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 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.

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.

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 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.

Surface/Interface Effect on Dynamic Stress Around a Nanoinclusion in a Semi-Infinite Slab Under Shear Waves

2012 ◽  
Vol 134 (6) ◽  
Author(s):  
Xue-Qian Fang ◽  
Le-Le Zhang ◽  
Jin-Xi Liu ◽  
Wen-Jie Feng
Keyword(s):  
Dynamic Stress ◽  
Numerical Solutions ◽  
Shear Waves ◽  
Expansion Method ◽  
Interface Effect ◽  
Image Method ◽  
Dynamic Stress Concentration Factor ◽  
Wave Function Expansion Method ◽  
Infinite Slab ◽  
Incident Waves

This work examines the surface/interface effect on the dynamic stress around a cylindrical nanoinclusion embedded in an elastic semi-infinite slab subjected to antiplane shear waves, and the nanosize effect is considered. The wave function expansion method is employed to express the wave fields in the nanosized structure. The traction free boundary conditions at the three edges of this structure are considered and satisfied by using the image method. The analytical and numerical solutions of the dynamic stress concentration factor around the nanoinclusion are presented. Analyses show that the three edges of the nanosized structure manifest different effects of the dynamic stress around the nanoinclusion. The size effect is also related to the interface properties, the wave frequency of incident waves, and the material properties ratio of the nanoinclusion to matrix. To show the accuracy of the results for certain given parameters, comparison with the existing results is also given.

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.

scholarly journals Scattering of Incident P-Waves by a Semicylindrical Core-Shell Structure in an Elastically Constrained Half-Space at Nanoscale

2020 ◽  
Vol 2020 ◽  
pp. 1-11
Author(s):  
R. Zhang ◽  
D. X. Lei ◽  
Z. Y. Ou
Keyword(s):  
Half Space ◽  
Shell Structure ◽  
Dynamic Stress ◽  
Surface Elasticity ◽  
Core Shell ◽  
P Waves ◽  
Compressional Waves ◽  
The Core ◽  
Dynamic Stress Concentration Factor ◽  
Core Shell Structure

Under the premise of the theory of surface elasticity, the scattering of plane compressional waves (P-waves) in the surface of a semicylindrical core-shell structure within the nanoscale elastic confinement half-space is studied by using the method of eigen-function expansion. The generalized Y-L equation is used to give the nanoscale boundary conditions, and the dynamic stress concentration factor (DSCF) along the interface of core-shell structure induced by the plane elastic wave are derived and numerically evaluated. Under different incident wave frequencies, surface energy, and shear modulus, when the radius of the core-shell structure is reduced to the nanometer level, their influence on the DSCF is very significant. These have been confirmed by numerical calculations.

scholarly journals Influence of Bearing on Pier Failure Considering the Separation Condition under Near-Fault Earthquake

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 692
Author(s):  
Wenjun An ◽  
Guquan Song
Keyword(s):  
Expansion Method ◽  
Transient Wave ◽  
Earthquake Excitation ◽  
Near Fault ◽  
Continuous Beam Bridge ◽  
Wave Function Expansion Method ◽  
Earthquake Action ◽  
Stiffness And Damping ◽  
Beam Bridge ◽  
Bending Failure

To study the influence of the near-fault vertical earthquake, the beam-spring-damper-pier model is used to simulate the double-span continuous beam bridge. The transient wave function expansion method and the indirect mode function method are used to calculate the seismic response of the bridge. The theoretical solutions of the contact force and displacement response of the bridge under vertical earthquake excitation near-fault are derived. By using piers with three different heights, the influence of vertical separation on pier-bending failure is analyzed reasonably. The results show that under the near-fault earthquake action, the split has a certain influence on the pier failure. Moreover, the stiffness and damping of the bearing have an influence on the pier failure, and the change of the maximum pier height has different effects. Therefore, for bridges of different sizes, it is of great significance to select the appropriate stiffness and damping bearings to reduce pier failure.

