TY - JOUR

T1 - Wave function expansion method for the scattering of SH waves by two symmetrical circular cavities in two bonded exponentially graded half spaces

AU - Liu, Qijian

AU - Zhao, Mingjuan

AU - Liu, Zhongxian

PY - 2019

Y1 - 2019

N2 - A wave function expansion method for out-of-plane scattering of SH waves by two symmetrical circular cavities in two bonded exponentially graded half spaces is presented by using the plane elastic complex variable theory. The medium is composed of a semi-infinite homogeneous space with a circular cavity and a bonded exponentially graded half-space with a symmetrical circular cavity along the boundary interface. In terms of Helmholtz decomposition to the wave propagation equation, the stresses and displacements of the medium are expressed by the displacement potentials. The scattered waves by the boundary interface are assumed to transmit from the images of the origins of the respective two cavities. A conformal mapping function is introduced to convert the physical plane of two bonded semi-infinite spaces into two jointed concentric annular regions. The boundary value problem is formulated as a series of infinite algebraic equations. The convergence of the present solution is examined by investigating the variations of the solution results with the truncation of the series number. Parametric study shows that the interface displacements are almost independent to the inhomogeneous coefficient βR of the right medium. The amplification of the interface displacement becomes great for high incident frequency and with the decreasing of the distance-to-radius ratio h/R. The distribution of stress concentration of the right cavity depends significantly on the inhomogeneous coefficient βR, the distance-radius ratio h/R, the incident angle and frequency of the excitations.

AB - A wave function expansion method for out-of-plane scattering of SH waves by two symmetrical circular cavities in two bonded exponentially graded half spaces is presented by using the plane elastic complex variable theory. The medium is composed of a semi-infinite homogeneous space with a circular cavity and a bonded exponentially graded half-space with a symmetrical circular cavity along the boundary interface. In terms of Helmholtz decomposition to the wave propagation equation, the stresses and displacements of the medium are expressed by the displacement potentials. The scattered waves by the boundary interface are assumed to transmit from the images of the origins of the respective two cavities. A conformal mapping function is introduced to convert the physical plane of two bonded semi-infinite spaces into two jointed concentric annular regions. The boundary value problem is formulated as a series of infinite algebraic equations. The convergence of the present solution is examined by investigating the variations of the solution results with the truncation of the series number. Parametric study shows that the interface displacements are almost independent to the inhomogeneous coefficient βR of the right medium. The amplification of the interface displacement becomes great for high incident frequency and with the decreasing of the distance-to-radius ratio h/R. The distribution of stress concentration of the right cavity depends significantly on the inhomogeneous coefficient βR, the distance-radius ratio h/R, the incident angle and frequency of the excitations.

KW - Complex variable method

KW - Exponentially graded material

KW - Scattering of SH waves

KW - Two symmetrical circular cavities

KW - Wave function expansion method

UR - http://www.scopus.com/inward/record.url?scp=85067068055&partnerID=8YFLogxK

U2 - 10.1016/j.enganabound.2019.05.015

DO - 10.1016/j.enganabound.2019.05.015

M3 - Article

AN - SCOPUS:85067068055

VL - 106

SP - 389

EP - 396

JO - Engineering Analysis with Boundary Elements (Print)

JF - Engineering Analysis with Boundary Elements (Print)

SN - 0955-7997

ER -