Longitudinal lamb waves in a semi-infinite elastic layer

Gomilko, A. M.; Gorodetskaya, N. S.; Meleshko, V. V.

doi:10.1007/bf00896854

Cited by 4 publications

(5 citation statements)

References 5 publications

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“…In order to extend these results to general three-dimensional plates and different load distributions the Fourier transform and the Cauchy's theorem of residues can be used. For this approach it is referred to the works of Gomilko et al [79], Shi [233], Raghavan et al [205,206], Giurgiutiu [75,76], von Ende et al [262] and von Ende and Lammering [259,260]. In the work of Wilcox [268], the excitation matrices are defined to model Lamb waves excited by line and point forces.…”

Section: Methodsmentioning

confidence: 99%

Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review

Willberg

Duczek

Vivar-Perez

et al. 2015

Applied Mechanics Reviews

127

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This paper reviews the state-of-the-art in numerical wave propagation analysis. The main focus in that regard is on guided wave-based structural health monitoring (SHM) applications. A brief introduction to SHM and SHM-related problems is given, and various numerical methods are then discussed and assessed with respect to their capability of simulating guided wave propagation phenomena. A detailed evaluation of the following methods is compiled: (i) analytical methods, (ii) semi-analytical methods, (iii) the local interaction simulation approach (LISA), (iv) finite element methods (FEMs), and (v) miscellaneous methods such as mass–spring lattice models (MSLMs), boundary element methods (BEMs), and fictitious domain methods. In the framework of the FEM, both time and frequency domain approaches are covered, and the advantages of using high order shape functions are also examined.

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Section: Methodsmentioning

confidence: 99%

Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review

Willberg

Duczek

Vivar-Perez

et al. 2015

Applied Mechanics Reviews

127

View full text Add to dashboard Cite

show abstract

“…Here, the Fourier transform has proven to be an appropriate means and references [1] and [2] are early works dealing with this approach. More recent work using this method is presented in [3][4][5][6]. Alternative approaches have been developed in parallel.…”

Section: Introductionmentioning

confidence: 99%

Investigation on piezoelectrically induced Lamb wave generation and propagation

Ende¹,

Lammering²

2007

Smart Mater. Struct.

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An analytical solution for transient Lamb wave generation with piezoelectric wafers is presented. The time harmonic problem is solved in the wavenumber domain after Fourier transformation and subsequent inverse transformation by the residue theorem. To evaluate the solution for transient loading the Fourier transform is used again, this time with respect to the time variable. A standard numerical algorithm is utilized to evaluate the necessary integrals as well as the discrete Fourier transform. The solution is valid for the whole waveguide continuum and satisfies the underlying partial differential equations as well as the transient boundary conditions. A numerical example shows that the analytical solution coincides with the finite element result of the problem. The results of the analytical model are also confirmed by experimental investigations.

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“…: To obtain a practical solution of the system (5) we use the results of [5]. We obtain a finite system of N + 1 equations in the N + 2 unknowns A0, yk, k = 1, 2,..., N, and a0.…”

mentioning

confidence: 99%

“…where C is a coefficient determined according to [5] taking account of the solution of the system (5), and 1 r~-, ,, 2i~o ~a, 1 To verify the correctness of the computation of the coefficient C from formula (8) a control was placed on the precision with which the law of conservation of energy holds, in accordance with which the energy expended by the system must equal the energy carried off by the unique propagating wave. This is an additional criterion for the correctness of the results obtained.…”

mentioning

confidence: 99%

A dynamic saint-venant principle for an elastic semi-infinite strip

Gomilko¹,

Gorodetskaya²,

Meleshko³

1995

J Math Sci

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We consider the problem of longitudinal deformation of an elastic semi-infinite strip under the action of various kinds of self-balanced harmonic loads. Using numerical analysis we show that in a region of relatively low frequencies, when only one propagating wave ezists in the wave conductor, one can formulate an analog of Saint-Venant's principle. When this is done, the given frequency range decomposes into two subranges. In the first of these the main role in the Fourier series ezpansion of the load is played by the non-self-balanced component, while in the second it is necessary to take account of the first harmonic as well. One figure. Bibliography: 5 titles.The problem of enlarging the area of applicability of the static Saint-Venunt principle [1] to dynamic problems of the theory of elasticity has been studied for quite some time [2; 3], However, in the majority of existing publications only nonstationary processes were studied, and it was in relation to this case that the dynamic Saint-Venant principle for a semi-infinite elastic strip was stated. The study of the stationary harmonic problem for a semi-infinite strip is of equal interest, especially when one considers that in this case there will a priori be homogeneous waves propagating at any frequency, transporting energy to infinity. For that reason the statement of a dynamic Saint-Venant principle for an elastic semi-infinite strip has intrinsic scientific interest.: The purpose of the present article is to perform a quantitative analysis of the behavior of an elastic semi-infinite strip under the action of various kinds of self-balanced harmonic loads.Consider the two-dimensi0nal problem of the forced vibrations of a semi-infinite strip 0 < z < c~,

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Longitudinal lamb waves in a semi-infinite elastic layer

Cited by 4 publications

References 5 publications

Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review

Simulation Methods for Guided Wave-Based Structural Health Monitoring: A Review

Investigation on piezoelectrically induced Lamb wave generation and propagation

A dynamic saint-venant principle for an elastic semi-infinite strip

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