The method of wave-function expansion in elliptical coordinates,elliptical cosine half-range expansion and Mathieu function were applied to obtain an exact analytical solution of the dynamic stress concentration facto...The method of wave-function expansion in elliptical coordinates,elliptical cosine half-range expansion and Mathieu function were applied to obtain an exact analytical solution of the dynamic stress concentration factor(DSCF)around an elliptical cavity in a shallow,semi-elliptical hill.An infinite system of simultaneous linear equations for solving this problem was established by substituting the wave expression obtained by the Mathieu function including the standing wave expression of elliptical lining given herein into the boundary condition obtained by the region-matching method.The finite equations system with unknown coefficients obtained by truncation were solved numerically,and the results in the case of an ellipse degenerating into a circle were compared with previous results to verify the accuracy of the method.The effects of different aspect ratios,incident wave angles and aperture ratios on the dynamic stress concentration around the elliptical cavity were described.Some numerical results,when the elliptical hill was changed into a circular one,were analyzed and compared in detail.In engineering,this model can be regarded as a semi-cylindrical hill with an elliptical cylindrical unlined tunnel under the action of SH waves,and the results are significant in aseismic design.展开更多
The scattering of shear waves (SH waves) by nano-scale arbitrary shape inclusion in infinite plane is studied by complex variable function theory. Firstly, the governing equation and the relationships between stress a...The scattering of shear waves (SH waves) by nano-scale arbitrary shape inclusion in infinite plane is studied by complex variable function theory. Firstly, the governing equation and the relationships between stress and displacement are given by classical elastic theory. Secondly, the arbitrary shape inclusion in the two-dimensional plane is transformed into a unit circle domain by conformal mapping, the incident wave field and the scattered wave field are presented. Next, the stress and displacement boundary conditions are established by considering surface elasticity theory, The infinite algebraic equations for solving the unknown coefficients of the scattered and standing waves are obtained. Finally, the influence of surface effect, non-dimensional wave number, Shear modulus and hole curvature on the dynamic stress concentration factor are analyzed by some examples, the numerical results show that the surface effect weakens the dynamic stress concentration. With the increase of wave number, the dynamic stress concentration factor (DSCF) decreases. Shear modulus and hole curvature have significant effects on DSCF.展开更多
Wave propagation in an infinite elastic piezoelectric medium with a circular cavity and an impermeable crack subjected to steady-state anti-plane shearing was studied based on Green's function and the crack-divisi...Wave propagation in an infinite elastic piezoelectric medium with a circular cavity and an impermeable crack subjected to steady-state anti-plane shearing was studied based on Green's function and the crack-division technique.Theoretical solutions were derived for the whole elastic displacement and electric potential field in the interaction between the circular cavity and the impermeable crack.Expressions were obtained on the dynamic stress concentration factor(DSCF) at the cavity's edge,the dynamic stress intensity factor(DSIF) and the dynamic electric displacement intensity factor(DEDIF) at the crack tip.Numerical solutions were performed and plotted with different incident wave numbers,parameters of piezoelectric materials and geometries of the structure.Finally,some of the calculation results were compared with the case of dynamic anti-plane interaction of a permeable crack and a circular cavity in an infinite piezoelectric medium.This paper can provide a valuable reference for the design of piezoelectric actuators and sensors widely used in marine structures.展开更多
基金Fundamental Research Funds for Central Universities under Grant No.3072019CF0205。
文摘The method of wave-function expansion in elliptical coordinates,elliptical cosine half-range expansion and Mathieu function were applied to obtain an exact analytical solution of the dynamic stress concentration factor(DSCF)around an elliptical cavity in a shallow,semi-elliptical hill.An infinite system of simultaneous linear equations for solving this problem was established by substituting the wave expression obtained by the Mathieu function including the standing wave expression of elliptical lining given herein into the boundary condition obtained by the region-matching method.The finite equations system with unknown coefficients obtained by truncation were solved numerically,and the results in the case of an ellipse degenerating into a circle were compared with previous results to verify the accuracy of the method.The effects of different aspect ratios,incident wave angles and aperture ratios on the dynamic stress concentration around the elliptical cavity were described.Some numerical results,when the elliptical hill was changed into a circular one,were analyzed and compared in detail.In engineering,this model can be regarded as a semi-cylindrical hill with an elliptical cylindrical unlined tunnel under the action of SH waves,and the results are significant in aseismic design.
文摘The scattering of shear waves (SH waves) by nano-scale arbitrary shape inclusion in infinite plane is studied by complex variable function theory. Firstly, the governing equation and the relationships between stress and displacement are given by classical elastic theory. Secondly, the arbitrary shape inclusion in the two-dimensional plane is transformed into a unit circle domain by conformal mapping, the incident wave field and the scattered wave field are presented. Next, the stress and displacement boundary conditions are established by considering surface elasticity theory, The infinite algebraic equations for solving the unknown coefficients of the scattered and standing waves are obtained. Finally, the influence of surface effect, non-dimensional wave number, Shear modulus and hole curvature on the dynamic stress concentration factor are analyzed by some examples, the numerical results show that the surface effect weakens the dynamic stress concentration. With the increase of wave number, the dynamic stress concentration factor (DSCF) decreases. Shear modulus and hole curvature have significant effects on DSCF.
基金Supported by the Natural Science Foundation of Heilongjiang Province of China (A00-10)the Basis Research Foundation of Harbin Engineering University (HEUF04008)
文摘Wave propagation in an infinite elastic piezoelectric medium with a circular cavity and an impermeable crack subjected to steady-state anti-plane shearing was studied based on Green's function and the crack-division technique.Theoretical solutions were derived for the whole elastic displacement and electric potential field in the interaction between the circular cavity and the impermeable crack.Expressions were obtained on the dynamic stress concentration factor(DSCF) at the cavity's edge,the dynamic stress intensity factor(DSIF) and the dynamic electric displacement intensity factor(DEDIF) at the crack tip.Numerical solutions were performed and plotted with different incident wave numbers,parameters of piezoelectric materials and geometries of the structure.Finally,some of the calculation results were compared with the case of dynamic anti-plane interaction of a permeable crack and a circular cavity in an infinite piezoelectric medium.This paper can provide a valuable reference for the design of piezoelectric actuators and sensors widely used in marine structures.
