Scattering of the harmonic anti-plane shear waves by a crack in functionally graded piezoelectric materials

BIEM analysis of dynamically loaded anti-plane cracks in graded piezoelectric finite solids

“…The current FGPM used in surface acoustic wave (SAW) devices can produce interesting combinations of properties such as gradients in electrical conductivity across any desired spatial direction, see Chakraborty et al (2005) and Kumar and Simha (2007). This fact stimulates the modeling of graded materials with different types of modulus variation, see Li and Weng (2002a,b), Rangelov et al (2008), Ma et al (2005), Chen et al (2003) and . More or less the most of the mechanical models describing the inhomogeneous material profiles are based on the assumption that material properties vary in similar manner that is an idealization.…”

“…A strip with a crack parallel to the edge and exponentially varying material properties according to the space coordinates was treated by Wang et al (2003). Anti-plane crack analysis of graded piezoelectric materials under dynamic loading is investigated in Singh et al (2007Singh et al ( , 2009, Kwon et al (2002), Kwon and Lee (2004), Kwon (2003), Liang (2006), Jin and Zhong (2002), Ma et al (2004Ma et al ( , 2005. Recently also a variety of meshless methods has been proposed and applied for in-plane dynamic analysis in cracked graded piezoelectrics, see .…”

On acoustic and electric waves diffraction in piezoelectric medium by a permeable half-plane crack

“…Shindo [20], Shindo et al [23], Gu et al [11], Ueda [25], Ma et al [18], Grigoryan and Melkumyan [7], [8]. In all these papers authors have adopted the quasi-static approximation for piezoelectric materials.…”

Dynamic behavior of cracked magnetoelectroelastic composites at different boundary conditions

“…Here 44 c is the elastic module, 15 e is the piezoelectric coefficient, 15 q is the piezomagnetic coefficient, 11 is the dielectric permittivity, 11 is the magnetic permeability, 11 d is the magnetoelectric coefficient, 3 u is the out-ofplane mechanical displacement, and are electric and magnetic potential respectively, 3 i is the mechanical stress, i D is the inplane electrical displacement, i B is the inplane magnetic induction, 1, 2 i and comma means differentiation. Applying the equation of motion in the absence of body forces, the equations of Maxwell in the absence of electric charges and current densities and (2) 0, q u d where is a two-dimensional Laplace operator and is the density.…”