Effective spring boundary conditions for a damaged interface between dissimilar media in three-dimensional case

Golub, Mikhail V.; Doroshenko, Olga V.; Boström, Anders E

doi:10.1016/j.ijsolstr.2015.11.021

Cited by 22 publications

(14 citation statements)

References 37 publications

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“…More than two decades later, Bostrom & Golub extended this concept for SH waves in a plate [51]. Later, Golub et al further developed this idea by constructing an analytical formula for the reflection of bulk shear waves from a circular crack in a 3D system [52]. Despite the simplifications introduced by operating at the low frequency limit, the solutions developed generally still rely on numerical solvers to compute the solution to integral equations and are limited to certain canonical crack shapes.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Scattering of the Fundamental Shear Guided Wave From a Surface-Breaking Crack in Plate-Like Structures

Chua

Cawley

Nagy

2019

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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Cracks in critical sections of steel structures pose a major safety concern in many industries. Existing high frequency ultrasonic techniques offer high detection sensitivity to cracks but have poor inspection volume coverage, limiting their practical use for monitoring large areas of structures. Low frequency guided waves have relatively high inspection area coverage and are currently used in pipeline monitoring for corrosion defects, but face challenges in detecting critical cracks which often cause over an order of magnitude lower cross sectional area loss. A study of scattering from small cracks in a thin-walled (<12 mm) section with an incident plane SH0 guided wave at higher frequencies but remaining below the SH1 cut-off is presented here using quasistatic approximations, the aim being to explore the possibility of using this regime for crack growth monitoring applications. A 3D solution was developed using dimensional analysis, which showed that the SH0 reflection ratio is proportional to frequency to the power 1.5, to the effective crack size cubed, and is inversely proportional to the plate thickness and to the square root of the distance from the crack to the receiving sensor. Finite element analysis was used to validate these power coefficients and to calculate the proportionality constant. The results show that a higher inspection frequency offers improved sensitivity but the validity of the results here is limited to the SH1 cut-off frequency. The predicted 3D solution was validated by measurements on a pipe with a progressively grown notch.

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Section: Introduction and Related Workmentioning

confidence: 99%

Scattering of the Fundamental Shear Guided Wave From a Surface-Breaking Crack in Plate-Like Structures

Chua

Cawley

Nagy

2019

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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“…In the case of debonding, a crack of width a at the interface S is assumed so that the interface

consists of the debonded area

, where the stress-free boundary conditions ( 9 ) are assumed, and contact area

, where wave-fields satisfy continuous boundary conditions ( 10 ). For degradation modeling, i.e., for the the second kind of damage, the spring boundary condition [ 36 , 37 ]

with diagonal stiffness matrix

, is introduced. SBC ( 12 ) assumes the continuity of the traction vector at the interface, where the displacement vector has a jump proportional to the traction vector.…”

Section: Analysis: Wave Phenomenamentioning

confidence: 99%

“…Two kinds of defects were considered: the partial degradation of the interface simulated by the spring boundary conditions (SBCs) and a one-sided open crack between the obstacle and the waveguide, simulating a debonding. For the first kind, SBCs were used, since the analytic relations derived in [ 36 , 37 , 38 ] can be used for the estimation of the severity of damage. It should be noted that the detection of the concentration of micro-cracks is among the current SHM problems.…”

Section: Introductionmentioning

confidence: 99%

Lamb Wave Scattering Analysis for Interface Damage Detection between a Surface-Mounted Block and Elastic Plate

Golub

Shpak

Mueller

et al. 2021

Sensors

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Since stringers are often applied in engineering constructions to improve thin-walled structures’ strength, methods for damage detection at the joints between the stringer and the thin-walled structure are necessary. A 2D mathematical model was employed to simulate Lamb wave excitation and sensing via rectangular piezoelectric-wafer active transducers mounted on the surface of an elastic plate with rectangular surface-bonded obstacles (stiffeners) with interface defects. The results of a 2D simulation using the finite element method and the semi-analytical hybrid approach were validated experimentally using laser Doppler vibrometry for fully bonded and semi-debonded rectangular obstacles. A numerical analysis of fundamental Lamb wave scattering via rectangular stiffeners in different bonding states is presented. Two kinds of interfacial defects between the stiffener and the plate are considered: the partial degradation of the adhesive at the interface and an open crack. Damage indices calculated using the data obtained from a sensor are analyzed numerically. The choice of an input impulse function applied at the piezoelectric actuator is discussed from the perspective of the development of guided-wave-based structural health monitoring techniques for damage detection.

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“…(19)- (24) and (29) with the property that det 1, Eqs. (17) and (18) can be rewritten explicitly as,…”

Section: Calculation Of the Amplitude Reflection And Transmission Coementioning

confidence: 99%

“…Spring-type interface models have been utilized extensively to characterize a contacting interface between rough surfaces of solid bodies [8]- [13], a partially closed crack [14], [15], concentration of microcracks [16]- [18], a fracture in rock mass [19]- [23], adhesion at double interfaces between an adhesive layer and two adherents [24]- [28], multiple interlayer thin resin-rich zones of polymer-based composite laminates [29]- [33], and multiple rock joints [34], [35].…”

Section: Introductionmentioning

confidence: 99%

Second-harmonic generation in a multilayered structure with nonlinear spring-type interfaces embedded between two semi-infinite media

2018

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The acoustic second-harmonic generation behavior in a multilayered structure with nonlinear spring-type interlayer interfaces is analyzed theoretically to investigate the frequency dependence of second-harmonic amplitudes in the reflected and transmitted fields when the structure is subjected to the normal incidence of a monochromatic longitudinal wave. The multilayered structure consists of identical linear elastic layers and is embedded between two identical linear elastic semi-infinite media. The layers are bonded to each other by spring-type interfaces possessing identical linear stiffness but different quadratic nonlinear parameters. By combining a perturbation analysis with the transfer-matrix method, analytical expressions are derived for the second-harmonic amplitudes of the reflected and transmitted waves. The second-harmonic amplitudes due to a single nonlinear interface are shown to vary remarkably with the fundamental frequency, reflecting the pass and stop band characteristics of the Bloch wave in the corresponding infinitely extended layered structure. By calculating the spatial distribution of second-harmonic amplitude inside the multilayered structure, the influence of the position of the nonlinear interface as well as the number of layers on the frequency dependence of second-harmonic amplitudes of the reflected and transmitted waves is elucidated. When all interlayer interfaces possess the identical nonlinearity, the second-harmonic amplitudes on both sides of the structure are shown to increase monotonically with the number of layers in the frequency ranges where both fundamental and double frequencies are within the pass bands of Bloch wave. The influence of two non-dimensional parameters, i.e., the relative linear compliance of the interlayer interfaces and the acoustic impedance ratio between the layer and the surrounding semi-infinite medium, on the second-harmonic amplitudes is elucidated.

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Effective spring boundary conditions for a damaged interface between dissimilar media in three-dimensional case

Cited by 22 publications

References 37 publications

Scattering of the Fundamental Shear Guided Wave From a Surface-Breaking Crack in Plate-Like Structures

Scattering of the Fundamental Shear Guided Wave From a Surface-Breaking Crack in Plate-Like Structures

Lamb Wave Scattering Analysis for Interface Damage Detection between a Surface-Mounted Block and Elastic Plate

Second-harmonic generation in a multilayered structure with nonlinear spring-type interfaces embedded between two semi-infinite media

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