Dynamic stress analysis of scattering by a circular cavity in a radially inhomogeneous unbounded space under SH waves

Abstract The density of a radially inhomogeneous unbounded space is derived as a function form. Harmonic dynamics stress of the radially inhomogeneous medium with a circular cavity is investigated by the complex variable function method. The governing equation under incident SH waves in the radially inhomogeneous unbounded medium is expressed as a Helmholtz equation with a variable coefficient. It is equivalently transformed into a standard Helmholtz equation by the conformal transformation method. Then, the stress fields in the radially inhomogeneous medium can be proposed. The results indicate that the changes in density parameter of the medium and wave number further affect the dynamic stress concentration factor around the circular cavity.

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Dynamic Stress Analysis Around a Circular Cavity in Two-Dimensional Inhomogeneous Medium with Density Variation

Journal of Mechanics ◽

10.1017/jmech.2016.7 ◽

2016 ◽

Vol 32 (5) ◽

pp. 519-526

Author(s):

B.-P. Hei ◽

Z.-L. Yang ◽

B.-T. Sun ◽

D.-K. Liu

Keyword(s):

Stress Concentration ◽

Helmholtz Equation ◽

Inhomogeneous Medium ◽

Dynamic Stress ◽

Complex Function ◽

Transformation Method ◽

Dynamic Stress Concentration ◽

Circular Cavity ◽

Two Dimensional ◽

Complex Function Theory

AbstractBased on the complex function theory and the homogenization principle, an universal approach of solving the dynamic stress concentration around a circular cavity in two-dimensional (2D) inhomogeneous medium is developed. The Helmholtz equation with variable coefficient is converted to the standard Helmholtz equation by means of the general conformal transformation method (GCTM) analytically. As an example, the inhomogeneous medium with density varying as a function of two spatial coordinates and the constant elastic modulus is studied. The dynamic stress concentration factors (DSCF) are calculated numerically. It shows that medium inhomogeneous parameters and wave numbers have significant influence on the dynamic stress concentration by the circular cavity in two-dimensional inhomogeneous medium.

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Dynamic Stress Analysis of SH Waves Scattering Around a Circular Cavity in Inhomogeneous Medium

2019 13th Symposium on Piezoelectrcity, Acoustic Waves and Device Applications (SPAWDA) ◽

10.1109/spawda.2019.8681882 ◽

2019 ◽

Author(s):

Ji-sheng PAN ◽

Zai-lin YANG ◽

Yong YANG ◽

Guan-xi-xi JIANG ◽

Yun-qiu SONG ◽

...

Keyword(s):

Stress Analysis ◽

Inhomogeneous Medium ◽

Dynamic Stress ◽

Circular Cavity ◽

Sh Waves ◽

Dynamic Stress Analysis

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Surface Effects on the Scattering of SH-Wave Around an Arbitrary Shaped Nano-Cavity

Advances in Mathematical Physics ◽

10.1155/2019/3084581 ◽

2019 ◽

Vol 2019 ◽

pp. 1-9

Author(s):

Hongmei Wu ◽

Zhiying Ou

Keyword(s):

Stress Concentration ◽

Dynamic Stress ◽

Numerical Solutions ◽

Surface Effects ◽

Numerical Results ◽

Wave Number ◽

Dynamic Stress Concentration ◽

Sh Wave ◽

Special Cases ◽

Variable Function

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.

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