Influence of initial stresses on the critical velocity of the moving load acting in the interior of the hollow cylinder surrounded by an infinite elastic medium

다국어 초록 (Multilingual Abstract)

The bi-material elastic system consisting of the pre-stressed hollow cylinder and pre-stresses surrounding infinite elastic medium is considered and it is assumed that the mentioned initial stresses in this system are caused with the compressing or stretching uniformly distributed normal forces acting at infinity in the direction which is parallel to the cylinder's axis. Moreover, it is assumed that on the internal surface of the cylinder the ring load which moves with constant velocity acts and within these frameworks it is required to determine the influence of the aforementioned initial stresses on the critical velocity of the moving load. The corresponding investigations are carried out within the framework of the so-called three-dimensional linearized theory of elastic waves in initially stresses bodies and the axisymmetric stress-strain state case is considered. The “moving coordinate system” method is used and the Fourier transform is employed for solution to the formulated mathematical problem and Fourier transformation of the sought values are determined analytically. However, the originals of those are determined numerically with the use of the Sommerfeld contour method. The critical velocity is determined from the criterion, according to which, the magnitudes of the absolute values of the stresses and displacements caused with the moving load approaches an infinity. Numerical results on the influence of the initial stresses on the critical velocity and interface normal and shear stresses are presented and discussed. In particular, it is established that the initial stretching (compressing) of the constituents of the system under consideration causes a decrease (an increase) in the values of the critical velocity.

참고문헌 (Reference)

1 Babich, S.Y., "To the solution of the problem of the action of a live load on a two-layer halfspace with initial stress" 24 (24): 775-780, 1988

2 Hussein M.F.M., "The fictitious force method for efficient calculation of vibration from a tunnel embedded in a multi-layered half-space" 333 (333): 6996-7018, 2014

3 Kerr, A.D., "The critical velocity of a load moving on a floating ice plate that is subjected to in-plane forces" 6 (6): 267-274, 1983

4 Ilhan, N., "The critical speed of a moving time-harmonic load acting on a system consisting a pre-stressed orthotropic covering layer and a pre-stressed half-plane" 36 (36): 3663-3672, 2012

5 Akbarov, S.D., "The critical speed of a moving load on a pre-stressed load plate resting on a pre-stressed half-plan" 43 (43): 173-182, 2007

6 Metrikine, A.V., "Surface ground vibration due to a moving load in a tunnel: Twodimensional model" 234 (234): 43-66, 2000

7 Parnes, R., "Response of an infinite elastic medium to traveling loads in a cylindrical bore" 36 (36): 51-58, 1969

8 Pozhuev, V.I., "Reaction of a cylindrical shell in a transversely isotropic medium when acted upon by a moving load" 16 (16): 958-964, 1980

9 Parnes, R., "Progressing torsional loads along a bore in an elastic medium" 36 (36): 653-670, 1980

10 Sheng, X., "Prediction of ground vibration from trains using the wavenumber finite and boundary element methods" 293 (293): 575-586, 2006

11 Akbarov, S.D., "On the dynamics of a finite pre-strained bi-layered slab resting on a rigid foundation under the action of an oscillating moving load" 327 (327): 454-472, 2009

12 Achenbach, J.D., "Moving load on a plate resting on an elastic half-space" 34 (34): 183-189, 1967

13 Ouyang, H., "Moving load dynamic problems: A tutorial (with a brief overview)" 25 (25): 2039-2060, 2011

14 Abdulkadirov, S.A., "Low-frequency resonance waves in a cylindrical layer surrounded by an elastic medium" 80 : 229-234, 1981

15 Metrikine, A.V., "Lateral vibration of an axially compressed beam on an elastic half-space due to a moving lateral load" 18 (18): 147-158, 1999

16 Guz, A.N., "Fundamentals of the Three-Dimensional theory of Stability of Deformable Bodies" Springer-Verlag 1999

17 Akbarov, S.D., "Frequency response of a pre-stressed metal elastic plate under compressible viscous fluid loading" 15 (15): 172-188, 2016

18 Surkay D. Akbarov, "Forced vibration of the elastic system consisting of the hollow cylinder and surrounding elastic medium under perfect and imperfect contact" 국제구조공학회 62 (62): 113-123, 2017

19 Eringen, A.C., "Elastodynamics, Finite motion, Vol. I; Linear Theory, Vol. II" Academic Press 1975

20 Guz, A.N., "Elastic Waves in Bodies with Initial (Residual) Stresses" 2004

21 Hung, H.H., "Effect of railway roughness on soil vibrations due to moving trains by 2.5D finite/infinite element approach" 57 : 254-266, 2013

22 Surkay D. Akbarov, "Dynamics of the oscillating moving load acting on the hydro- elastic system consisting of the elastic plate, compressible viscous fluid and rigid wall" 국제구조공학회 59 (59): 403-430, 2016

23 Akbarov, S.D., "Dynamics of the moving load acting on the hydro-elastic system consisting of the elastic plate, compressible viscous fluid and rigid wall" 45 (45): 75-105, 2015

24 Akbarov, S.D., "Dynamics of a system comprising an orthotropic layer and ortho- tropic half-plane under the action of an oscillating moving load" 46 (46): 3873-3881, 2009

25 Akbarov, S.D., "Dynamics of a system comprising a pre-stressed orthotropic layer and pre-stressed orthotropic half-plane under the action of a moving load" 45 (45): 4222-4235, 2008

26 Babich, S.Y., "Dynamics of a pre-stressed incompressible layered half-space under load" 44 (44): 268-285, 2008

27 Babich, S.Y., "Dynamics of a layered compressible pre-stressed half-space under the influence of moving load" 22 (22): 808-815, 1986

28 Akbarov, S.D., "Dynamics of Pre-strained Bi-Material Elastic Systems: Linearized Three-Dimensional Approach" Springer 2015

29 Dincsoy, E., "Dynamical response of a prestrained system comprising a substrate and bond and covering layers to moving load" 45 (45): 527-536, 2009

30 Chonan, S., "Dynamic response of a cylindrical shell imperfectly bonded to a surrounding continuum of infinite extent" 78 (78): 257-267, 1981

31 Dieterman H.A., "Critical velocities of a harmonic load moving uniformly along an elastic layer" 64 (64): 596-600, 1997

32 Yuan, Z., "Benchmark solution for vibration from a moving point source in a tunnel embedded in a half-space" 387 : 177-193, 2017

33 Forrest, J.A., "A three-dimensional tunnel model for calculation of train-induced ground vibration" 294 (294): 678-705, 2006

34 Babich, S.Y., "A dynamic for a pre-stressed compressible layered half-space under moving load" 44 (44): 388-405, 2008

35 Akbarov, S.D., "3D Dynamics of a system comprising a pre-stressed covering layer and a prestressed half-space under the action of an oscillating moving point-located load" 39 : 1-18, 2015