Abstract
By using the complex variable function theory and the conformal mapping method, the scattering of plane shear wave (SH-wave) around an arbitrary shaped nano-cavity is studied. Surface effects at the nanoscale are explained based on the surface elasticity theory. According to the generalized Yong–Laplace equations, the boundary conditions are given, and the infinite algebraic equations for solving the unknown coefficients of the scattered wave solutions are established. The numerical solutions of the stress field can be obtained by using the orthogonality of trigonometric functions. Lastly, the numerical results of dynamic stress concentration factor around a circular hole, an elliptic hole and a square hole as the special cases are discussed. The numerical results show that the surface effect and wave number have a significant effect on the dynamic stress concentration, and prove that our results from theoretical derivation are correct.
Highlights
Since the scattering problem plays an important role in understanding the propagation phenomena of various waves in engineering materials and structures, the elastic wave scattering by the cavity embedded in the elastic matrix have always been a hot topic in wave motion theory. e application and development of mineral exploration, petroleum acquisition, quantitative nondestructive exploration, radar, underwater sonar, blasting and other technologies are all based on understanding the relationship between the scattering of elastic waves and the geometrical dimensions and physical parameters of defective bodies in elastic matrix
In this work, based on the theory of surface elasticity, the scattering of shear wave (SH-wave) around an arbitrary shaped nano-cavity embedded in an in nite elastic medium is studied, in which the numerical solutions of displacement elds are expressed by employing the complex variable function theory and the conformal mapping. e numerical results of dynamic stress concentration factor about a circular hole, an elliptic hole are illustrated graphically. e e ects of surface energy on the dynamic stress concentration factor in the matrix material are analyzed. e paper is organized as follows
In order to study the e ect of surface e ects on dynamic stress concentration factors (DSCF), we de ne DSCF to be DSCF = ᐈᐈᐈᐈᐈᐈᐈᐈᐈ 0 ᐈᐈᐈᐈᐈᐈᐈᐈᐈ, (31)
Summary
Since the scattering problem plays an important role in understanding the propagation phenomena of various waves in engineering materials and structures, the elastic wave scattering by the cavity embedded in the elastic matrix have always been a hot topic in wave motion theory. e application and development of mineral exploration, petroleum acquisition, quantitative nondestructive exploration, radar, underwater sonar, blasting and other technologies are all based on understanding the relationship between the scattering of elastic waves and the geometrical dimensions and physical parameters of defective bodies in elastic matrix. Using the complex variable function theory, Liu [2] discussed the dynamic stress concentration around a circular hole caused by SH-wave in an anisotropic medium. Wu and Ou [24, 25] studied the interface e ects of SH-waves’ scattering around a cylindrical nano-inclusion by wave functions expansion method and complex variable function theory respectively. In this work, based on the theory of surface elasticity, the scattering of SH-wave around an arbitrary shaped nano-cavity embedded in an in nite elastic medium is studied, in which the numerical solutions of displacement elds are expressed by employing the complex variable function theory and the conformal mapping.
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
