Hành vi động học của dầm ray hư hỏng dưới tác động của tải trọng di động: Nghiên cứu tham số về đặc tính rạn nứt

<p>[1] E. Winkler. <em>Vorträge über Eisenbahnbau</em>, Vol. 11. H. Dominicus, (1878).</p>

<p>[2] P. Pasternak. Basis of a new method for the calculation of structures on elastic foundation using two bed constants. <em>Gosstroiizdat</em>, (1954). (in Russian).</p>

<p>[3] V. Vlasov and N. Leontiev. Technical theory of analysis of foundations on an elastic base. <em>MISI Sbornik Trudov</em>, <strong>14</strong>, (1956).</p>

<p>[4] A. D. Kerr. Elastic and viscoelastic foundation models. <em>Journal of Applied Mechanics</em>, <strong>81</strong>, (1964), pp. 491–498. <a href="https://doi.org/10.1115/1.3629667">https://doi.org/10.1115/1.3629667</a>.</p>

<p>[5] G. D. Zhang and B. Z. Guo. On the spectrum of Euler–Bernoulli beam equation with Kelvin–Voigt damping. <em>Journal of Mathematical Analysis and Applications</em>, <strong>374</strong>, (2011), pp. 210–229. <a href="https://doi.org/10.1016/j.jmaa.2010.08.070">https://doi.org/10.1016/j.jmaa.2010.08.070</a>.</p>

<p>[6] F. Hassine. Logarithmic stabilization of the Euler–Bernoulli transmission plate equation with locally distributed Kelvin–Voigt damping. <em>Journal of Mathematical Analysis and Applications</em>, <strong>455</strong>, (2017), pp. 1765–1782. <a href="https://doi.org/10.1016/j.jmaa.2017.06.068">https://doi.org/10.1016/j.jmaa.2017.06.068</a>.</p>

<p>[7] M. Javadi and M. Rahmanian. Nonlinear vibration of fractional Kelvin–Voigt viscoelastic beam on nonlinear elastic foundation. <em>Communications in Nonlinear Science and Numerical Simulation</em>, <strong>98</strong>, (2021). <a href="https://doi.org/10.1016/j.cnsns.2021.105784">https://doi.org/10.1016/j.cnsns.2021.105784</a>.</p>

<p>[8] Y. Lei, S. Adhikari, and M. I. Friswell. Vibration of nonlocal Kelvin–Voigt viscoelastic damped Timoshenko beams. <em>International Journal of Engineering Science</em>, <strong>66–67</strong>, (2013), pp. 1– 13. <a href="https://doi.org/10.1016/j.ijengsci.2013.02.004">https://doi.org/10.1016/j.ijengsci.2013.02.004</a>.</p>

<p>[9] W. R. Chen. Bending vibration of axially loaded Timoshenko beams with locally distributed Kelvin–Voigt damping. <em>Journal of Sound and Vibration</em>, <strong>330</strong>, (2011), pp. 3040–3056. <a href="https://doi.org/10.1016/j.jsv.2011.01.015">https://doi.org/10.1016/j.jsv.2011.01.015</a>.</p>

<p>[10] W. R. Chen. Vibration analysis of twisted Timoshenko beams with internal Kelvin–Voigt damping. <em>Procedia Engineering</em>, <strong>67</strong>, (2013), pp. 525–532. <a href="https://doi.org/10.1016/j.proeng.2013.12.053">https://doi.org/10.1016/j.proeng.2013.12.053</a>.</p>

<p>[11] W. R. Chen. Effect of local Kelvin–Voigt damping on eigenfrequencies of cantilevered twisted Timoshenko beams. <em>Procedia Engineering</em>, <strong>79</strong>, (2014), pp. 160–165. <a href="https://doi.org/10.1016/j.proeng.2014.06.325">https://doi.org/10.1016/j.proeng.2014.06.325</a>.</p>

<p>[12] W. R. Chen. Parametric studies on bending vibration of axially-loaded twisted Timoshenko beams with locally distributed Kelvin–Voigt damping. <em>International Journal of Mechanical Sciences</em>, <strong>88</strong>, (2014), pp. 61–70. <a href="https://doi.org/10.1016/j.ijmecsci.2014.07.006">https://doi.org/10.1016/j.ijmecsci.2014.07.006</a>.</p>

<p>[13] P. S. P. Zhang and H. Qing. Stress-driven local/nonlocal mixture model for buckling and free vibration of FG sandwich Timoshenko beams resting on a nonlocal elastic foundation. <em>Composite Structures</em>, <strong>289</strong>, (2022). <a href="https://doi.org/10.1016/j.compstruct.2022.115473">https://doi.org/10.1016/j.compstruct.2022.115473</a>.</p>

<p>[14] P. S. P. Zhang and H. Qing. Unified two-phase nonlocal formulation for vibration of functionally graded beams resting on nonlocal viscoelastic Winkler-Pasternak foundation. <em>Applied Mathematics and Mechanics</em>, <strong>44</strong>, (2023), pp. 89–108. <a href="https://doi.org/10.1007/s10483-023-2948-9">https://doi.org/10.1007/s10483-023-2948-</a><a href="https://doi.org/10.1007/s10483-023-2948-9">9</a>.</p>

<p>[15] L. Fryba. <em>Vibration of solids and structures under moving loads</em>. Springer Netherlands, (1972). <a href="https://doi.org/10.1007/978-94-011-9685-7">https://doi.org/10.1007/978-94-011-9685-7</a>.</p>

