An Experimental Determination of Differential Equations to Describe Simple Nonlinear Systems

1967 ◽  
Vol 89 (2) ◽  
pp. 393-398 ◽  
Author(s):  
L. L. Hoberock ◽  
R. H. Kohr
Keyword(s):  
Differential Equations ◽  
Continuous Functions ◽  
Nonlinear Functions ◽  
Physical Systems ◽  
Lumped Parameter ◽  
System Input ◽  
System Variables ◽  
Time Invariant ◽  
By Products

A method is presented for the determination of ordinary differential equations to describe the performance of existing lumped-parameter, time-invariant, nonlinear physical systems. It is assumed initially that the nonlinear elements can be described by products of continuous functions of system variables and these system variables themselves, which consist of the input and output of the system and their time derivatives. It is also assumed that the system input may be specified and that the output can be measured. The method yields graphical representations of unknown nonlinear functions in an assumed system differential equation. Examples illustrating the accuracy of the procedure are presented, and results obtained in the identification of two physical systems are given.

A Method to Find Non-Zero Operating Point Volterra Models for Port-Based Ordinary Differential Equations

2010 ◽  
Author(s):  
Eliot Motato ◽  
Clark Radcliffe ◽  
Jose Luis Viveros
Keyword(s):  
Differential Equations ◽  
Ordinary Differential Equations ◽  
Transfer Functions ◽  
Operating Conditions ◽  
Operating Point ◽  
Input Output ◽  
Nonlinear Functions ◽  
Nonlinear Odes ◽  
Physical Systems ◽  
Volterra Models

Nonlinear physical systems frequently perform around constant non-zero input-output operating conditions. This local behavior can be modeled using port-based nonlinear ordinary differential equations (ODEs). An ODE local solution around an specific input-output operating point can be obtained through the Volterra transfer function (VTF) model. In a past work a procedure for obtaining MIMO Volterra models from port-based nonlinear ODEs was presented. This previous work considered only systems operating at zero input-output conditions subject to linear inputs. In this work the process for obtaining MIMO Volterra transfer functions is extended for systems operating at non-zero input-output conditions. This extension also allows systems that are nonlinear functions of their inputs and input derivatives.

The Response of Distributed—Lumped Parameter Systems

1988 ◽  
Vol 202 (6) ◽  
pp. 421-429 ◽  
Author(s):  
R Whalley
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Partial Differential ◽  
Physical Systems ◽  
Lumped Parameter ◽  
Spatially Distributed ◽  
Lumped Elements ◽  
Mathematical Difficulties

Physical systems are constructed from a variety of components, some of which have relatively concentrated, pointwise features while others have spatially distributed characteristics. In contrast, models rarely reflect this structure, thereby avoiding the mathematical difficulties arising from the manipulation of sets of mixed algebraic, ordinary and partial differential equations which may generate irrational functions on transformation. In this paper general results are produced, enabling the response to systems comprising a series of distributed-lumped elements to be calculated. A simple example is included to illustrate the procedures outlined.

MODELING OF NONLINEAR VIBRATION PROBLEMS WITH FLUID FLOWS THROUGH PIPELINES

2018 ◽  
pp. 44-47
Author(s):  
F.J. Тurayev
Keyword(s):  
Differential Equations ◽  
Nonlinear Vibration ◽  
Viscoelastic Properties ◽  
Construction Material ◽  
Fluid Flows ◽  
Variable Coefficients ◽  
Algebraic Equations ◽  
Flowing Liquid ◽  
Vibration Problems

In this paper, mathematical model of nonlinear vibration problems with fluid flows through pipelines have been developed. Using the Bubnov–Galerkin method for the boundary conditions, the resulting nonlinear integro-differential equations with partial derivatives are reduced to solving systems of nonlinear ordinary integro-differential equations with both constant and variable coefficients as functions of time.A system of algebraic equations is obtained according to numerical method for the unknowns. The influence of the singularity of heredity kernels on the vibrations of structures possessing viscoelastic properties is numerically investigated.It was found that the determination of the effect of viscoelastic properties of the construction material on vibrations of the pipeline with a flowing liquid requires applying weakly singular hereditary kernels with an Abel type singularity.

On modelling physical systems with stochastic models: diffusion versus Lévy processes

2008 ◽  
Vol 366 (1875) ◽  
pp. 2455-2474 ◽  
Author(s):  
Cécile Penland ◽  
Brian D Ewald
Keyword(s):  
Differential Equations ◽  
Stochastic Models ◽  
Lévy Processes ◽  
Numerical Models ◽  
Gaussian White Noise ◽  
Levy Processes ◽  
Physical Systems ◽  
Random Forcing ◽  
Weather And Climate ◽  
Made In

Stochastic descriptions of multiscale interactions are more and more frequently found in numerical models of weather and climate. These descriptions are often made in terms of differential equations with random forcing components. In this article, we review the basic properties of stochastic differential equations driven by classical Gaussian white noise and compare with systems described by stable Lévy processes. We also discuss aspects of numerically generating these processes.

scholarly journals Steady State Response of Linear Time Invariant Systems Modeledby Multibond Graphs

2021 ◽  
Vol 11 (4) ◽  
pp. 1717
Author(s):  
Gilberto Gonzalez Avalos ◽  
Noe Barrera Gallegos ◽  
Gerardo Ayala-Jaimes ◽  
Aaron Padilla Garcia
Keyword(s):  
Steady State ◽  
Linear Time ◽  
Direct Determination ◽  
The State ◽  
Steady State Response ◽  
State Variables ◽  
Linear Time Invariant ◽  
State Response ◽  
Time Invariant

The direct determination of the steady state response for linear time invariant (LTI) systems modeled by multibond graphs is presented. Firstly, a multiport junction structure of a multibond graph in an integral causality assignment (MBGI) to get the state space of the system is introduced. By assigning a derivative causality to the multiport storage elements, the multibond graph in a derivative causality (MBGD) is proposed. Based on this MBGD, a theorem to obtain the steady state response is presented. Two case studies to get the steady state of the state variables are applied. Both cases are modeled by multibond graphs, and the symbolic determination of the steady state is obtained. The simulation results using the 20-SIM software are numerically verified.

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