Asymptotic Analyses of the Pulse Shape Evolution and of the Inverse Problem of Acoustic Evaluation in Case of the Nonlinear Hereditary Medium

Nigul, U. K.

doi:10.1007/978-3-642-82006-9_25

Search citation statements

Order By: Relevance

Paper Sections

Select...

Ri(t) = -Ko[alte) + 2#(e)]1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

1999

2002

Publication Types

Select...

Article3

Relationship

Self Cite0

Independent3

Authors

Journals

Cited by 3 publications

(1 citation statement)

References 3 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[26]- [28]). But sometimes the a priori intbrmation that we know about the kernel contains only the physical positivity and monotonicity.…”

Section: Ri(t) = -Ko[alte) + 2#(e)]mentioning

confidence: 99%

Nondestructive characterization of materials with variable properties

Ravasoo

Janno

2001

Acta Mechanica

View full text Add to dashboard Cite

Summary. Materials with continuous variable properties in time and space are considered. The possibiiity of nondestructive characterization of these materials on the basis of nonlinear longitudinal wave propagation data is discussed on the basis of recent results. The model direct and inverse problems are solved. The utilization of obtained results enables one to solve several nondestructive material characterization problems.

show abstract

“…[26]- [28]). But sometimes the a priori intbrmation that we know about the kernel contains only the physical positivity and monotonicity.…”

Section: Ri(t) = -Ko[alte) + 2#(e)]mentioning

confidence: 99%

Nondestructive characterization of materials with variable properties

Ravasoo

Janno

2001

Acta Mechanica

View full text Add to dashboard Cite

show abstract

Direct and inverse problems on nonlinear rods

Folkow

Kreider

1999

Mathematics and Computers in Simulation

View full text Add to dashboard Cite

An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods

Kim

Kreider

2002

Journal of Applied Mathematics

View full text Add to dashboard Cite

Elastic wave propagation in weakly nonlinear elastic rods is considered in the time domain. The method of wave splitting is employed to formulate a standard scattering problem, forming the mathematical basis for both direct and inverse problems. A quasi-linear version of the Wendroff scheme (FDTD) is used to solve the direct problem. To solve the inverse problem, an asymptotic expansion is used for the wave field; this linearizes the order equations, allowing the use of standard numerical techniques. Analysis and numerical results are presented for three model inverse problems: (i) recovery of the nonlinear parameter in the stress-strain relation for a homogeneous elastic rod, (ii) recovery of the cross-sectional area for a homogeneous elastic rod, (iii) recovery of the elastic modulus for an inhomogeneous elastic rod.

show abstract

Asymptotic Analyses of the Pulse Shape Evolution and of the Inverse Problem of Acoustic Evaluation in Case of the Nonlinear Hereditary Medium

Cited by 3 publications

References 3 publications

Nondestructive characterization of materials with variable properties

Nondestructive characterization of materials with variable properties

Direct and inverse problems on nonlinear rods

An asymptotic approach to inverse scattering problems on weakly nonlinear elastic rods

Contact Info

Product

Resources

About