Research Article
Surface Displacement Field of a Coated Elastic Half-Space Under the Influence of a Moving Distributional Load
Abstract
An analysis of the
distributed moving load along the surface of a coated half space is presented.
The formulation of the problem depends on the hyperbolic-elliptic asymptotic
model developed earlier by the authors. The integral solution of the
longitudinal and transverse displacements along the surface for the sub and
super-Rayleigh cases are obtained by using the uniform stationary phase method.
Numerical comparisons of the exact and asymptotic solutions of the longitudinal
displacement are illustrated for the certain cross-sections of the profile.
References
- Zhu XQ and Law SS. Dynamic load on continuous multi-lane bridge deck from moving vehicles. Journal of Sound and Vibration 2002; 251: 697-716
- Cao Y, Xia H and Li ZA. Semi-analytical/FEM model for predicting ground vibrations induced by high-speed train through continuous girder bridge. Journal of Mechanical Science and Technology 2012; 26: 2485-2496.
- Agostinacchio M, Ciampa D, Diomedi M, and Olita S. Parametrical analysis of the railways
- El Kacimi A, Woodward PK, Laghrouche O, and Medero G. Time domain 3D finite element
- Achenbach JD. Wave propagation in elastic solids, North-Holland, Amsterdam, 1973
- Miklowitz J. The theory of elastic waves and waveguides, Elsevier, 2012
- Kaplunov J, Zakharov A and Prikazchikov DA. Explicit models for elastic and piezoelastic surface waves. IMA J. Appl. Math. 2006; 71: 768-782
- Chadwick P. Surface and interfacial waves of arbitrary form in isotropic elastic media, J. of Elasticity 1976; 6: 73-80
- Courant R and Hilbert D. Methods of Mathematical Physics, John Wiley & Sons, 1989
- Dai HH, Kaplunov J and Prikazchikov DA. A long-wave model for the surface elastic wave in a coated half-space. Proc. R. Soc. A. 2010; 466: 3097–3116
- Kaplunov JD, Prikazchikov DA, Erbaş B, and Şahin O. On a 3D moving load problem for an elastic half space. Wave Motion 2013; 50: 1229–1238
- Erbaş B, Kaplunov J, Prikazchikov DA and Şahin O. The near-resonant regimes of a moving load in a 3D problem for a coated elastic half space. Math. Mech. Solids 2014; doi: 10.1177/1081286514555451
- Debnath L, and Dambaru B. Integral transforms and their applications, CRC press, 2014
- Borovikov VA. Uniform stationary phase method, Institution of Electrical Engineers, London, 1994
- Wong R. Asymptotic Approximations of Integrals, Academic Press, 2014
- Abramowitz M and Stegun IA. Handbook of mathematical functions, Dover Publications, New York, 2012
- Erbaş B, Şahin O. On the causality of the Rayleigh wave. Journal of mechanics of materials and structures 2016, 11: 449-461
- Erbaş B, Şahin O, Ege N. Response of a 3D elastic half-space to a distributed moving load. Hacettepe Journal of Mathematics and Statistics, in press
- Chester C, Friedman B, and Ursell F. An extension of the method of steepest descents, Cambridge University Press, 1957
- Bleistein N. Uniform asymptotic expansions of integrals with many nearby stationary points and algebraic singularities. Journal of Mathematics and Mechanics 1967; 17: 533-559
Surface Displacement Field of a Coated Elastic Half-Space Under the Influence of a Moving Distributional Load
Abstract
An analysis of the distributed moving load along the surface of a coated half space is presented. The formulation of the problem depends on the hyperbolic-elliptic asymptotic model developed earlier by the authors. The integral solution of the longitudinal and transverse displacements along the surface for the sub and super-Rayleigh cases are obtained by using the uniform stationary phase method. Numerical comparisons of the exact and asymptotic solutions of the longitudinal displacement are illustrated for the certain cross-sections of the profile.
References
- Zhu XQ and Law SS. Dynamic load on continuous multi-lane bridge deck from moving vehicles. Journal of Sound and Vibration 2002; 251: 697-716
- Cao Y, Xia H and Li ZA. Semi-analytical/FEM model for predicting ground vibrations induced by high-speed train through continuous girder bridge. Journal of Mechanical Science and Technology 2012; 26: 2485-2496.
- Agostinacchio M, Ciampa D, Diomedi M, and Olita S. Parametrical analysis of the railways
- El Kacimi A, Woodward PK, Laghrouche O, and Medero G. Time domain 3D finite element
- Achenbach JD. Wave propagation in elastic solids, North-Holland, Amsterdam, 1973
- Miklowitz J. The theory of elastic waves and waveguides, Elsevier, 2012
- Kaplunov J, Zakharov A and Prikazchikov DA. Explicit models for elastic and piezoelastic surface waves. IMA J. Appl. Math. 2006; 71: 768-782
- Chadwick P. Surface and interfacial waves of arbitrary form in isotropic elastic media, J. of Elasticity 1976; 6: 73-80
- Courant R and Hilbert D. Methods of Mathematical Physics, John Wiley & Sons, 1989
- Dai HH, Kaplunov J and Prikazchikov DA. A long-wave model for the surface elastic wave in a coated half-space. Proc. R. Soc. A. 2010; 466: 3097–3116
- Kaplunov JD, Prikazchikov DA, Erbaş B, and Şahin O. On a 3D moving load problem for an elastic half space. Wave Motion 2013; 50: 1229–1238
- Erbaş B, Kaplunov J, Prikazchikov DA and Şahin O. The near-resonant regimes of a moving load in a 3D problem for a coated elastic half space. Math. Mech. Solids 2014; doi: 10.1177/1081286514555451
- Debnath L, and Dambaru B. Integral transforms and their applications, CRC press, 2014
- Borovikov VA. Uniform stationary phase method, Institution of Electrical Engineers, London, 1994
- Wong R. Asymptotic Approximations of Integrals, Academic Press, 2014
- Abramowitz M and Stegun IA. Handbook of mathematical functions, Dover Publications, New York, 2012
- Erbaş B, Şahin O. On the causality of the Rayleigh wave. Journal of mechanics of materials and structures 2016, 11: 449-461
- Erbaş B, Şahin O, Ege N. Response of a 3D elastic half-space to a distributed moving load. Hacettepe Journal of Mathematics and Statistics, in press
- Chester C, Friedman B, and Ursell F. An extension of the method of steepest descents, Cambridge University Press, 1957
- Bleistein N. Uniform asymptotic expansions of integrals with many nearby stationary points and algebraic singularities. Journal of Mathematics and Mechanics 1967; 17: 533-559
There are 20 citations in total.
Details
| Journal Section | Articles |
|---|---|
| Authors | |
| Publication Date | April 7, 2017 |
| Published in Issue | Year 2017 Volume: 5 Issue: 1 |
