Bond Graph Models for Fluid Dynamic Systems

1972 ◽  
Vol 94 (3) ◽  
pp. 222-229 ◽  
Author(s):  
D. Karnopp
Keyword(s):  
Fluid Dynamic ◽  
Nonlinear Behavior ◽  
Bond Graph ◽  
Distributed Parameter ◽  
Graph Models ◽  
Modeling Process ◽  
Fluid Systems ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Control Volumes

The modeling process whereby distributed parameter fluid systems are described approximately by lumped parameter models is discussed using bond graph techniques. It is shown that despite the analogies which exist between some fluid systems and other physical systems, the lumping process for fluid systems introduces forms of nonlinear behavior not often encountered in other types of systems. Many such effects may be traced to the desire to use control volumes and Eulerian rather than Lagrangian descriptions of the fluid systems.

On Gyrobondgraphs and Their Uses

1978 ◽  
Vol 100 (1) ◽  
pp. 76-82 ◽  
Author(s):  
R. C. Rosenberg
Keyword(s):  
Bond Graph ◽  
Energy Structure ◽  
Engineering Systems ◽  
Graph Models ◽  
Point Of Interest ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Five Elements ◽  
System Equations ◽  
Recent Arrival

Graphical representations of lumped-parameter models for physical and engineering systems have been in use for some time. A relatively recent arrival is the bond graph, which displays energy flow and energy structure explicitly. Bond graphs are finding increasing use in a variety of applications, including classical electromechanical, hydraulic, and thermal energy systems as well as chemical and biological processes. In addition, there has been some effort to extend the approach to energy-like macroeconomic systems. The standard bond graph approach uses the same basic elements commonly found in network theory, although the graphing scheme is different. This paper defines a specific type of bond graph—the gyrobondgraph—and shows how it serves as a canonical form for a large class of lumped-parameter multiport models. The gyrobondgraph is based on only five elements and a standard graph format. A transformation procedure is described for obtaining a gyrobondgraph from a standard bond graph. The formulation of system equations associated with a gyrobondgraph is discussed briefly, and, as a point of interest, Tellegen’s Theorem in quasi-power form is derived. The gyrobondgraph appears to be an important new tool for the exploration of multiport system theory; furthermore, it is a source of new techniques for the computer simulation of bond graph models.

A Lumped Parameter Electromechanical Model for Describing the Nonlinear Behavior of Piezoelectric Actuators

1997 ◽  
Vol 119 (3) ◽  
pp. 478-485 ◽  
Author(s):  
M. Goldfarb ◽  
N. Celanovic
Keyword(s):  
System Analysis ◽  
Nonlinear Behavior ◽  
Piezoelectric Actuators ◽  
Bond Graph ◽  
Lumped Parameter Model ◽  
Input Output ◽  
Mechanical Stiffness ◽  
Analysis And Design ◽  
Lumped Parameter ◽  
Proposed Model

A lumped-parameter model of a piezoelectric stack actuator has been developed to describe actuator behavior for purposes of control system analysis and design, and in particular for control applications requiring accurate position tracking performance. In addition to describing the input-output dynamic behavior, the proposed model explains aspects of nonintuitive behavioral phenomena evinced by piezoelectric actuators, such as the input-output rate-independent hysteresis and the change in mechanical stiffness that results from altering electrical load. Bond graph terminology is incorporated to facilitate the energy-based formulation of the actuator model. The authors propose a new bond graph element, the generalized Maxwell resistive capacitor, as a lumped-parameter causal representation of rate-independent hysteresis. Model formulation is validated by comparing results of numerical simulations to experimental data.

A Numerical Method for the Analysis of the Theoretical Flow in Crescent-Type Internal Gear Machines With Involute Teeth Profile

2019 ◽  
Author(s):  
Dinghao Pan ◽  
Andrea Vacca
Keyword(s):  
Numerical Method ◽  
Fluid Dynamic ◽  
Analytical Formula ◽  
Simulation Models ◽  
Design Tool ◽  
Multiple Control ◽  
Analysis And Design ◽  
Lumped Parameter ◽  
Control Volumes ◽  
Internal Gear

Abstract Lumped parameter approaches for the description of the flow displaced by hydrostatic pumps and motors have proven to be very effective for both analysis and design purposes. However, while these methods are relatively easy to implement for most of the existing design architectures for positive displacement machines, the case of a crescent-type internal gear machine (CIGM) presents clear challenges as it pertains to the definition of lumped control volumes within the machine. This paper proposes an original scheme for defining lumped control volumes within a CIGM with involute teeth profiles, which is suitable for developing fluid dynamic simulation models for CIGMs. The proposed method strictly obeys fundamental rules on continuous volumes required by lumped parameters models. This is achieved by defining not only multiple control volumes for each displacement chamber but also two variable porting volumes to respect the volume conservation. To prove the validity of the proposed numerical method, the paper provides comparisons between the displaced volume found by the proposed lumped parameter approach and the theoretical kinematic flow ripple provided by an analytical formula available from literature. The results show how the method can be used as a design tool for CIGMs, and particularly to further develop lumped parameter simulation models for detailed fluid dynamic analysis of CIGMs.

