Frequency Domain Approach to the Computation of the Impulse Response of Population Systems

1977 ◽  
Vol 99 (4) ◽  
pp. 249-252
Author(s):  
I. B. Huang ◽  
W. T. Chang ◽  
F. C. Kung
Keyword(s):  
Frequency Domain ◽  
Impulse Response ◽  
Time Lag ◽  
Information Loss ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Mathematical Methods ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Frequency Domain Approach

Since a population inherently is a distributed system, it usually is complex and difficult to find an exact solution by conventional mathematical methods. To facilitate the solution of population systems, in this paper, the distributed-parameter model is reduced to a lumped-parameter model with distributed time lag, and two methods in frequency domain approach are developed to compute the impulse response of population systems. Since there is no information loss in the computation, the result is considered to be exact. The data and procedure required for the computation are rather simple. A typical example is given.

Comparison of Modelling Methods for Hydraulic Valve Gear

1987 ◽  
Author(s):  
H. Shang ◽  
G. K. Matthew ◽  
W. Luo
Keyword(s):  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Comparison Results ◽  
Hydraulic Valve ◽  
Modelling Methods ◽  
Measured Response ◽  
Valve Gear

Abstract A combined lumped/distributed parameter model for the follower system of a hydraulically operated valve is compared to a lumped parameter model of the same system. Since previous results show excellent correspondence between the lumped/distributed parameter model and measured response, it is natural to attempt to simplify the model and to again perform a comparison. Results of several examples are shown.

scholarly journals An Improved Lumped Parameter Model for a Piezoelectric Energy Harvester in Transverse Vibration

2014 ◽  
Vol 2014 ◽  
pp. 1-12 ◽  
Author(s):  
Guang-qing Wang ◽  
Yue-ming Lu
Keyword(s):  
Correction Factor ◽  
Transverse Vibration ◽  
Energy Harvester ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Piezoelectric Energy ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Tip Mass

An improved lumped parameter model (ILPM) is proposed which predicts the output characteristics of a piezoelectric vibration energy harvester (PVEH). A correction factor is derived for improving the precisions of lumped parameter models for transverse vibration, by considering the dynamic mode shape and the strain distribution of the PVEH. For a tip mass, variations of the correction factor with PVEH length are presented with curve fitting from numerical solutions. The improved governing motion equations and exact analytical solution of the PVEH excited by persistent base motions are developed. Steady-state electrical and mechanical response expressions are derived for arbitrary frequency excitations. Effects of the structural parameters on the electromechanical outputs of the PVEH and important characteristics of the PVEH, such as short-circuit and open-circuit behaviors, are analyzed numerically in detail. Accuracy of the output performances of the ILPM is identified from the available lumped parameter models and the coupled distributed parameter model. Good agreement is found between the analytical results of the ILPM and the coupled distributed parameter model. The results demonstrate the feasibility of the ILPM as a simple and effective means for enhancing the predictions of the PVEH.

scholarly journals The effect of a hydrological model structure and rainfall data on the accuracy of flood description in an upland catchment

2015 ◽  
Vol 47 (4) ◽  
pp. 305-320 ◽  
Author(s):  
Andrzej Wałęga ◽  
Leszek Książek
Keyword(s):  
Hydrological Model ◽  
Model Performance ◽  
Rainfall Data ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Model Structure ◽  
Related Data ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Starting Point

Abstract The effect of a hydrological model structure and rainfall data on the accuracy of flood description in an upland catchment. The aim of this paper was to determine the influence of a hydrological model structure and rainfall- -related data on flood parameters obtained from a simulation. The study included an upland river Stobnica, right tributary of the Wisłok. The following assumptions were investigated: (i) the greater number of rainfall stations, the more accurate a flood description, i.e. the resulting hydrograph much better describes the actual flood, (ii) a distributed parameter model provides a more precise description of a catchment response to rainfall than a lumped parameter model. All calculations were performed using HEC-HMS 3.4 software. The analyses showed that increasing the number of rainfall stations slightly improved the model performance (by on average 4.1%). Furthermore, it was showed that in the catchment characterized by low topographical variability and stable land use, more reliable flood simulation results were obtained in the lumped parameter model than in the distributed parameter model. Considering the calibration process slightly improved the model performance, irrespective of its structure and the number of rainfall stations. Multivariate analysis of variance (MANOVA) revealed that the resulting differences in the model efficiency for individual variants were not significant. Considering limited empirical evidence on rainfall-runoff episodes, uncertainty of these results is probably high and thus they should be treated as a starting point for further studies.

