Vibration and Wave Propagation Approaches Applied to Assess Damage Influence on the Behavior of Euler-Bernoulli Beams: Part II Inverse Problem

2009 ◽  
Author(s):  
K.M. Fernandes ◽  
L.T. Stutz ◽  
R.A. Tenenbaum ◽  
A.J. Silva Neto
Keyword(s):  
Inverse Problem ◽  
Wave Propagation

scholarly journals Reconstruction of Initial Wave Field of a Nonsteady-State Wave Propagation from Limited Measurements at a Specific Spatial Point Based on Stochastic Inversion

2013 ◽  
Vol 2013 ◽  
pp. 1-10 ◽  
Author(s):  
S. L. Han ◽  
Takeshi Kinoshita
Keyword(s):  
Inverse Problem ◽  
Wave Propagation ◽  
Wave Field ◽  
Simulated Data ◽  
Initial Surface ◽  
Reconstruction Procedure ◽  
Inference Problem ◽  
State Wave ◽  
Initial Wave ◽  
Nonsteady State

This paper studies an inverse problem that can be used for reconstructing initial wave field of a nonsteady-state wave propagation. The inverse problem is ill posed in the sense that small changes in the input data can greatly affect the solution of the problem. To address the difficulty, the problem is formulated in the form of an inference problem in an appropriately constructed stochastic model. It is shown that the stochastic inverse model enables the initial surface disturbance to be reconstructed, including its confidence intervals given the noisy measurements. The reconstruction procedure is illustrated through applications to some simulated data for two- and three-dimensional problem.

Inverse problem of wave propagation in a random medium

1982 ◽  
Vol 19 (4) ◽  
pp. 1329-1334
Author(s):  
A. S. Blagoveshchenskii
Keyword(s):  
Inverse Problem ◽  
Wave Propagation ◽  
Random Medium

scholarly journals Inverse boundary-value problem for the equation of longitudinal wave propagation with non-self-adjoint boundary conditions

Filomat ◽  
2019 ◽  
Vol 33 (16) ◽  
pp. 5259-5271
Author(s):  
Elvin Azizbayov ◽  
Yashar Mehraliyev
Keyword(s):  
Inverse Problem ◽  
Wave Propagation ◽  
Boundary Value Problem ◽  
Boundary Conditions ◽  
Longitudinal Wave ◽  
Existence And Uniqueness ◽  
Original Problem ◽  
Boundary Value ◽  
Inverse Boundary ◽  
Longitudinal Wave Propagation

We study the inverse coefficient problem for the equation of longitudinal wave propagation with non-self-adjoint boundary conditions. The main purpose of this paper is to prove the existence and uniqueness of the classical solutions of an inverse boundary-value problem. To investigate the solvability of the inverse problem, we carried out a transformation from the original problem to some equivalent auxiliary problem with trivial boundary conditions. Applying the Fourier method and contraction mappings principle, the solvability of the appropriate auxiliary inverse problem is proved. Furthermore, using the equivalency, the existence and uniqueness of the classical solution of the original problem are shown.

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