Dynamics of the moving ring-load acting in the interior of the bi-layered hollow cylinder with imperfect contact between the layers. (English) Zbl 1495.74005
Summary: The dynamics of the moving-with-constant-velocity internal ring-load (-pressure) acting on the inner surface of the bi-layered hollow circular cylinder is studied within the scope of the piecewise homogeneous body model by employing the exact field equations of the linear theory of elastodynamics. It is assumed that the internal pressure is point-located with respect to the cylinder axis and is axisymmetric in the circumferential direction. Moreover, it is assumed that shear-spring type imperfect contact conditions on the interface between the layers of the cylinder are satisfied. The focus is on determination of the critical velocity with analyses of the interface stress distribution and their attenuation rules with respect to time. At the same time, there is analysis of the problem parameters such as the ratio of modulus of elasticity, the ratio of the cylinder’s layers thickness to the external radius of inner layer-cylinder, and the shear-spring type parameter which characterizes the degree of the contact imperfection on the values of the critical velocity and stress distribution. Corresponding numerical results are presented and discussed. In particular, it is established that the values of the critical velocity of the moving ring-load increase with the thickness of the external layer of the cylinder.
MSC:
| 74B05 | Classical linear elasticity |
| 74E05 | Inhomogeneity in solid mechanics |
| 74H15 | Numerical approximation of solutions of dynamical problems in solid mechanics |
| 74M15 | Contact in solid mechanics |
Keywords:
critical velocity; shear-spring imperfection; interface stress; linear elastodynamics; Sommerfeld contour integration methodReferences:
| [1] | Abdulkadirov, S.A., (1981), Low-frequency resonance waves in a cylindrical layer surrounded by an elastic medium, Journal of Mining Sci., 80, pp.229-234. |
| [2] | Achenbach, J.D., Keshava, S.P., Hermann, G., (1967), Moving load on a plate resting on an elastic half space, Trans ASME Ser E J. Appl. Mech., 34(4), pp.183-189. |
| [3] | Akbarov, S.D., (2010), Dynamical (time-harmonic) axisymmetric stress field in the pre-stretched non-linear elastic bi-layered slab resting on the rigid foundation, TWMS J. Pure Appl. Math., 1(2), pp.146-154. · Zbl 1432.74088 |
| [4] | Akbarov, S.D., (2013), On the axisymmetric time-harmonic Lamb’s problem for a system comprising a half-space and a covering layer with finite initial strains, CMES: Comp. Model. Eng. Sci., 95(3), pp.143-175. · Zbl 1356.74029 |
| [5] | Akbarov, S.D., (2015), Dynamics of Pre-Strained Bi-Material Elastic Systems: Linearized Three-Dimensional Approach, Springer, New-York, 1004p. |
| [6] | Akbarov, S.D., Guler, C., Dincoy, E., (2007), The critical speed of a moving load on a pre-stressed load plate resting on a pre-stressed half-plan, Mech. Comp. Mater., 43(2), pp.173-182. |
| [7] | Akbarov, S.D., Salmanova, K.A., (2009), On the dynamics of a finite pre-strained bi-layered slab resting on a rigid foundation under the action of an oscillating moving load, J. Sound. Vibr., 327(3-5), pp.454-472. |
| [8] | Akbarov, S.D., Ilhan, N., (2008), Dynamics of a system comprising a pre-stressed orthotropic layer and pre-stressed orthotropic half-plane under the action of a moving load, Int. J. Solid. Str., 45(14-15), pp.42224235. · Zbl 1169.74419 |
| [9] | Akbarov, S.D., Ilhan, N., (2009), Dynamics of a system comprising an orthotropic layer and orthotropic half-plane under the action of an oscillating moving load, Int. J. Solid. Str., 46(21), pp.3873-3881. · Zbl 1176.74094 |
| [10] | Akbarov, S.D., Ilhan, N., Temugan, A., (2015), 3D Dynamics of a system comprising a pre-stressed covering layer and a pre-stressed half-space under the action of an oscillating moving point-located load, Appl. Math. Model., 39(1), pp.1-18. · Zbl 1449.74038 |
| [11] | Akbarov, S.D., Ismailov M.I., (2015), Dynamics of the moving load acting on the hydro-elastic system consisting of the elastic plate, compressible viscous fluid and rigid wall, CMC- Comput. Mater. Contin., 45(2), pp.75-105. |
| [12] | Akbarov, S.D., Ismailov M.I., (2016), Frequency response of a pre-stressed metal elastic plate under compressible viscous fluid loading, Appl. Comput. Math., 15(2), pp.172-188. · Zbl 1342.74048 |
