1. bookVolume 15 (2021): Issue 1 (March 2021)
Journal Details
License
Format
Journal
First Published
22 Jan 2014
Publication timeframe
4 times per year
Languages
English
access type Open Access

Near-Resonant Regimes of a Moving Load on a Pre-Stressed Incompressible Elastic Half-Space

Published Online: 15 May 2021
Page range: 30 - 36
Received: 15 Oct 2020
Accepted: 19 Apr 2021
Journal Details
License
Format
Journal
First Published
22 Jan 2014
Publication timeframe
4 times per year
Languages
English
Abstract

The article is concerned with the analysis of the problem for a concentrated line load moving at a constant speed along the surface of a pre-stressed, incompressible, isotropic elastic half-space, within the framework of the plane-strain assumption. The focus is on the near-critical regimes, when the speed of the load is close to that of the surface wave. Both steady-state and transient regimes are considered. Implementation of the hyperbolic–elliptic asymptotic formulation for the surface wave field allows explicit approximate solution for displacement components expressed in terms of the elementary functions, highlighting the resonant nature of the surface wave. Numerical illustrations of the solutions are presented for several material models.

Keywords

1. Alekseeva L.A., Ukrainets V.N. (2009), Dynamics of an elastic half-space with a reinforced cylindrical cavity under moving loads, Int. Appl. Mech., 45(9), 981-990. Search in Google Scholar

2. Bratov V. (2011), Incubation time fracture criterion for FEM simulations, Acta Mech. Sin., 27(4), 541. Search in Google Scholar

3. Cao Y., Xia H., Li Z. (2012), A semi-analytical/FEM model for predicting ground vibrations induced by high-speed train through continuous girder bridge, J. Mech. Sci. Technol., 26, 2485-2496. Search in Google Scholar

4. Cole J., Huth J. (1958), Stresses produced in a half plane by moving loads, J. Appl. Mech., 25, 433-436. Search in Google Scholar

5. de Hoop A.T. (2002), The moving-load problem in soil dynamics – the vertical displacement approximation, Wave Motion, 36(4), 335-346. Search in Google Scholar

6. Dimitrovová Z. (2017), Analysis of the critical velocity of a load moving on a beam supported by a finite depth foundation, Int. J. Solids Struct., 122, 128-147 Search in Google Scholar

7. Dowaikh M.A., Ogden R.W. (1990), On surface waves and deformations in a pre-stressed incompressible elastic solid, IMA J. Appl. Math., 44, 261-284. Search in Google Scholar

8. Ege N., Erbaş B., Kaplunov J., Wootton P. (2018), Approximate analysis of surface wave-structure interaction, J. Mech. Mater. Struct., 13(3), 297-309. Search in Google Scholar

9. Ege N., Şahin O., Erbaş B. (2017), Response of a 3D elastic half-space to a distributed moving load, Hacet J. Math. Stat., 46(5), 817-828. Search in Google Scholar

10. Erbaş B., Kaplunov J., Nolde E., Palsü M. (2018), Composite wave models for elastic plates, P. Roy. Soc. A-Math. Phy., 474(2214), 1-16. Search in Google Scholar

11. Erbaş B., Kaplunov J., Palsü M. (2019), A composite hyperbolic equation for plate extension, Mech. Res. Commun., 99, 64-67. Search in Google Scholar

12. Erbaş B., Kaplunov J., Prikazchikov D.A., Şahin O. (2017), The near-resonant regimes of a moving load in a three-dimensional problem for a coated elastic half-space, Math. Mech. Solids, 22(1), 89–100. Search in Google Scholar

13. Fryba L. (1999), Vibration of solids and structures under moving loads, 3rd ed, Thomas Telford, London. Search in Google Scholar

14. Fu Y., Kaplunov J., Prikazchikov D. (2020), Reduced model for the surface dynamics of a generally anisotropic elastic half-space, P. Roy. Soc. A-Math. Phy., 476(2234), 1-19. Search in Google Scholar

15. Gakenheimer D.C., Miklowitz J. (1969), Transient excitation of an elastic half space by a point load traveling on the surface, J. Appl. Mech., 36(3), 505-515. Search in Google Scholar

16. Gent A.N. (1996), A new constitutive relation for rubber, Rubber Chem. Technol., 69(1), 59-61. Search in Google Scholar

17. Goldstein R.V. (1965), Rayleigh waves and resonance phenomena in elastic bodies, J. Appl. Math. Mech. (PMM), 29(3), 516-525. Search in Google Scholar

18. Gourgiotis P.A., Piccolroaz A. (2014), Steady-state propagation of a mode II crack in couple stress elasticity, Int. J. Fract., 188(2), 119-145. Search in Google Scholar

19. Kaplunov J., Nolde E., Prikazchikov D.A. (2010a), A revisit to the moving load problem using an asymptotic model for the Rayleigh wave, Wave Motion, 47, 440-451. Search in Google Scholar

