scholarly journals Reflection of plane longitudinal waves from the stress-free boundary of a nonlocal, micropolar solid half-space

2013 ◽  
Vol 8 (1) ◽  
pp. 95-107 ◽  
Author(s):  
Aarti Khurana ◽  
Sushil K. Tomar
Keyword(s):  
Free Boundary ◽  
Half Space ◽  
Longitudinal Waves ◽  
Stress Free Boundary

On Wave Reflection in an Elastic Plate

1974 ◽  
Vol 41 (4) ◽  
pp. 1031-1035
Author(s):  
R. Doby
Keyword(s):  
Free Boundary ◽  
Theoretical Analysis ◽  
Wave Reflection ◽  
Transverse Waves ◽  
Reflected Waves ◽  
Longitudinal Waves ◽  
Free Boundary Conditions ◽  
Transverse Modes ◽  
Parallel Surfaces ◽  
Stress Free Boundary

A precursor boundary concept is introduced which decouples the stress-free boundary conditions at the parallel surfaces of the plate. The resulting orthogonal eigenfunctions are longitudinal and transverse waves. This property is exploited so as to satisfy stress-free conditions at the edge. The theoretical analysis reveals that the reflected waves are reordered so that the longitudinal and transverse modes represent the gradients of the incident transverse and longitudinal waves.

scholarly journals Dispersion equation of Rayleigh waves in transversely isotropic nonlocal piezoelastic solids half-space

2019 ◽  
Vol 41 (4) ◽  
pp. 363-371
Author(s):  
Do Xuan Tung
Keyword(s):  
Free Surface ◽  
Free Boundary ◽  
Dispersion Equation ◽  
Half Space ◽  
Rayleigh Waves ◽  
Plane Waves ◽  
Transversely Isotropic ◽  
Frequency Parameter ◽  
Free Condition ◽  
Stress Free Boundary

This study is devoted to investigate the propagation of Rayleigh-type waves in transversely isotropic nonlocal piezoelastic half-space.  When the stress-free boundary is maintained at charge-free condition, the dispersion equation for the propagation of Rayleigh waves at the free surface of transversely isotropic piezoelastic solids has been obtained. Based on the obtained dispersion equation, the effect of the nonlocality on the speed of Rayleigh wave is numerically considered. The dependence of velocities of plane waves in transversely isotropic nonlocal piezoelastic medium on the direction of propagation as well as non-dimensional frequency parameter has been also illustrated.

Reflection of Thermoelastic Waves From the Insulated Surface of a Solid Half-Space With Time-Delay

2020 ◽  
Vol 142 (9) ◽  
Author(s):  
Nihar Sarkar ◽  
Soumen De ◽  
Narayan Das ◽  
Nantu Sarkar
Keyword(s):  
Free Boundary ◽  
Half Space ◽  
Plane Waves ◽  
Generalized Thermoelasticity ◽  
Elastic Half Space ◽  
Reflection Coefficients ◽  
Angle Of Incidence ◽  
Energy Ratios ◽  
Thermally Conducting ◽  
Stress Free Boundary

Abstract This paper is devoted to study the reflection of thermoelastic plane waves from the thermally insulated stress-free boundary of a homogeneous, isotropic and thermally conducting elastic half-space. A new linear theory of generalized thermoelasticity under heat transfer with memory-dependent derivative (MDD) is employed to address this study. It has been found that three basic waves consisting of two sets of coupled longitudinal waves and one independent vertically shear-type wave may travel with distinct phase speeds. The formulae for various reflection coefficients and their respective energy ratios are determined in case of an incident coupled longitudinal elastic wave at the thermally insulated stress-free boundary of the medium. The results for the reflection coefficients and their respective energy ratios for various values of the angle of incidence are computed numerically and presented graphically for copper-like material and discussed.

Dynamic Analysis for Circular Inclusion Near Interfacial Crack Impacted by SH-Wave in Half Space

2012 ◽  
Vol 28 (1) ◽  
pp. 143-151 ◽  
Author(s):  
H. Qi ◽  
J. Yang ◽  
Y. Shi ◽  
J. Y. Tian
Keyword(s):  
Free Boundary ◽  
Dynamic Analysis ◽  
Green’S Function ◽  
Half Space ◽  
Green's Function ◽  
Interfacial Crack ◽  
Circular Inclusion ◽  
Wave Number ◽  
Complex Method ◽  
Sh Wave

ABSTRACTComplex method and Green's function method are used here to investigate the dynamic analysis for circular inclusion near interfacial crack impacted by SH-wave in bi-material half-space. Firstly, the displacement expression of the scattering wave was constructed which satisfied the free boundary conditions, then Green's function could be constructed, which was an essential solution to the displacement field for an elastic right-angle space with a circular inclusion impacted by out-plane harmonic line source loading at vertical surface. Secondly, crack was made out with “crack-division” technique. Meanwhile, the bi-material media was divided into two parts along the bi-material interface based on the idea of interface “conjunction”, and then the vertical surfaces of the two right-angle spaces were loaded with undetermined anti-plane forces in order to satisfy displacement continuity and stress continuity conditions at linking section. So a series of algebraic equations for determining the unknown forces could be set up through continuity conditions and the Green's function. Finally, some examples and results for dynamic stress concentration factor of the circular elastic inclusion were given. Numerical results show that they are influenced by interfacial crack, the incident wave number and the free boundary in some degree.

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