the maximum bandwidth under a given damping requirement or conversely the maximum damping under a given bandwidth requirement. The idea of this study is based on the observation that the performance of the complete manipulator system is largely determined by the operational dynamics of the fundamental vibration mode. A lumped element method is thus applied to model this dynamics in terms of simple lumped mechanical elements. It subsequently turns out that the original servo control problem is analogous to a conventional Zener mount design problem, that is, mathematically, to optimize a third‐order dynamic system consisting of the Zener model of a viscoelastic mount and an inertial object upon it. A design methodology is finally established to analytically determine the optimal elements of the mount, corresponding to the optimal control gains. Simulations and experiments were also conducted with a single‐link flexible beam to support the model and the design methodology developed.

Sensitivity-Based Reliability Analysis of MEMS Acceleration Switch

MEMS acceleration switches have been used in many engineering applications. In this paper, the reliability of MEMS switch is evaluated under various uncertainties from materials and manufacturing process. First, the performance of MEMS switch is modeled using 1D mass-spring-damper-contact system. Different from conventional lumped element methods, the model includes the effect of geometric parameters as well as contact conditions. The parameters of 1D models are calibrated using a high-fidelity finite element model. For reliability assessment, four different methods are used in order to compare computational cost as well as accuracy in predicting reliability. It turned out that sensitivity-based reliability method has several benefits, such as computational time and identifying important parameters that contribute significantly to reliability. The sensitivity analysis showed that the cross-sectional height and the length of folded-beam contribute most significantly to the reliability of switch-on condition. After changing the length of the beam, the probability of failure was improved from 0.168 to 0.0003.

Acoustic impact of the gradual glottal abduction degree on the production of fricatives: A numerical study.

The paper presents a numerical study about the acoustic impact of the gradual glottal opening on the production of fricatives. Sustained fricatives are simulated by using classic lumped circuit element methods to compute the propagation of the acoustic wave along the vocal tract. A recent glottis model is connected to the wave solver to simulate a partial abduction of the vocal folds during their self-oscillating cycles. Area functions of fricatives at the three places of articulation of French have been extracted from static MRI acquisitions. Simulations highlight the existence of three distinct regimes, named A, B, and C, depending on the degree of abduction of the glottis. They are characterized by the frication noise level: A exhibits a low frication noise level, B, which is a transitional unstable regime, is a mixed noise/voice signal, and C contains only frication noise. They have significant impacts on the first spectral moments. Simulations show that their boundaries depend on articulatory and glottal configurations. The transition regime B is shown to be unstable: it requires very specific configurations in comparison with other regimes, and acoustic features are very sensitive to small perturbations of the glottal configuration abduction in this regime.

Calculating scale tunings of Polynesian nose flutes

The Polynesian nose flute is found in two versions that are blown in a similar manner but fingered and tuned differently. The Eastern Polynesian flute, known in Hawai'i as 'ohe hano ihu, but is found also to Tahiti and Niue. The tube is closed by a segment node at one end but with a hole for blowing and open at the other end. It typically has two or three finger holes along the tube and three or four playable notes. Being similar to other flutes, the scale tunings can be calculated from hole and tube dimensions by analytic expressions. In Fiji, New Zealand, Samoa, and Tonga, where it is known as fangufangu, both ends of the Western Polynesian flute are closed by segment nodes. There are five holes are placed along the top, usually evenly spaced from one end to the other, with a sixth hole in the middle underneath, giving a variety of fingering options with four to six notes and two registers. The scale tunings are determined by first calculating the frequency response using a lumped-element method.

A lumped element method for modeling the two-phase choking flow through hydraulic orifices

A novel lumped element methodology for modeling the oil–gas two-phase flow through the hydraulic orifice has been presented, focus on the choking condition. The proposed approach consists of a gas cavitation model developed based on “Full Cavitation Model” and a formulation considering the homogenous fluid assumption for evaluating the mass flow rate. The two-phase choking flow occurring at extreme condition is characterized in detail by using the present method, in terms of the critical pressure, sound speed, filling ratio and the critical speed of pump operation in the hydraulic circuit. Mach number is found to be 1 and the critical speed is estimated by the inlet volumetric flow rate at choking condition of the two-phase flow. The effects of different parameters including the orifice diameter, the upstream pressure and the cavitation model coefficient are investigated to find possible ways of improving the operation of the pump circuit. Reducing the cavitation model coefficient is identified to be both advantageous for reducing the critical pressure and increasing the critical speed.