An asymmetric magnetic-coupled bending-torsion piezoelectric energy harvester: modeling and experimental investigation

2021 ◽  
Author(s):  
Huirong Zhang ◽  
Wentao Sui ◽  
Chongqiu Yang ◽  
Leian Zhang ◽  
Rujun Song ◽  
...  
Keyword(s):  
Energy Harvester ◽  
Average Power ◽  
Harmonic Excitation ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Piezoelectric Energy ◽  
Distributed Parameter Model ◽  
Piezoelectric Beam ◽  
Lumped Parameter ◽  
Torsion Energy

Abstract This paper presents a detailed investigation on an asymmetric magnetic-coupled bending-torsion piezoelectric energy harvester based on harmonic excitation. There is an eccentricity between the shape center of moving magnets and the axis of the piezoelectric beam, which results in the bending and torsion simultaneously in working condition. The distributed mathematical model is derived from the energy method to describe the dynamic characteristics of the harvester, and the correctness of the model is verified by experiments. To further demonstrate the improvement performance of the proposed energy harvester, the bending-torsion energy harvester (i.e. magnetic-coupled was not configured) is experimented and compared. The theoretical and experimental results indicate that the average power increases about 300% but the resonance frequency decreases approximately 2 Hz comparing to the harvester without magnetic-coupled. According to the characteristic of distributed parameter model, the magnetic force and the size of the piezoelectric beam are investigated respectively. And the lumped-parameter model is introduced to analyze the steady-state characteristic. Accordingly, this paper provides a feasible method to improve performance for piezoelectric energy harvester.

Modeling of Oscillations in Partially Penetrated Weld Pools

1990 ◽  
Vol 112 (3) ◽  
pp. 469-474 ◽  
Author(s):  
C. D. Sorensen ◽  
T. W. Eagar
Keyword(s):  
Surface Tension ◽  
Weld Pool ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Gas Tungsten Arc ◽  
Geometric Conditions ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Weld Pool Geometry ◽  
Weld Pools

Several investigators have proposed controlling the size and shape of the weld pool based on the weld pool oscillations. This paper proposes two models that could be used to predict the weld pool geometry based on the natural frequency of the pool. The models, one a lumped parameter model and the other a distributed parameter model, included effects of liquid metal density and surface tension along with weld pool geometry. Weld pool oscillations were measured through signal processing of arc voltage and current for stationary gas-tungsten arc (GTA) welds. Welds were performed at different weld voltages and currents on different materials in order to vary width, depth, density, and surface tension. The models developed here were shown to have reasonable agreeement with experimentally measured weld pool resonant frequencies. Also, with geometric conditions similar to those commonly found in GTA weld pools, the different models tend to agree well with one another.

Dynamic Model of a Rotating Channel Used in the Steel Industry and Implementation of a Controller

2004 ◽  
Vol 10 (3) ◽  
pp. 423-445 ◽  
Author(s):  
Alessandro Gasparetto ◽  
Stefano Miani
Keyword(s):  
Dynamic Model ◽  
Coming Out ◽  
Steel Industry ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Distributed Parameter Model ◽  
Lumped Parameter ◽  
Control Scheme ◽  
Steel Bars ◽  
Rotating Channel

In the steel industry, the steel bars coming out from the last stand of the rolling train must be conveyed to the cooling bed. For this purpose, various types of devices are used in the different steel factories. In this paper, the rotating channel used in a single steel company is described and investigated. The problem of deriving an adequate dynamic model for the rotating channel is tackled; the model is then exploited to design a controller which can be employed in the real application of the rotating channel. A lumped parameter model of the rotating channel has been designed and used in this work. Moreover, a distributed parameter model has also been implemented, so as to be able to compare the two models and to evaluate the error made by using the lumped parameter model instead of the distributed parameter model. The lumped parameter model has then been used as a basis for the implementation of a time-varying control scheme, which is also presented in the paper. The control has then been successfully tested on an accurate simulator of the plant. The results obtained from the tests have been very encouraging.

