Numerical analysis for a nonlinear model of elastic strings with moving ends

2019 ◽  
Vol 135 ◽  
pp. 146-164 ◽  
Author(s):  
M.A. Rincon ◽  
I.-S. Liu ◽  
W.R. Huarcaya ◽  
B.A. Carmo
Keyword(s):  
Numerical Analysis ◽  
Nonlinear Model ◽  
Elastic Strings

Dynamics of a Supported Cylinder in Axial Flow

2011 ◽  
Vol 99-100 ◽  
pp. 1059-1062
Author(s):  
Ji Duo Jin ◽  
Ning Li ◽  
Zhao Hong Qin
Keyword(s):  
Nonlinear Dynamics ◽  
Numerical Analysis ◽  
Numerical Simulations ◽  
Nonlinear Model ◽  
Dynamical Behavior ◽  
Axial Flow ◽  
Viscous Force ◽  
Friction Drag ◽  
Flutter Instability ◽  
Nonlinear Force

The nonlinear dynamics are studied for a supported cylinder subjected to axial flow. A nonlinear model is presented for dynamics of the cylinder supported at both ends. The nonlinear terms considered here are the quadratic viscous force and the structural nonlinear force induced by the lateral motions of the cylinder. Using two-mode discretized equation, numerical simulations are carried out for the dynamical behavior of the cylinder to explain the flutter instability found in the experiment. The results of numerical analysis show that at certain value of flow velocity the system loses stability by divergence, and the new equilibrium (the buckled configuration) becomes unstable at higher flow leading to post-divergence flutter. The effect of the friction drag coefficients on the behavior of the system is investigated.

scholarly journals Analysis of the Impact of Model Nonlinearities in Inverse Problem Solving

2008 ◽  
Vol 65 (9) ◽  
pp. 2803-2823 ◽  
Author(s):  
T. Vukicevic ◽  
D. Posselt
Keyword(s):  
Inverse Problem ◽  
Numerical Analysis ◽  
Probability Density ◽  
Prior Knowledge ◽  
Nonlinear Model ◽  
Model Error ◽  
Forward Model ◽  
Time Space ◽  
Analysis Technique ◽  
The Impact

Abstract In this study, the relationship between nonlinear model properties and inverse problem solutions is analyzed using a numerical technique based on the inverse problem theory formulated by Mosegaard and Tarantola. According to this theory, the inverse problem and solution are defined via convolution and conjunction of probability density functions (PDFs) that represent stochastic information obtained from the model, observations, and prior knowledge in a joint multidimensional space. This theory provides an explicit analysis of the nonlinear model function, together with information about uncertainties in the model, observations, and prior knowledge through construction of the joint probability density, from which marginal solution functions can then be evaluated. The numerical analysis technique derived from the theory computes the component PDFs in discretized form via a combination of function mapping on a discrete grid in the model and observation phase space and Monte Carlo sampling from known parametric distributions. The efficacy of the numerical analysis technique is demonstrated through its application to two well-known simplified models of atmospheric physics: damped oscillations and Lorenz’s three-component model of dry cellular convection. The major findings of this study include the following: (i) Use of a nonmonotonic forward model in the inverse problem gives rise to the potential for a multimodal posterior PDF, the realization of which depends on the information content of the observations and on observation and model uncertainties. (ii) The cumulative effect of observations over time, space, or both could render the final posterior PDF unimodal, even with the nonmonotonic forward model. (iii) A greater number of independent observations are needed to constrain the solution in the case of a nonmonotonic nonlinear model than for a monotonic nonlinear or linear forward model for a given number of degrees of freedom in control parameter space. (iv) A nonlinear monotonic forward model gives rise to a skewed unimodal posterior PDF, implying a well-posed maximum likelihood inverse problem. (v) The presence of model error greatly increases the possibility of capturing multiple modes in the posterior PDF with the nonmonotonic nonlinear model. (vi) In the case of a nonlinear forward model, use of a Gaussian approximation for the prior update has a similar effect to an increase in model error, which indicates there is the potential to produce a biased mean central estimate even when observations and model are unbiased.

A novel nonlinear model of rotor/bearing/seal system and numerical analysis

2011 ◽  
Vol 46 (5) ◽  
pp. 618-631 ◽  
Author(s):  
Wei Li ◽  
Yi Yang ◽  
Deren Sheng ◽  
Jianhong Chen
Keyword(s):  
Numerical Analysis ◽  
Nonlinear Model ◽  
Rotor Bearing

Numerical analysis of a SWEAT structure with an improved one dimensional nonlinear model

1994 ◽  
Vol 34 (4) ◽  
pp. 689-702
Author(s):  
Marijan Maček ◽  
Al.V. Kordesch ◽  
Radko Osredkar
Keyword(s):  
Numerical Analysis ◽  
Nonlinear Model ◽  
One Dimensional

Modeling altruism and selfishness in welfare dynamics: The role of nonlinear interactions

2014 ◽  
Vol 24 (12) ◽  
pp. 2361-2381 ◽  
Author(s):  
Marina Dolfin ◽  
Mirosław Lachowicz
Keyword(s):  
Numerical Analysis ◽  
Probability Distribution ◽  
Nonlinear Model ◽  
Initial Value Problem ◽  
Wealth Distribution ◽  
System Of Equations ◽  
Nonlinear Interactions ◽  
Initial Value ◽  
Dynamic Variables

This paper deals with the modeling, qualitative and numerical analysis, of welfare dynamics in societies viewed as complex evolutive systems subject to different policies of wealth distribution. A nonlinear model of wealth distribution is presented. The state of a population is modeled by a probability distribution over wealth classes and the dynamic of interaction is parameterized by a threshold, whose dynamics depends on an internal competition related to the wealth distribution. Therefore, the model is a system of equations in which the threshold is one of the dynamic variables. The approach contains the whole path from modeling to simulations, through a qualitative analysis of the initial value problem.

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