| [13] | Aliyev, F.A., Larin, V.B., Veliyeva, N.I., Gasimova, K., Faradjova, Sh.A., (2019), Algorithm for solving the systems of the generalized Sylvester transpose matrix equations using LMI, TWMS J. Pure Appl. Math., 10(2), pp.239-245. · Zbl 1431.65056 |
| [14] | Aman, T., Ishak, A., (2014), Stagnation-point flow and heat transfer over a nonlinearly stretching sheet in a micropolar fluid with viscous dissipation, Appl. Comput. Math., 13(2), pp.230-238. · Zbl 1446.76101 |
| [15] | Ashraf, M., Asghar, S., Hossain, M.A., (2014), The computational study of the effects of magnetic field and free stream velocty oscillation on boundary layer flow past a magnetized vertical plate, Appl. Comput. Math., 13(2), pp.175-193. · Zbl 1308.76086 |
| [16] | Babich, S.Y., Glukhov, Y.P., Guz, A.N., (1986), Dynamics of a layered compressible pre-stressed half-space under the influence of moving load, Int. Appl. Mech., 22(6), pp.808-815. · Zbl 0631.73027 |
| [17] | Babich, S.Y., Glukhov, Y.P., Guz, A.N., (1988), To the solution of the problem of the action of a live load on a two-layer half-space with initial stress, Int. Appl. Mech., 24(8), pp.775-780. · Zbl 0711.73022 |
| [18] | Babich, S.Y., Glukhov, Y.P., Guz, A.N., (2008), Dynamics of a pre-stressed incompressible layered half-space under load, Int. Appl. Mech., 44(3), pp.268-285. · Zbl 1177.74042 |
| [19] | Babich, S.Y., Glukhov, Y.P., Guz, A.N. (2008), A dynamic for a pre-stressed compressible layered half-space under moving load, Int. Appl. Mech., 44(4), pp.388-405. · Zbl 1177.74075 |
| [20] | Demiray, H.,(2014), A note on the interactions of nonlinear waves governed by the generalized Boussinesq equation, Appl. Comp. Math., 13(3), pp.376-380. · Zbl 1314.35135 |
| [21] | Dieterman H.A., Metrikine, A.V., (1997), Critical velocities of a harmonic load moving uniformly along an elastic layer, Trans ASME J. Appl. Mech., 64(3), pp.596-600. · Zbl 0906.73023 |
| [22] | Dincsoy, E., Guler, C., Akbarov, S.D., (2009), Dynamical response of a prestrained system comprising a substrate and bond and covering layers to moving load, Mech. Comp. Mater., 45(5), pp.527-536. |
| [23] | Eringen, A.C., Suhubi, E.S., (1975), Elastodynamics, Finite Motion, vol. I; Linear Theory, II, Academic Press, New-York. · Zbl 0344.73036 |
| [24] | Ilhan, N., (2012), The critical speed of a moving time-harmonic load acting on a system consisting a prestressed orthotropic covering layer and a pre-stressed half-plane, Appl. Math. Model., 36(8), pp.3663-3672. |
| [25] | Ilyasov, M.X., (2011), Dynamical torsion of viscoelastic cone, TWMS J. Pure Appl. Math., 2(2), pp.203-220. · Zbl 1292.74006 |
| [26] | Jensen, F.B., Kuperman, W.A., Porter, M.B., Schmidt, H., (2011), Computational Ocean Acoustic, 2nd ed. Springer, Berlin, 794p. · Zbl 1234.76003 |
| [27] | Kerr, A.D., (1983), The critical velocity of a load moving on a floating ice plate that is subjected to in-plane forces, Cold. Reg. Sci. Technol., 6(3), pp.267-274. |
| [28] | Metrikine, A.V., Dieterman, H.A., (1999), Lateral vibration of an axially compressed beam on an elastic half-space due to a moving lateral load, Eur. J. Mech. A/Solids, 18, pp.147-158. · Zbl 0930.74027 |
| [29] | Sevdimaliyev, Y.M., Akbarov, S.A., Guliyev, H.H., Yahnioglu, N., (2020), On the natural oscillation of an inhomogeneously pre-stressed multilayered hollow sphere filled with a compressible fluid, Appl. Comput. Math., 19(1), pp.132-146. · Zbl 1451.74107 |
| [30] | Simos, T.E., Tsitouras, Ch., (2020), 6th order Runge-Kutta pairs for scalar autonomous IVP, Appl. Comput. Math., 19(1), pp.392-401. · Zbl 1480.65176 |
| [31] | Sharma, J.R., Kumar, D., (2018), Desing and analysis of a class of weighted - Newton methods with frozen derivative, TWMS J. Pure Appl. Math., 9(2), pp.207-22. · Zbl 1423.49030 |
| [32] | Tsang, L., (1978), Time-harmonic solution of the elastic head wave problem incorporating the influence of Rayleigh poles, J. Acoust. Soc. Am., 65(5), pp.1302-1309. · Zbl 0375.73022 |
| [33] | Zhou, J.X., Deng, Z.C., Hou, X.H., (2008), Critical velocity of sandwich cylindrical shell under moving internal pressure, Appl. Math. Mech., 29(12), pp.1569-1578 · Zbl 1165.74329 |
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