Scattering of SH wave by a crack in a functionally graded one dimensional hexagonal piezoelectric quasicrystals

Yang, Junfeng; Wang, Xu; Ding, Shenghu; Li, Xing

doi:10.1002/zamm.202200071

Cited by 4 publications

(4 citation statements)

References 39 publications

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“…Using the above expression of 𝑓(𝑡 2 ) and the value of 𝐿(𝑣, 𝑤) given by the Equation (28) into Equation (25) and equating the coefficients of similar power of 𝑘 𝑠 we get…”

Section: Solutionmentioning

confidence: 99%

“…The constitutive equations () are simplified as follows Yang et al. [25, 26]:

\begin{matrix} {\hat{τ}}_{z y} & = C_{44} \partial_{y} {\overset{u}{true}}_{z} + R_{3} \partial_{y} {\overset{w}{true}}_{z} + e_{15} \partial_{y} \hat{φ} \\ {\hat{τ}}_{z x} & = C_{44} \partial_{x} {\overset{u}{true}}_{z} + R_{3} \partial_{x} {\overset{w}{true}}_{z} + e_{15} \partial_{x} \hat{φ} \\ {\hat{scriptH}}_{z y} & = R_{3} \partial_{y} {\overset{u}{true}}_{z} + K_{2} \partial_{y} {\overset{w}{true}}_{z} + d_{15} \partial_{y} \hat{φ} \\ {\hat{scriptH}}_{z x} & = R_{3} \partial_{x} {\overset{u}{true}}_{z} + K_{2} \partial_{x} {\overset{w}{true}}_{z} + d_{15} \partial_{x} \hat{φ} \\ {\hat{scriptD}}_{y} & = e_{15} \partial_{y} {\overset{u}{true}}_{z} + d_{15} \partial_{y} {\overset{w}{true}}_{z} - ε_{11} \partial_{y} \hat{φ} \\ {\hat{scriptD}}_{x} & = e_{15} \partial_{x} {\overset{u}{true}}_{z} + d_{15} \partial_{x} {\overset{w}{true}}_{z} \end{matrix}

…”

Section: Description and Formulation Of The Problemmentioning

confidence: 99%

“…Using Fourier transform, the general solution of Equation () is given by (Yang et al. [25, 26])

\begin{equation} \begin{aligned} &\varphi _1(x,y)=\frac{2}{\pi }\int _{0}^{\infty }\mathcal {A}_1(s)e^{-\gamma _1y}\cos (sx)ds\\ &\varphi _2(x,y)=\frac{2}{\pi }\int _{0}^{\infty }\mathcal {A}_2(s)e^{-\gamma _2y}\cos (sx)ds\\ &\varphi _3(x,y)=\frac{2}{\pi }\int _{0}^{\infty }\mathcal {A}_3(s)e^{-sy}\cos (sx)ds \end{aligned} \end{equation}

where,

\gamma _1=\sqrt {s^2-\frac{k_s^2}{\mathcal {K}+a}},\;\gamma _2=\sqrt {s^2-\frac{k_s^2}{\mathcal {C}-a}}

and

\mathcal {A}_1(s),\;\mathcal {A}_2(s)

and

\mathcal {A}_3(s)

are unknown functions...…”

Section: Induction Of Dual Integral Equationsmentioning

confidence: 99%

“…A Yoffe type running crack in 1D hexagonal PQCs under anti-plane shear load is examined by Zhou and Li [24]. Yang et al [25,26] studied the dynamic crack problem in a non-homogeneous 1D hexagonal PQCs under SH-wave. Shear wave interaction with two collinear dynamic cracks in 1D hexagonal PQCs is not studied yet according to the authors knowledge.…”

Section: Introductionmentioning

confidence: 99%

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Interaction of anti‐plane shear waves with two collinear cracks in 1D hexagonal piezoelectric quasicrystals

Panja,

Mandal

2023

Z Angew Math Mech

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The present article presents the interaction of anti‐plane shear waves by two collinear cracks in one dimensional (1D) hexagonal piezoelectric quasicrystals (PQCs). With the aid of Fourier transform, the mixed boundary value problem (MBVP) is transformed into three pairs of dual integral equations, which are solved analytically by Hilbert transform. The explicit expressions for dynamic stress intensity factors (DSIFs) of phonon and phason fields, crack opening displacement (COD) and electric displacement (ED) are derived in closed form and some special cases are studied. Numerical values of DSIFs of phonon and phason fields, COD and ED are plotted to show the effect of crack length and electric boundary condition. Moreover, the DSIFs of phonon field and COD are represented graphically for single crack.

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Section: Solutionmentioning

confidence: 99%

“…The constitutive equations () are simplified as follows Yang et al. [25, 26]: