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The interaction of four parallel non-symmetric permeable cracks in a piezoelectric/piezomagnetic composite plane subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through a Fourier transform into four pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded as a series of Jacobi polynomials. Finally, the relationships among the electric displacement, magnetic flux and stress fields near the crack tips were obtained. The results show that the stress, the electric displacement and the magnetic flux intensity factors at the crack tips depend on the lengths and spacing of cracks. It was also revealed that the crack shielding effect is present in piezoelectric/piezomagnetic composites. 相似文献
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In this paper, we investigate the SH wave propagation in a layered piezoelectric (PE) and piezomagnetic (PM) plate with an imperfect magnetoelectroelastic interface. A linear magnetoelectroelastic spring model is used to describe the weakness of the imperfect interface. On the basis of this model, dispersion curves and mode shapes of the SH waves are computed. In particular, a PZT-5A/CoFe2O4 composite plate is considered in the numerical examples to calculate the dispersion curves and the mode shapes for different combinations of the magnetic, electrical and elastic spring constants. The effects of the layer thickness ratio and the electric-magnetic boundary conditions on the dispersion curves are discussed in details. Our results show that for a general weak bonding case, the high modes of the dispersion curves are not monotonous in the range of small wave numbers. With the layer thickness ratio increasing, the wave velocities of the SH waves increase. The electric boundary conditions mainly determine the dispersion curves of the SH waves in the case of a small layer thickness ratio, i.e. a large thickness of the PE layer. The present results have relevant applications in the nondestructive testing and evaluation of the layered PE/PM plate-like wave devices. 相似文献
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Using a stiffness matrix method, we in- vestigate the propagation behaviors of elastic waves in one-dimensional (1D) piezoelectric/piezomagnetic (PE/PM) phononic crystals (PCs) with line defects by calculating energy reflection/transmittion coefficients of quasi-pressure and quasi-shear waves. Line defects are created by the re- placement of PE or PM constituent layer. The defect modes existing in the first gap are considered and the influences on defect modes of the material properties and volume fraction of the defect layers, the type of incident waves, the location of defect layer and the number of structural layers are discussed in detail. Numerical results indicate that defect modes are the most obvious when the defect layers are inserted in the middle of the perfect PCs; the types of incidence wave and material properties of the defect layers have important effects on the numbers, the location of frequencies and the peaks of defect modes, and the defect modes are strongly de- pendent on volume fraction of the defect layers. We hope this paper will be found useful for the design of PE/PM acoustic filters or acoustic transducer with PCs structures. 相似文献
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Using a polarization method, the scattering problem for a two-dimensional inclusion embedded in infinite piezoelectric/piezomagnetic matrices is investigated. To achieve the purpose, the polarization method for a two-dimensional piezoelectric/piezo-magnetic "comparison body" is formulated. For simple harmonic motion, kernel of the polarization method reduces to a 2-D time-harmonic Green's function, which is ob-tained using the Radon transform. The expression is further simplified under condi-tions of low frequency of the incident wave and small diameter of the inclusion. Some analytical expressions are obtained. The analytical solutions for generalized piezoelec-tric/piezomagnetic anisotropic composites are given followed by simplified results for piezoelectric composites. Based on the latter results, two numerical results are provided for an elliptical cylindrical inclusion in a PZT-5H-matrix, showing the effect of different factors including size, shape, material properties, and piezoelectricity on the scattering cross-section. 相似文献
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Pei-Wei Zhang Zhen-Gong Zhou Lin-Zhi Wu 《Archive of Applied Mechanics (Ingenieur Archiv)》2009,79(10):965-979
In this paper, the behavior of three parallel non-symmetric permeable cracks in a piezoelectric/piezomagnetic material plane
subjected to anti-plane shear stress loading was studied by the Schmidt method. The problem was formulated through Fourier
transform into three pairs of dual integral equations, in which unknown variables are jumps of displacements across the crack
surfaces. To solve the dual integral equations, the jumps of displacements across the crack surfaces were directly expanded
as a series of Jacobi polynomials. Finally, the relations among the electric displacement, the magnetic flux and the stress
fields near the crack tips can be obtained. The results show that the stress, the electric displacement and the magnetic flux
intensity factors at the crack tips depend on the lengths and spacing of cracks. It was also revealed that the crack shielding
effect is present in piezoelectric/piezomagnetic materials. 相似文献
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This paper is concerned with the dynamic behaviors of wave propagation in layered periodic composites consisting of piezoelectric and piezomagnetic phases. The dispersion relations of Lamb waves axe derived. Dispersion curves and displacement fields are calculated with different piezoelectric volume fractions. Numerical results for BaTiO3/CoFe2O4 composites show that the dispersion curves resemble the symmetric Lamb waves in a plate. Exchange between the longitudinal (i.e. thickness) mode and coupled mode takes place at the crossover point between dispersion curves of the first two branches. With the increase of BaTiO3 volume fraction, the crossover point appears at a lower wave number and wave velocity is higher. These findings are useful for magnetoelectric transducer applications. 相似文献
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本文利用Hankel 变换及Copson 求解方法,得到了在无穷远处磁荷载以及对称力荷载作用下的无限大压磁材料中,硬币型裂纹在裂纹尖端含有环状力磁双屈服区情况下的相关解析解.本文考虑了磁屈服区尺寸小于、大于、等于力屈服区尺寸的三种情况.结果表明:屈服区尺寸不仅与外荷载及材料常数相关,更与力磁屈服区尺寸的相对大小有关;其中,较大尺寸的屈服区仅受同性质单一荷载影响,与材料常数无关;而较小尺寸屈服区受力磁两荷载与材料常数共同影响;裂纹张开位移、磁势跳变均沿裂纹面径向增大而减小;裂尖张开位移、裂尖磁势跳变与材料常数相关,且随外荷载增大而增大. 相似文献
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Zhen-Gong Zhou Pei-Wei Zhang Lin-Zhi Wu 《Archive of Applied Mechanics (Ingenieur Archiv)》2007,77(12):861-882
The solutions of a limited-permeable crack (case I) or two collinear limited-permeable cracks (case II) in piezoelectric/piezomagnetic materials subjected to a uniform tension loading were investigated in this paper using the
generalized Almansi’s theorem. At the same time, the electric permittivity and the magnetic permeability of air in crack were
firstly considered. Through the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations,
in which the unknown variables were jumps of displacements across crack surfaces, not the dislocation density functions or
the complex variable functions. To solve the dual integral equations, the jumps of displacements across crack surfaces were
directly expanded in a series of Jacobi polynomials to obtain the relations among electric displacement intensity factors,
magnetic flux intensity factors and stress intensity factors at crack tips. 相似文献