Computer Simulation for Active Control of Vibration in Beam Structures

1995 ◽  
Author(s):  
Masa. Tanaka ◽  
T. Matsumoto ◽  
L. Huang
Keyword(s):  
Inverse Problem ◽  
Active Control ◽  
Inverse Analysis ◽  
Taylor Series Expansion ◽  
Integral Equation Method ◽  
Unknown Parameters ◽  
Bending Vibration ◽  
Linear System Of Equations ◽  
Elastic Beams ◽  
The Laplace Transform

Abstract This paper is concerned with an inverse problem of the active control of non-steady dynamic vibration in elastic beams. A simulation technique based on the boundary element method and the extended Kalman filter or a new filter theory is successfully applied to the inverse problem. The Laplace-transform integral equation method is used for the solution of dynamic bending vibration in elastic beams. Through a Taylor series expansion, the linear system of equations is derived for modification of the unknown parameters, and it is solved iteratively so that an appropriate norm is minimized. The usefulness of the proposed method of inverse analysis is demonstrated through numerical computation of a few examples.

scholarly journals Reconstructing The Moore-Gibson-Thompson Equation

2020 ◽  
Vol 7 (1) ◽  
pp. 219-223
Author(s):  
Waled Al-Khulaifi ◽  
Amin Boumenir
Keyword(s):  
Inverse Problem ◽  
Laplace Transform ◽  
Arbitrary Point ◽  
Unknown Parameters ◽  
Third Order ◽  
Memory Kernel ◽  
Single Observation ◽  
The Laplace Transform

AbstractWe are concerned with the inverse problem of recovering a third order Moore-Gibson-Thompson equation from a single observation of its solution at an arbitrary point. We show how to reconstruct its three unknown parameters and the memory kernel by using the Laplace transform.

Lipschitz stability for a semi-linear inverse stochastic transport problem

2020 ◽  
Vol 28 (2) ◽  
pp. 185-193
Author(s):  
Zhongqi Yin
Keyword(s):  
Inverse Problem ◽  
Main Tool ◽  
Terminal State ◽  
Lipschitz Stability ◽  
Unknown Parameters ◽  
Initial Displacement ◽  
Stochastic Transport ◽  
Random Term ◽  
Global Carleman Estimate ◽  
Stochastic Transport Equation

AbstractThis paper is addressed to a semi-linear stochastic transport equation with three unknown parameters. It is proved that the initial displacement, the terminal state and the random term in diffusion are uniquely determined by the state on partial boundary and a Lipschitz stability of the inverse problem is established. The main tool we employ is a global Carleman estimate for stochastic transport equations.

scholarly journals Comparison Methods for Solving Non-Linear Sturm–Liouville Eigenvalues Problems

Symmetry ◽  
2020 ◽  
Vol 12 (7) ◽  
pp. 1179 ◽  
Author(s):  
Kamel Al-Khaled ◽  
Ashwaq Hazaimeh
Keyword(s):  
Variational Iteration Method ◽  
The Other ◽  
Sinc Method ◽  
Linear System Of Equations ◽  
Non Linear ◽  
The Laplace Transform ◽  
Sturm Liouville ◽  
Linear Differential ◽  
Non Linear System ◽  
Adomian’S Polynomials

In this paper, we present a comparative study between Sinc–Galerkin method and a modified version of the variational iteration method (VIM) to solve non-linear Sturm–Liouville eigenvalue problem. In the Sinc method, the problem under consideration was converted from a non-linear differential equation to a non-linear system of equations, that we were able to solve it via the use of some iterative techniques, like Newton’s method. The other method under consideration is the VIM, where the VIM has been modified through the use of the Laplace transform, and another effective modification has also been made to the VIM by replacing the non-linear term in the integral equation resulting from the use of the well-known VIM with the Adomian’s polynomials. In order to explain the advantages of each method over the other, several issues have been studied, including one that has an application in the field of spectral theory. The results in solutions to these problems, which were included in tables, showed that the improved VIM is better than the Sinc method, while the Sinc method addresses some advantages over the VIM when dealing with singular problems.

Research on Interval Reversible Inverse Analysis Method Based on Interval Parameters

2013 ◽  
Vol 706-708 ◽  
pp. 556-559 ◽  
Author(s):  
Jing Bo Su ◽  
Hong Bing Liu ◽  
Hui De Zhao ◽  
Dong Zhang
Keyword(s):  
Inverse Analysis ◽  
Measured Data ◽  
Analysis Method ◽  
Analysis Model ◽  
Parameter Perturbation ◽  
Unknown Parameters ◽  
Interval Parameters ◽  
Linear Elastic ◽  
Interval Analysis Method ◽  
Inverse Analysis Method

In this paper, the interval analysis method is introduced and an uncertainty inverse analysis method is presented. The intervals of unknown parameters can be obtained by the input of measured data. Even for few measured data, the analysis results can be also obtained by the inverse analysis method. And the analysis results can be applied to appraise the uncertainty in interval. Based on parameter perturbation, the reversible inverse analysis model is proposed for linear-elastic problems. A numerical example is given to illustrate the validity of the present method. The influence is illustrated about different measured precisions and different numbers of analyzing parameters on the inverse analysis results. And the conditions of existence or convergence of the solution are given.

Computation of residual statics using projectors

Geophysics ◽  
1985 ◽  
Vol 50 (9) ◽  
pp. 1502-1504 ◽  
Author(s):  
Koraljka Čaklović ◽  
Lavoslav Čaklović
Keyword(s):  
System Of Equations ◽  
Unknown Parameters ◽  
Linear System Of Equations ◽  
Common Depth Point ◽  
Reference Trace ◽  
Position Index ◽  
Static Corrections ◽  
The Common ◽  
System 1 ◽  
Text Correction

The residual statics problem, as we know, is treated as the solution of one linear system of equations. If we assume that the static corrections are “surface consistent,” then we know that time shifts of each trace can be written as the sum of three terms [Formula: see text] where i = 1, …, [Formula: see text] is the shot position index with [Formula: see text] the number of shot positions, j = 1, …, [Formula: see text] is the receiver position index with [Formula: see text] the number of receiver positions, k = 1, …, [Formula: see text] is the common‐depth‐point (CDP) position index with [Formula: see text] the number of common depth points, [Formula: see text] = correction for ith shot position, [Formula: see text] = correction for jth receiver position, and [Formula: see text] = correction for each trace in the kth CDP gather. For every pair (i, j) we have one equation. We write system (1) in matrix form as [Formula: see text] where [Formula: see text] is the vector of unknown parameters; and [Formula: see text] is the vector which consists of the time shifts obtained by crosscorrelation of each trace in CDP gather with the corresponding reference trace.

scholarly journals A Nonlinear Solute Transport Model and Data Reconstruction with Parameter Determination in an Undisturbed Soil-Column Experiment

2011 ◽  
Vol 2011 ◽  
pp. 1-14 ◽  
Author(s):  
Gongsheng Li ◽  
De Yao ◽  
Yongzai Wang ◽  
Xianzheng Jia
Keyword(s):  
Inverse Problem ◽  
Solute Transport ◽  
Transport Model ◽  
Soil Column ◽  
Parameter Determination ◽  
Nonlinear Transport ◽  
Inversion Algorithm ◽  
Unknown Parameters ◽  
Undisturbed Soil ◽  
Optimal Perturbation

A real undisturbed soil-column infiltrating experiment in Zibo, Shandong, China, is investigated, and a nonlinear transport model for a solute ion penetrating through the column is put forward by using nonlinear Freundlich's adsorption isotherm. Since Freundlich's exponent and adsorption coefficient and source/sink terms in the model cannot be measured directly, an inverse problem of determining these parameters is encountered based on additional breakthrough data. Furthermore, an optimal perturbation regularization algorithm is introduced to determine the unknown parameters simultaneously. Numerical simulations are carried out and then the inversion algorithm is applied to solve the real inverse problem and reconstruct the measured data successfully. The computational results show that the nonlinear advection-dispersion equation discussed in this paper can be utilized by hydrogeologists to research solute transport behaviors with nonlinear adsorption in porous medium.

Inverse Problem of the Interval Linear System of Equations

Computing ◽  
1999 ◽  
Vol 63 (2) ◽  
pp. 185-200 ◽  
Author(s):  
N. P. Seif ◽  
M. A. Hassanein ◽  
A. S. Deif
Keyword(s):  
Inverse Problem ◽  
Linear System ◽  
System Of Equations ◽  
Linear System Of Equations ◽  
Interval Linear System ◽  
Interval Linear
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