Nonlinearity of solids with micro- and nanodefects and characteristic features of its macroscopic manifestations

Руденко, О. В.; Коробов, А. И.; Izosimova, M. Yu.

doi:10.1134/s1063771010020053

Cited by 13 publications

(3 citation statements)

References 3 publications

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“…8b, the background reproduces the amplitude dis tribution corresponding to the disk excitation at the eigenfrequency. On this background, one can see regions of an increase in local amplitude, which corre spond to the mouths of cracks, which represent regions of the specimen where the nonclassical non linear elasticity is maximal [9].…”

Section: Nonlinear Interaction Of Amplitude Modulated Lamb Waves In Amentioning

confidence: 99%

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Diagnostics of metal plates with residual stresses and defects by nonlinear scanning laser vibrometry

2015

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Nonlinear scanning laser vibrometry is used for diagnostics of cylindrical resonators made of poly crystalline aluminum alloy with residual stresses and defects. The diagnostics is performed with flexural Lamb waves. The eigenmode frequency of such a resonator is found to depend on the amplitude of flexural Lamb waves excited in it (the fast dynamics effect), which points to the presence of a nonclassical nonlinear elastic ity in the resonator material. Studying the nonlinear interactions between amplitude modulated flexural Lamb waves in resonators allow the determination of the coordinates of defects and residual strains in them.

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Section: Nonlinear Interaction Of Amplitude Modulated Lamb Waves In Amentioning

confidence: 99%

“…The structural nonlinearity may far exceed the classical nonlinearity [5]. Possible phys ical mechanisms of nonclassical nonlinearity were considered in [6][7][8][9][10]. It was demonstrated that non classical nonlinearity is local and exhibits a threshold type behavior.…”

Section: Introductionmentioning

confidence: 99%

Diagnostics of metal plates with residual stresses and defects by nonlinear scanning laser vibrometry

2015

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“…There are four common sources of nonlinearity in a vibrating beam: (1) geometric nonlinearity, i.e., nonlinearity in the strain-displacement relationship, (2) material nonlinearity, i.e., nonlinearity in the stress-strain relationship, (3) combined geometric and material nonlinearity, and (4) physical nonlinearity arising from cracks and defects in the solid. Sources 1 through 3 are termed as classical sources of nonlinearity, while the nonlinearity arising from cracks and defects is termed as nonclassical nonlinearity [11][12][13][14][15]. Of the classical sources, there is abundant literature on geometric nonlinearity of beams since this applies to cases of thin beams which can undergo large deformations, such as thin composite beams, microelectromechanical systems (MEMS), etc.…”

Section: Introductionmentioning

confidence: 99%

Analytical Study of Nonlinear Flexural Vibration of a Beam with Geometric, Material and Combined Nonlinearities

Madhuranthakam,

Chakrapani

2024

Vibration

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This article explores the nonlinear vibration of beams with different types of nonlinearities. The beam vibration was modeled using Hamilton’s principle, and the equation of motion was solved using method of multiple time scales. Three models were developed assuming (a) geometric nonlinearity, (b) material nonlinearity and (c) combined geometric and material nonlinearity. The material nonlinearity also included both third and fourth nonlinear elasticity terms. The frequency response equation of these models were further evaluated quantitatively and qualitatively. The models capture the hardening effect, i.e., increase in resonant frequency as a function of forcing amplitude for geometric nonlinearity, and the softening effect, i.e., decrease in resonant frequency for material nonlinearity. The model is applied on the first three bending modes of the cantilever beam. The effect of the fourth-order material nonlinearity was smaller compared to the third-order term in the first mode, whereas it is significantly larger in second and third mode. The combined nonlinearity models shows a discontinuous frequency shift, which was resolved by utilizing a set of transition assumptions. This results in a smooth transition between the material and geometric zones in amplitude. These parametric models allow us to fine tune the nonlinear response of the system by changing the physical properties such as geometry, linear and nonlinear elastic properties.

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Non-destructive evaluation of corrosion in steel liner plates embedded in concrete using nonlinear ultrasonics

Nilsson,

Huttunen-Saarivirta,

Bohner

et al. 2023

Construction and Building Materials

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Nonlinearity of solids with micro- and nanodefects and characteristic features of its macroscopic manifestations

Cited by 13 publications

References 3 publications

Diagnostics of metal plates with residual stresses and defects by nonlinear scanning laser vibrometry

Diagnostics of metal plates with residual stresses and defects by nonlinear scanning laser vibrometry

Analytical Study of Nonlinear Flexural Vibration of a Beam with Geometric, Material and Combined Nonlinearities

Non-destructive evaluation of corrosion in steel liner plates embedded in concrete using nonlinear ultrasonics

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