20. Kaplunov J., Prikazchikov D., Sultanova L. (2019), Rayleigh-type waves on a coated elastic half-space with a clamped surface, Phil. Trans. Roy. Soc. A, 377(2156), 1-15. Search in Google Scholar

21. Kaplunov J., Prikazchikov D.A. (2017), Asymptotic theory for Rayleigh and Rayleigh-type waves, Adv. Appl. Mech., 50, 1-106. Search in Google Scholar

22. Kaplunov J., Prikazchikov D.A., Erbaş B., Şahin O. (2013), On a 3D moving load problem for an elastic half space, Wave Motion, 50(8), 1229-1238. Search in Google Scholar

23. Kaplunov J., Voloshin V., Rawlins A.D. (2010b), Uniform asymptotic behaviour of integrals of Bessel functions with a large parameter in the argument, Quart. J. Mech. Appl. Math., 63(1), 57-72. Search in Google Scholar

24. Khajiyeva L.A., Prikazchikov D.A., Prikazchikova L.A. (2018), Hyperbolic-elliptic model for surface wave in a pre-stressed incompressible elastic half-space, Mech. Res. Commun., 92, 49-53. Search in Google Scholar

25. Krylov V.V. (1996), Vibrational impact of high-speed trains. I. Effect of track dynamics, J. Acoust. Soc. Am., 100(5), 3121-3134. Search in Google Scholar

26. Kumar R., Vohra R. (2020), Steady state response due to moving load in thermoelastic material with double porosity, Mater. Phys. Mech., 44(2), 172-185. Search in Google Scholar

27. Lefeuve-Mesgouez G., Le Houédec D., Peplow A.T. (2000), Ground vibration in the vicinity of a high-speed moving harmonic strip load, J. Sound Vib., 231(5), 1289-1309. Search in Google Scholar

28. Lu T., Metrikine A.V., Steenbergen M.J.M.M. (2020), The equivalent dynamic stiffness of a visco-elastic half-space in interaction with a periodically supported beam under a moving load, Europ. J. Mech.-A/Solids, 84, 104065. Search in Google Scholar

29. Mishuris G., Piccolroaz A., Radi E. (2012), Steady-state propagation of a Mode III crack in couple stress elastic materials, Int. J. Eng. Sci., 61, 112-128. Search in Google Scholar

30. Ogden R.W. (1984), Non-linear elastic deformations, Dover, New York. Search in Google Scholar

31. Payton R.G. (1967), Transient motion of an elastic half-space due to a moving surface line load, Int. J. Eng. Sci., 5(1), 49-79. Search in Google Scholar

32. Pucci E., Saccomandi G. (2002), A note on the Gent model for rubber-like materials, Rubber Chem. Technol., 75(5), 839-852. Search in Google Scholar

33. Smirnov V., Petrov Yu.V., Bratov V. (2012), Incubation time approach in rock fracture dynamics, Sci. China Phys., Mech. Astr., 55(1), 78-85. Search in Google Scholar

34. Sun Z., Kasbergen C., Skarpas A., Anupam K., van Dalen K.N., Erkens S.M. (2019), Dynamic analysis of layered systems under a moving harmonic rectangular load based on the spectral element method, Int. J. Solids Struct., 180, 45-61. Search in Google Scholar

35. van Dalen K.N., Tsouvalas A., Metrikine A.V., Hoving J.S. (2015), Transition radiation excited by a surface load that moves over the interface of two elastic layers, Int. J. Solids Struct., 73, 99-112. Search in Google Scholar

36. Wang F., Han X., Ding T. (2021), An anisotropic layered poroelastic half-space subjected to a moving point load, Soil Dyn. Earth. Eng., 140, 106427. Search in Google Scholar

37. Wang Y., Zhou A., Fu T., Zhang W. (2020), Transient response of a sandwich beam with functionally graded porous core traversed by a non-uniformly distributed moving mass, Int. J. Mech. Mater. Design, 16(3), 519-540. Search in Google Scholar

38. Wootton P.T., Kaplunov J., Colquitt D.J. (2019), An asymptotic hyperbolic-elliptic model for flexural-seismic metasurfaces, P. Roy. Soc. A-Math. Phy., 475(2227), 1-18. Search in Google Scholar

39. Wootton P.T., Kaplunov J., Prikazchikov D. (2020), A second-order asymptotic model for Rayleigh waves on a linearly elastic half plane, IMA J. Appl. Math., 85, 113-131. Search in Google Scholar

40. Zhou L., Wang S., Li L., Fu Y. (2018), An evaluation of the Gent and Gent-Gent material models using inflation of a plane membrane, Int. J. Mech. Sci., 146-147, 39-48. Search in Google Scholar

Recommended articles from Trend MD

Plan your remote conference with Sciendo