Diffraction of Plane Compressional Waves by an Array of Nanosized Cylindrical Holes

2010 ◽  
Vol 78 (2) ◽  
Author(s):  
Q. F. Zhang ◽  
G. F. Wang ◽  
P. Schiavone
Keyword(s):  
Surface Energy ◽  
Dynamic Stress ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Stress Concentrations ◽  
Compressional Waves ◽  
Circular Holes ◽  
Cylindrical Holes ◽  
Effect Of Surface ◽  
Dynamic Stress Concentrations

When the radius of a hole reduces to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the present paper, we consider the diffraction of plane compressional waves by an array of nanosized circular holes in an elastic medium. The effect of surface energy is taken into account through surface elasticity theory. Using the wave expansion method, we derive the corresponding elastic diffraction fields. Dynamic stress concentrations around the holes and the scattering cross section are calculated to address the surface effects on the diffraction phenomena.

Effects of Surface Energy on Scattering of SH Waves by an Elastic Half-Plane with a Semi-Cylindrical Cavity

2012 ◽  
Vol 627 ◽  
pp. 698-704
Author(s):  
Zhi Ying Ou ◽  
Xiao Wei Liu ◽  
Qiong Deng
Keyword(s):  
Surface Energy ◽  
Cylindrical Cavity ◽  
Dynamic Stress ◽  
Shear Waves ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Stress Fields ◽  
Sh Waves ◽  
Wave Function Expansion Method ◽  
Incident Waves

When the radius of materials and structral devices reduces to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the frame of surface elasticity, the scattering of anti-plan shear waves by an elastic half-plan with a semi-cylindrical cavity considered the surface energy are investigated in this paper. When the boundary condition at the straight edge of the half-plan is traction free, the analytical solutions of stress fields of the half plan with semi-culindrical cavity are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of anti-plan shear waves as the radius of the semi-cylindrical cavity shrinks to nanoscale. The effects of incident waves with different frequencies and incident angel, radius of semi-cylindrical cavity and surface energy on the dynamic stress concentration around the semi-cylindrical cavity are discussed in detail.

Dynamic Stress Concentrations at Circular Holes in Struts

1965 ◽  
Vol 7 (1) ◽  
pp. 23-27 ◽  
Author(s):  
J. W. Dally ◽  
W. F. Halbleib
Keyword(s):  
Fringe Pattern ◽  
Dynamic Stress ◽  
Static Stress ◽  
Stress Concentrations ◽  
Circular Holes ◽  
The Difference ◽  
Dynamic Stress Concentrations

Dynamic stress concentrations were determined for a strut with a centrally located hole by employing photoelastic measurements. Single spark photography together with controlled repeated loadings on Columbia resin CR-39 models was utilized to obtain the dynamic fringe pattern. In general, it was found that the dynamic stress concentrations differed significantly from the static stress concentrations. The difference depended upon the geometry of the model and the location at the boundary of the hole.

Effect of Surface Elasticity on Scattering of Plane P-Waves by an Elastic Half-Plane with a Semi-Cylindrical Cavity

2013 ◽  
Vol 303-306 ◽  
pp. 2656-2660 ◽  
Author(s):  
H. M Wu ◽  
Z. Y. Ou
Keyword(s):  
Surface Energy ◽  
Half Plane ◽  
Cylindrical Cavity ◽  
Surface Elasticity ◽  
Expansion Method ◽  
P Waves ◽  
Compressional Waves ◽  
Wave Function Expansion Method ◽  
Plane P Waves ◽  
Incident Waves

When the characteristic sizes of materials and elements reduce to nanometers, the influence of surface energy becomes prominent in its mechanical behavior. In the frame of surface elasticity, the scattering of of plane compressional waves (P-waves) by a semi-cylindrical cavity embedded in an elastic half-plane is investigated in this paper. By using the wave function expansion method, we obtain the analytical solutions of elastci fields. The results show that surface energy has a significant effect on the diffractions of P-waves as the radius of the semi-cylindrical cavity shrinks to nanoscale. For incident waves with different frequencies, radius of semi-cylindrical cavity, the effects of surface elasticity on the dynamic stress concentration around the semi-cylindrical cavity are discussed in detail.