scholarly journals A Lumped-Parameter Model of Multiscale Dynamics in Steam Supply Systems

2016 ◽  
Vol 11 (6) ◽  
Author(s):  
Hikaru Hoshino ◽  
Yoshihiko Susuki ◽  
Takashi Hikihara
Keyword(s):  
Power Systems ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Short Term ◽  
Distributed Parameter Model ◽  
Multiscale Dynamics ◽  
Lumped Parameter ◽  
Normally Hyperbolic Invariant Manifold ◽  
Supply Systems

This paper focuses on multiscale dynamics occurring in steam supply systems. The dynamics of interest are originally described by a distributed-parameter model for fast steam flows over a pipe network coupled with a lumped-parameter model for slow internal dynamics of boilers. We derive a lumped-parameter model for the dynamics through physically relevant approximations. The derived model is then analyzed theoretically and numerically in terms of existence of normally hyperbolic invariant manifold in the phase space of the model. The existence of the manifold is a dynamical evidence that the derived model preserves the slow–fast dynamics, and suggests a separation principle of short-term and long-term operations of steam supply systems, which is analog to electric power systems. We also quantitatively verify the correctness of the derived model by comparison with brute-force simulation of the original model.

APPROXIMATING THE EFFECT OF VAN DER WAALS FORCE ON THE INSTABILITY OF ELECTROSTATIC NANO-CANTILEVERS

2011 ◽  
Vol 25 (29) ◽  
pp. 3965-3976 ◽  
Author(s):  
ALI KOOCHI ◽  
AMINREZA NOGHREHABADI ◽  
MOHAMADREZA ABADYAN
Keyword(s):  
Van Der Waals ◽  
Convergent Series ◽  
Lumped Parameter Model ◽  
Distributed Parameter ◽  
Analytical Results ◽  
Lumped Parameter ◽  
Fringing Field ◽  
Beam Type ◽  
Nano Electromechanical System ◽  
Good Agreement

Beam-type nano-electromechanical system (NEMS) is one of the most components in constructing nano-devices. Herein, a distributed parameter model is used to study the influence of van der Waals (vdW) attraction on the pull-in performance of the cantilever NEMS. Homotopy perturbation method (HPM) is applied to solve the nonlinear governing equation of the actuators in the form of convergent series. Moreover, analytical results are compared with those of numerical method as well as a lumped parameter model. The pull-in voltage and critical cantilever tip deflection of NEMS are determined. Results depict that vdW attraction decreases the pull-in deflection and voltage of the NEMS. On the other hand, the fringing field increases the pull-in deflection while decreases the pull-in voltage of the system. The analytical results have good agreement with numerical results and those available in the literature.

Comparison of Golf Ball/Driver Impact Models With Respect to Mechanical Impedance Matching Theory

2009 ◽  
Author(s):  
Willem Petersen ◽  
Armaghan Salehian ◽  
John McPhee
Keyword(s):  
Impedance Matching ◽  
Mechanical Impedance ◽  
Element Model ◽  
Golf Ball ◽  
Lumped Parameter Model ◽  
Matching Theory ◽  
Beam Equation ◽  
Distributed Parameter ◽  
Piecewise Constant ◽  
Lumped Parameter

Three models of a golf ball and a golf clubhead are created to investigate the efficiency of the collision with respect to the theory of mechanical impedance matching, normally derived from oversimplified models. While the results obtained from a lumped-parameter model do validate the mechanical impedance matching theory, the results obtained from a finite element model used to investigate this phenomenon with more fidelity by varying the clubface flexibility disagree. Therefore, a distributed-parameter model is developed. In this model, the clubface is modelled using the Euler-Bernoulli beam equation with clamped-clamped boundary conditions, and the golf ball is modelled using a 3-piece rod with piecewise constant material properties representing the multiple layers of a real golf ball. The number of modes considered in the calculations is varied to determine the influence of the complexity of the model. The results obtained from this model are compared against those from the previous approaches and from the mechanical impedance matching theory.

Sign in / Sign up

Export Citation Format

Share Document