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 Modeling of blood clot removal with aspiration Thrombectomy devices

2020 ◽  
Vol 14 (1) ◽  
pp. 6238-6250
Author(s):  
G. Romero ◽  
C. Talayero ◽  
G. Pearce ◽  
J. Wong
Keyword(s):  
Mathematical Model ◽  
Interventional Procedure ◽  
Fluid Dynamic ◽  
Blood Clot ◽  
Bond Graph ◽  
Graph Models ◽  
Aspiration Thrombectomy ◽  
Potential Damage ◽  
Mass Spring

Thrombectomy by aspiration is a highly effective method of accomplishing vessel recanalization. This study aims to obtain a mathematical model that allows the prediction of the dynamic response of a thrombus in response to different suction conditions, in order to avoid potential damage or the breakage of the clot during the interventional procedure. Virtual computing models have been created using Bond-Graph data and mass-spring Multi-Degree of Freedom equations. The model allows the use of tensile and torsion loads that could potentially be generated by the suction pressure together with different catheter geometries. The stress generated in the clot depends on its length and on its stiffness. The results obtained with the mathematical model are validated with a Finite Element Method (FEM) model, shows good agreement in terms of stress and elongation values. The results are consistent with previous Bond Graph models which indicated that the forces needed to extract a blood clot from an artery in in-vitro experiments are within the range used experimentally (~40-90 kPa). Qualitative experiments are undertaken with 3D printed scale prototypes and gelatin. The results are consistent with Computer Fluid Dynamic (CFD) simulations.

New Bond Graph Primitive Elements for Modeling Systems Modeled by Practical Derivatives

2006 ◽  
Author(s):  
Thomas J. M. Connolly ◽  
Jaime A. Contreras
Keyword(s):  
Bond Graph ◽  
Engineering Systems ◽  
Fluid Structure Interactions ◽  
Primitive Elements ◽  
Graph Models ◽  
Frequency Dependent ◽  
Fluid Structure ◽  
Lumped Parameter ◽  
Dependent Behavior ◽  
Modeling Systems

This paper describes our work in creating and using new bond graph primitive elements to represent time-varying and/or frequency-dependent effects in engineering systems. These phenomena can be mathematically represented by fractional-order differential and integral operators. Equations with such operators arise from the analysis and application of several classes of partial differential equations [1]. Previous researchers (Bagley, Torvik, et. al.) have used this approach to further the modeling of fluid-structure interactions, heat transfer, and related control systems [3–6]. These new primitive elements represent visco-inertial and visco-elastic phenomena, whose constitutive laws are dictated by half-order derivatives and integrals. After a brief overview of the fractional derivative, we continue with a formalized mathematical development of these new primitive elements using an impedance-based approach, which provides further support in the argument for their necessity. This approach provides the system modeler with new tools to widen the range of systems that he can accurately model using a lumped-parameter bond graph approach. We illustrate the application and utility of the approach with an example problem in fluid-structure interactions by presenting bond graph models and corresponding simulations. The simulations reveal that the use of these new elements accurately captures the frequency-dependent behavior of the physical system.

Improved Lumped Models for a One-Dimensional Nonlinear Heat Conduction Problem

2007 ◽  
Author(s):  
Ge Su ◽  
Zheng Tan ◽  
Jian Su
Keyword(s):  
Heat Conduction ◽  
Heat Conduction Problem ◽  
Distributed Parameter ◽  
Nonlinear Heat Conduction ◽  
Lumped Model ◽  
One Dimensional ◽  
Average Temperature ◽  
Lumped Parameter ◽  
Lumped Parameter Models ◽  
Lumped Models

This work reports improved lumped-parameter models for a class of one-dimensional nonlinear heat conduction problems in a slab, cylinder or sphere with linearly temperature-dependent thermal conductivity and subject to combined convective and radiative boundary condition. The improved lumped models are obtained through two point Hermite approximations for integrals. It is shown by comparison with numerical solution of the original distributed parameter models that the higher order lumped models (H1, 1/H0, 0 approximation for slab and cylinder, H2, 1/H0, 0 for sphere) yield significant improvement of average temperature predictions over the classical lumped model.

Delay-Bond Graph Models for Geared Torsional Systems

1974 ◽  
Vol 41 (2) ◽  
pp. 366-370 ◽  
Author(s):  
N. T. Tsai ◽  
S. M. Wang
Keyword(s):  
Transmission Line ◽  
Gear Tooth ◽  
Nonlinear Damping ◽  
Bond Graph ◽  
Dynamic Responses ◽  
State Variables ◽  
Graph Models ◽  
Wave Variables ◽  
Tooth Stiffness ◽  
Line Elements

The dynamic responses of geared torsional systems are analyzed with the delay-bond graph technique. By transforming the power variables into torsional wave variables, the torsional elements are modeled as transmission line elements. The nonlinear elements, e.g., varying tooth stiffness, gear-tooth backlash, and nonlinear damping, are incorporated into the ideal transmission line element. A computational algorithm is established where the state variables of the system are expressed in terms of wave scattering variables and the dynamic responses are then obtained in both time and space domains. The simulation results of several simple examples of linear and nonlinear geared torsional systems are presented to demonstrate the feasibility of this algorithm.

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