EFFECTS OF INTERFACE ENERGY ON MULTIPLE SCATTERING OF PLANE COMPRESSIONAL WAVES BY TWO CYLINDRICAL FIBERS

2012 ◽  
Vol 04 (04) ◽  
pp. 1250040 ◽  
Author(s):  
Z. Y. OU ◽  
D. W. LEE
Keyword(s):  
Surface Energy ◽  
Multiple Scattering ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Interface Energy ◽  
Dynamic Mechanical Properties ◽  
Addition Theorem ◽  
Inhomogeneous Materials ◽  
Compressional Waves ◽  
Eigenfunction Expansion Method

The multiple scattering of plane compressional waves by two cylindrical fibers with interface effects is investigated. Based on surface elasticity theory, the wave fields in a nanoscale solid medium can be obtained by applying the eigenfunction expansion method and the Graf's addition theorem. Our results indicate that surface energy significantly affects the diffraction of elastic waves, as the radii of the fibers approach nanometers. The dynamic stress concentration factors at the interfaces between the fibers and the matrix under incident plane compressional waves at different frequencies are examined to determine the effects of surface energy, properties of inhomogeneous materials, and the interaction between fibers in multiple scattering phenomena. These results are helpful in understanding the dynamic mechanical properties of nanocomposites, and the proposed method for investigating the multiple scattering of plane compressional waves can be extended to the case of fiber-reinforced composites.

Dynamic Stress Concentrations Due to Scattering of Elastic SV Waves from a Coated Nanoinclusion with Considerations in the Interfacial Region

2016 ◽  
Vol 33 (3) ◽  
pp. 279-288
Author(s):  
A. R. Ghanei Mohammadi ◽  
P. Hosseini Tehrani
Keyword(s):  
Dynamic Stress ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Interface Energy ◽  
Interfacial Region ◽  
Stress Concentrations ◽  
Wave Function Expansion Method ◽  
Navier Equation ◽  
Stress Concentration Factors ◽  
Elastic Shear

AbstractThe problem of plane elastic shear waves (SV waves) scattering from a circular nanoinclusion surrounded by an inhomogeneous interphase embedded in an elastic matrix is investigated analytically in this paper. An approach is introduced to account for the simultaneous effects of a graded interphase and surface/interface energy based on Gurtin-Murdoch's model of surface elasticity. Using the wave function expansion method, the Navier equation is solved for all three phases (nanofiber-interphase- matrix). Presenting the results in dimensionless manner, Dynamic Stress Concentration Factors (DSCF) for the present problem are obtained and the effects of several parameters on the results are studied in detail. It is understood that taking the effects of both surface/interface and interphase inhomogeneity into account leads to a significant influence on the DSCF results and consequently on the overall dynamic behavior of the nanocomposites.

Effects of Surface Elasticity on Scattering of P Waves by an Elastic Half-Plane with a Nanosized Semi-Cylindrical Inclusion

2013 ◽  
Vol 303-306 ◽  
pp. 2661-2666
Author(s):  
Zhi Ying Ou ◽  
Cheng Liu ◽  
Xiao Wei Liu
Keyword(s):  
Surface Energy ◽  
Half Plane ◽  
Surface Effect ◽  
Surface Elasticity ◽  
Expansion Method ◽  
Cylindrical Inclusion ◽  
P Waves ◽  
Wave Function Expansion Method ◽  
Plane P Waves ◽  
Incident Waves

The scattering of plane P waves by a nanosized semi-cylindrical inclusion embedded in an elastic half-plan has been studied in this paper. To account for the surface effect at nanoscale, the surface elasticity is also adopted. When the boundary condition at the straight edge of the half-plane is traction free, the analytical solutions of stress fields of the half plan with semi-cylindrical inclusion are expressed by employing a wave function expansion method. The results show that surface energy has a significant effect on the scattering of plane P waves as the radius of the semi-cylindrical inclusion shrinks to nanoscale. For incident waves with different frequencies, radius of semi-cylindrical inclusion, the effects of surface energy on the dynamic stress concentration near the semi-cylindrical inclusion are discussed in detail.

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