Quaternion-based anisotropic inversion for flexural waves in horizontal transverse isotropic formations with unmatched sources: A synthetic example

Geophysics ◽  
2018 ◽  
Vol 83 (5) ◽  
pp. A69-A74 ◽  
Author(s):  
Fuqiang Zeng ◽  
Wenzheng Yue ◽  
Chao Li
Keyword(s):  
Structural Information ◽  
Amplitude Ratio ◽  
Flexural Wave ◽  
Data Sets ◽  
Flexural Waves ◽  
P Waves ◽  
Source Type ◽  
Transverse Isotropic ◽  
Sonic Logging ◽  
Incident Waves

The anisotropy of elastic waves has been widely used to obtain structural information on formations in geosciences research. Flexural wave splitting is generally applied to evaluate anisotropy with geophysical inversion methods. Cross-dipole sonic logging has been widely used for anisotropic inversions in horizontal transverse isotropic formations. Traditional methods assume that fast and slow flexural waves are similar in shape and are not dispersive and that the radiation characteristics of the two orthogonal dipole sources are identical. The two above assumptions cannot be satisfied in field conditions. Therefore, the methods used in anisotropy inversion based on these assumptions will lead to inaccurate results. The introduction of the amplitude ratio (AR), the ratio of slow to fast flexural waves, which is not dependent on the source type, can eliminate the wave-shape assumption. Two data sets from orthogonally oriented receivers can be constructed as a quaternion array. Fast and slow flexural waves are the two main incident waves, and other arrivals such as P-waves can be taken as noise. The AR and a quaternion multiple signal classification algorithm are used to demonstrate how to improve the anisotropic inversion and avoid these assumptions. Compared with the traditional method, the new method presents better inversion results for the synthetic example with two different sources. We have determined that the inversion residual from the new objective function can be used to indicate the inversion quality.

Pull-In Instability of Functionally Graded Cantilever Nanoactuators Incorporating Effects of Microstructure, Surface Energy and Intermolecular Forces

2018 ◽  
Vol 10 (08) ◽  
pp. 1850091 ◽  
Author(s):  
Mohamed A. Attia ◽  
Salwa A. Mohamed
Keyword(s):  
Residual Stress ◽  
Surface Energy ◽  
Boundary Conditions ◽  
Van Der Waals ◽  
Surface Elasticity ◽  
Van Der Waals Forces ◽  
Functionally Graded ◽  
Surface Residual Stress ◽  
Electrically Actuated ◽  
Classical Boundary

In this paper, an integrated non-classical continuum model is developed to investigate the pull-in instability of electrostatically actuated functionally graded nanocantilevers. The model accounts for the simultaneous effects of local-microstructure, surface elasticity and surface residual in the presence of fringing field as well as Casimir and van der Waals forces. The modified couple stress and Gurtin–Murdoch surface elasticity theories are employed to conduct the scaling effects of microstructure and surface energy, respectively, in the context of Euler–Bernoulli beam hypothesis. Bulk and surface material properties are varied according to the power-law distribution through the beam thickness. The physical neutral axis position for mentioned FG nanobeams is considered. Hamilton principle is employed to derive the nonlinear size-dependent governing equations and the non-classical boundary conditions. The resulting nonlinear differential equations are solved utilizing the generalized differential quadrature method (GDQM). In addition, the non-classical boundary conditions of nanocantilever beams due to surface residual stress are exactly implemented. After validation of the obtained results by previously available data in the literature, the influences of different geometrical and material parameters on the pull-in instability of the FG nanocantilevers are examined in detail. It is concluded that the pull-in behavior of electrically actuated FG micro/nanocantilevers is significantly influenced by the material distribution, material length scale parameter, surface elasticity constant, surface residual stress, initial gap, slenderness ratio, Casimir, and van der Waals forces. The obtained results can be considered for modeling and analysis of electrically actuated FG nanocantilevers.

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