Non-Local Theory Solution for an Anti-Plane Shear Permeable Crack in Functionally Graded Piezoelectric Materials

Zhou, Zhen-Gong; Wang, Biao

doi:10.1007/s10443-006-9021-z

Cited by 11 publications

(4 citation statements)

References 50 publications

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“…However, in the nonlocal continuum theory presented by Eringen [24,25], the stress at a reference point is considered as a function of the strain at every point in the body. Then, the long-range force of microstructures can be considered and are applied widely in fracture mechanics [38], contact mechanics [39] and dislocation theory [40]. The most general form of the constitutive equation for nonlocal elasticity involves an integral over the entire region of interest.…”

Section: Mathematical Formulationmentioning

confidence: 99%

Dispersion of Transverse Waves in Single-Wall Carbon Nanotubes

Selim

2019

Acta Phys. Pol. A

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In this work we investigate the influence of initial stress on the transverse waves propagation in single-wall carbon nanotubes with small scale effects under ultrahigh frequency (above k = 1nm −1 ), using the nonlocal continuum theory. The phase and group velocities are derived in a simple way. The effects of wave numbers, scale coefficients and initial stress parameter on phase and group velocity are analyzed. The results show that the dispersion properties of the transverse wave propagation in a single-wall carbon nanotube are induced by small scale effects, which cannot appear in classical models. Also, it is clear that the increase of the scale coefficient and wave number could be strengthened by the dispersion degree of the phase and group velocity of transverse waves. In particular, the analysis shows that the compression initial stress in a single-wall carbon nanotube does not only affect the number of transverse wave speeds and the magnitude of transverse wave speeds, but also the critical value of the wave number at the wave speed changes. The effects of the initial stress and small scale on the transverse wave propagation in single-wall carbon nanotubes may result in some complex dynamic phenomena of terahertz sound waves propagation in the carbon nanotubes, which can be used as a useful reference for the designs of nanodrive devices, nanooscillators and nanosensors.

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Section: Mathematical Formulationmentioning

confidence: 99%

Dispersion of Transverse Waves in Single-Wall Carbon Nanotubes

Selim

2019

Acta Phys. Pol. A

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“…and Yong and Zhou (2007) studied both the impermeable and permeable cracks in a FGPM layer bonded to two dissimilar homogeneous piezoelectric half spaces. Zhou and Wang (2006) solved an anti-plane shear crack in FGPMs using non-local theory. Jiang (2008) investigated the fracture behavior of FGPMs with dielectric cracks.…”

Section: Introductionmentioning

confidence: 99%

A moving interface crack between two dissimilar functionally graded piezoelectric layers under electromechanical loading

Shin

Lee

2010

International Journal of Solids and Structures

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a b s t r a c tThe dynamic propagation of an interface crack between two dissimilar functionally graded piezoelectric material (FGPM) layers under anti-plane shear is analyzed using the integral transform method. The properties of the FGPM layers vary continuously along the thickness. The properties of the FGPM layers vary differently and the two layers are connected weak-discontinuously. A constant velocity Yoffe-type moving crack is considered. Fourier transform is used to reduce the problem to two sets of dual integral equations, which are then expressed to the Fredholm integral equations of the second kind. Numerical values on the dynamic energy release rate (DERR) are presented for the FGPM to show the effects on the electric loading, gradient of material properties, crack moving velocity, and thickness of layers. Followings are helpful to increase of the resistance of the interface crack propagation of FGPM: (a) certain direction and magnitude of the electric loading; (b) increase of the gradient of material properties; (c) increase of the material properties from the interface to the upper and lower free surface; (d) increase of the thickness of FGPM layer. The DERR increases or decreases with increase of the crack moving velocity.

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“…In this field, the effects of initial stress on the non-coaxial resonance of multi-walled nanotubes (MWNTs) have been investigated by the theories of Euler–Bernoulli and Timoshenko beams, respectively, in Wang et al [ 24 ] and Cai et al [ 25 ]. Based on the Euler–Bernoulli beam theory, Zhang et al [ 26 ] studied the transverse vibrations of DWNTs under compressive axial load. They pointed out that the natural frequencies are dependent on the axial load and decrease with an increase in the axial load, and that the associated amplitude ratios of the inner to the outer tubes of DWNTs are independent of the axial load.…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Vibration of a Pre-Stressed Water-Filled Single-Walled Carbon Nanotube Using Shell Model

Selim

Musa

2020

Nanomaterials

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This paper is an attempt to study the nonlinear vibration of a pre-stressed single-walled carbon nanotube (SWCNT) with water-filled and simply supported ends. A new analytical formula is obtained for the nonlinear model based on the simplified Donnell’s shell theory. The effects of internal fluid on the coupling vibration of the SWCNT–water system are discussed in detail. Furthermore, the influence of the different nanotube thicknesses and radiuses on the nonlinear vibration frequencies is investigated according to the shell theory. Numerical calculations are done to show the effectiveness of the proposed schemes. The results show that the nonlinear frequency grew with the increasing nonlinear parameters (radius and thickness of nanotube). In addition, it is shown that the influence of the nonlinear parameters is greater at the lower mode in comparison with the higher mode for the same nanotube thickness and radius.

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Non-Local Theory Solution for an Anti-Plane Shear Permeable Crack in Functionally Graded Piezoelectric Materials

Cited by 11 publications

References 50 publications

Dispersion of Transverse Waves in Single-Wall Carbon Nanotubes

Dispersion of Transverse Waves in Single-Wall Carbon Nanotubes

A moving interface crack between two dissimilar functionally graded piezoelectric layers under electromechanical loading

Nonlinear Vibration of a Pre-Stressed Water-Filled Single-Walled Carbon Nanotube Using Shell Model

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