Abstract
Complex function and general conformal mapping methods are used to investigate the scattering of elastic shear waves by an elliptical cylindrical cavity in a radially inhomogeneous medium. The conformal mappings are introduced to solve scattering by an arbitrary cavity for the Helmholtz equation with variable coefficient through the transformed standard Helmholtz equation with a circular cavity. The medium density depends on the distance from the origin with a power-law variation and the shear elastic modulus is constant. The complex-value displacements and stresses of the inhomogeneous medium are explicitly obtained and the distributions of the dynamic stress for the case of an elliptical cavity are discussed. The accuracy of the present approach is verified by comparing the present solution results with the available published data. Numerical results demonstrate that the wave number, inhomogeneous parameters and different values of aspect ratio have significant influence on the dynamic stress concentration factors around the elliptical cavity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Afsar AM and Go J (2010), “Finite Element Analysis of Thermoelastic Field in a Rotating FGM Circular Disk,” Applied Mathematical Modelling, 34(11):3309–3320.
Ashrafi H, Asemi K and Shariyat M (2013), “A Threedimensional Boundary Element Stress and Bending Analysis of Transversely/Longitudinally Graded Plates with Circular Cutouts under Biaxial Loading,” European Journal of Mechanics — A/Solids, 42: 344–357.
Liu DK, Gai BZ and Tao GY (1982), “Applications of the Method of Complex Functions to Dynamic Stress Concentrations,” Wave Motion, 4(3):293–304.
Liu QJ, Zhao MJ and Zhang C (2014), “Antiplane Scattering of SH Waves by a Circular Cavity in an Exponentially Graded Half Space,” International Journal of Engineering Science, 78: 61–72.
Martin PA (2009), “Scattering by a Cavity in an Exponentially Graded Half-space,” Journal of Applied Mechanics, 76(3):31009.
Martin PA (2011), “Scattering by Defects in an Exponentially Graded Layer and Misuse of the Method of Images,” International Journal of Solids and Structures, 48(14):2164–2166.
Mohammadi M, Dryden JR and Jiang L (2011), “Stress Concentration around a Hole in a Radially Inhomogeneous Plate,” International Journal of Solids and Structures, 48(3):483–491.
Nie GJ and Batra RC (2010), “Static Deformations of Functionally Graded Polar-orthotropic Cylinders with Elliptical Inner and Circular Outer Surfaces,” Composites Science and Technology, 70(3):450–457.
Pao YH and Mow CC (1973), Diffraction of Elastic Waves and Dynamic Stress Concentrations, Crane and Russak, New York.
Yang Q and Gao CF (2013), “Dynamic Stress Analysis of a Functionally Graded Material Plate with a Circular Hole,” Meccanica, 48(1):91–101.
Yang Q, Gao CF and Chen W (2010), “Stress Analysis of a Functional Graded Material Plate with a Circular Hole,” Archive of Applied Mechanics, 80(8):895–907.
Zhou CP, Hua C, Fai M and Liu DK (2013), “Elastic Wave Scattering and Dynamic Stress Concentrations in Exponential Graded Materials with Two Elliptic Holes,” Wave Motion, 51(3):466–475.
Author information
Authors and Affiliations
Corresponding author
Additional information
Supported by: National Science & Technology Pillar Program under Grant No. 2015BAK17B06, Natural Science Foundation of Heilongjiang Province, China under Grant No. A201310, Scientific Research Starting Foundation for Post Doctorate of Heilongjiang Province, China under Grant No. LBH-Q13040 and the Fundamental Research Funds for the Central Universities of China under Grant No. HEUCF150203
Rights and permissions
About this article
Cite this article
Hei, B., Yang, Z. & Chen, Z. Scattering of shear waves by an elliptical cavity in a radially inhomogeneous isotropic medium. Earthq. Eng. Eng. Vib. 15, 145–151 (2016). https://doi.org/10.1007/s11803-016-0311-7
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11803-016-0311-7