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

Kudaibergenov, Askar; Kudaibergenov, Askat; Prikazchikov, Danila

doi:10.2478/ama-2021-0005

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.

References

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), 981-990.10.1007/s10778-010-0238-z
Search in Google Scholar Back to article
2. Bratov V. (2011), Incubation time fracture criterion for FEM simulations, Acta Mech. Sin., 27(4), 541.10.1007/s10409-011-0484-2
Search in Google Scholar Back to article
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, 2485-2496.10.1007/s12206-012-0630-1
Search in Google Scholar Back to article
4. Cole J., Huth J. (1958), Stresses produced in a half plane by moving loads, J. Appl. Mech., 25, 433-436.10.1115/1.4011853
Search in Google Scholar Back to article
5. de Hoop A.T. (2002), The moving-load problem in soil dynamics – the vertical displacement approximation, Wave Motion, 36(4), 335-346.10.1016/S0165-2125(02)00028-8
Search in Google Scholar Back to article
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, 128-14710.1016/j.ijsolstr.2017.06.009
Search in Google Scholar Back to article
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, 261-284.10.1093/imamat/44.3.261
Search in Google Scholar Back to article
8. Ege N., Erbaş B., Kaplunov J., Wootton P. (2018), Approximate analysis of surface wave-structure interaction, J. Mech. Mater. Struct., 13(3), 297-309.10.2140/jomms.2018.13.297
Search in Google Scholar Back to article
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), 817-828.10.15672/HJMS.2017.434
Search in Google Scholar Back to article
10. Erbaş B., Kaplunov J., Nolde E., Palsü M. (2018), Composite wave models for elastic plates, P. Roy. Soc. A-Math. Phy., 474(2214), 1-16.10.1098/rspa.2018.0103
Search in Google Scholar Back to article
11. Erbaş B., Kaplunov J., Palsü M. (2019), A composite hyperbolic equation for plate extension, Mech. Res. Commun., 99, 64-67.10.1016/j.mechrescom.2019.06.008
Search in Google Scholar Back to article
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), 89–100.10.1177/1081286514555451
Search in Google Scholar Back to article
13. Fryba L. (1999), Vibration of solids and structures under moving loads, 3rd ed, Thomas Telford, London.10.1680/vosasuml.35393
Search in Google Scholar Back to article
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), 1-19.10.1098/rspa.2019.0590
Search in Google Scholar Back to article
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), 505-515.10.1115/1.3564708
Search in Google Scholar Back to article
16. Gent A.N. (1996), A new constitutive relation for rubber, Rubber Chem. Technol., 69(1), 59-61.10.5254/1.3538357
Search in Google Scholar Back to article
17. Goldstein R.V. (1965), Rayleigh waves and resonance phenomena in elastic bodies, J. Appl. Math. Mech. (PMM), 29(3), 516-525.10.1016/0021-8928(65)90066-3
Search in Google Scholar Back to article
18. Gourgiotis P.A., Piccolroaz A. (2014), Steady-state propagation of a mode II crack in couple stress elasticity, Int. J. Fract., 188(2), 119-145.10.1007/s10704-014-9950-8
Search in Google Scholar Back to article
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, 440-451.10.1016/j.wavemoti.2010.01.005
Search in Google Scholar Back to article
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), 1-15.10.1098/rsta.2019.0111
Search in Google Scholar Back to article
21. Kaplunov J., Prikazchikov D.A. (2017), Asymptotic theory for Rayleigh and Rayleigh-type waves, Adv. Appl. Mech., 50, 1-106.10.1016/bs.aams.2017.01.001
Search in Google Scholar Back to article
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), 1229-1238.10.1016/j.wavemoti.2012.12.008
Search in Google Scholar Back to article
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), 57-72.10.1093/qjmam/hbp024
Search in Google Scholar Back to article
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, 49-53.10.1016/j.mechrescom.2018.07.006
Search in Google Scholar Back to article
25. Krylov V.V. (1996), Vibrational impact of high-speed trains. I. Effect of track dynamics, J. Acoust. Soc. Am., 100(5), 3121-3134.10.1121/1.417123
Search in Google Scholar Back to article
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 Back to article
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), 1289-1309.10.1006/jsvi.1999.2731
Search in Google Scholar Back to article
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, 104065.10.1016/j.euromechsol.2020.104065
Search in Google Scholar Back to article
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, 112-128.10.1016/j.ijengsci.2012.06.015
Search in Google Scholar Back to article
30. Ogden R.W. (1984), Non-linear elastic deformations, Dover, New York.10.1016/0264-682X(84)90061-3
Search in Google Scholar Back to article
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), 49-79.10.1016/0020-7225(67)90054-7
Search in Google Scholar Back to article
32. Pucci E., Saccomandi G. (2002), A note on the Gent model for rubber-like materials, Rubber Chem. Technol., 75(5), 839-852.10.5254/1.3547687
Search in Google Scholar Back to article
33. Smirnov V., Petrov Yu.V., Bratov V. (2012), Incubation time approach in rock fracture dynamics, Sci. China Phys., Mech. Astr., 55(1), 78-85.10.1007/s11433-011-4579-3
Search in Google Scholar Back to article
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, 45-61.10.1016/j.ijsolstr.2019.06.022
Search in Google Scholar Back to article
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, 99-112.10.1016/j.ijsolstr.2015.07.001
Search in Google Scholar Back to article
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, 106427.10.1016/j.soildyn.2020.106427
Search in Google Scholar Back to article
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), 519-540.10.1007/s10999-019-09483-9
Search in Google Scholar Back to article
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), 1-18.10.1098/rspa.2019.0079
Search in Google Scholar Back to article
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, 113-131.10.1093/imamat/hxz037
Search in Google Scholar Back to article
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, 39-48.10.1016/j.ijmecsci.2018.07.035
Search in Google Scholar Back to article

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

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