<p>[16] V. H. Nguyen and D. Duhamel. Finite element procedures for nonlinear structures in moving coordinates. part 1: Infinite bar under moving axial loads. <em>Computers and Structures</em>, <strong>84</strong>, (2006), pp. 1368–1380. <a href="https://doi.org/10.1016/j.compstruc.2006.02.018">https://doi.org/10.1016/j.compstruc.2006.02.018</a>.</p>

<p>[17] V. H. Nguyen and D. Duhamel. Finite element procedures for nonlinear structures in moving coordinates. Part II: Infinite beam under moving harmonic loads. <em>Computers and Structures</em>, <strong>86</strong>, (2008), pp. 2056–2063. <a href="https://doi.org/10.1016/j.compstruc.2008.04.010">https://doi.org/10.1016/j.compstruc.2008.04.010</a>.</p>

<p>[18] P. C. Jorge, F. Simoes, and A. P. da Costa. Dynamics of beams on non-uniform nonlinear foundations subjected to moving loads. <em>Computers and Structures</em>, <strong>148</strong>, (2014), pp. 26–34. <a href="https://doi.org/10.1016/j.compstruc.2014.11.002">https://doi.org/10.1016/j.compstruc.2014.11.002</a>.</p>

<p>[19] L. H. Tran, T. Hoang, D. Duhamel, G. Foret, S. Messad, and A. Loac. Analytical model of the dynamics of railway sleeper. In <em>Proceedings of the 6th International Conference on Computational Methods in Structural Dynamics and Earthquake Engineering (COMPDYN 2015)</em>, Institute of Structural Analysis and Antiseismic Research School of Civil Engineering National Technical University of Athens (NTUA) Greece, COMPDYN 2017, (2017), pp. 3937–3948. <a href="https://doi.org/10.7712/120117.5695.18372">https://doi.org/10.7712/120117.5695.18372</a>.</p>

<p>[20] L. H. Tran, T. Hoang, G. Foret, D. Duhamel, S. Messad, and A. Loaec. A fast analytic method to calculate the dynamic response of railways sleepers. <em>Journal of Vibration and Acoustics</em>, <strong>141</strong>, (2018), pp. 1368–1380. <a href="https://doi.org/10.1115/1.4040392">https://doi.org/10.1115/1.4040392</a>.</p>

<p>[21] L. H. Tran, T. Hoang, G. Foret, D. Duhamel, S. Messad, and A. Loaec. Influence of non-homogeneous foundations on the dynamic responses of railway sleepers. <em>International Journal of Structural Stability and Dynamics</em>, <strong>21</strong>, (2021). <a href="https://doi.org/10.1142/s0219455421500024">https://doi.org/10.1142/s0219455421500024</a>.</p>

<p>[22] L. H. Tran, K. Le-Nguyen, and T. Hoang. A comparison of beam models for the dynamics of railway sleepers. <em>International Journal of Rail Transportation</em>, <strong>11</strong>, (2022), pp. 92–110. <a href="https://doi.org/10.1080/23248378.2022.2034062">https://doi.org/10.1080/23248378.2022.2034062</a>.</p>

<p>[23] L.-H. Tran and K. Le-Nguyen. Calculation of dynamic responses of a cracked beam on visco-elastic foundation subjected to moving loads, and its application to a railway track model. <em>International Journal of Applied Mechanics</em>, <strong>15</strong>, (2023). <a href="https://doi.org/10.1142/s1758825123500266">https://doi.org/10.1142/s1758825123500266</a>.</p>

<p>[24] L.-H. Tran, T.-M. Duong, T. Hoang, G. Foret, and D. Duhamel. An analytical model to calculate the forced vertical vibrations of two rails subjected to the dynamic loads of ballasted railway track. <em>Structures</em>, <strong>68</strong>, (2024). <a href="https://doi.org/10.1016/j.istruc.2024.107203">https://doi.org/10.1016/j.istruc.2024.107203</a>.</p>

<p>[25] L.-H. Tran, T.-M. Duong, B. Claudet, K. Le-Nguyen, A. Nordborg, and F. Schmidt. Comparative analysis of beam models for vertical rail vibrations under dynamic forces. <em>European Journal of Mechanics - A/Solids</em>, <strong>110</strong>, (2025). <a href="https://doi.org/10.1016/j.euromechsol.2024.105497">https://doi.org/10.1016/j.euromechsol.2024.105497</a>.</p>

<p>[26] P. Fieguth and S. Sinha. Automated analysis and detection of cracks in underground scanned pipes. In <em>Proceedings 1999 International Conference on Image Processing (Cat. 99CH36348)</em>, IEEE, Vol. 4 of <em>ICIP-99</em>, (1999), pp. 395–399. <a href="https://doi.org/10.1109/icip.1999.819622">https://doi.org/10.1109/icip.1999.819622</a>.</p>

<p>[27] Q. Feng, Q. Kong, L. Huo, and G. Song. Crack detection and leakage monitoring on reinforced concrete pipe. <em>Smart Materials and Structures</em>, <strong>24</strong>, (2015). <a href="https://doi.org/10.1088/0964-1726/24/11/115020">https://doi.org/10.1088/0964-</a> <a href="https://doi.org/10.1088/0964-1726/24/11/115020">1726/24/11/115020</a>.</p>

<p>[28] R. D. Adams, P. Cawley, C. J. Pye, and B. J. Stone. A vibration technique for non-destructively assessing the integrity of structures. <em>Journal of Mechanical Engineering Science</em>, <strong>20</strong>, (2), (1978), pp. 93–100. <a href="https://doi.org/10.1243/jmes_jour_1978_020_016_02">https://doi.org/10.1243/jmes jour 1978 020 016 02</a>.</p>

<p>[29] H. J. Petroski. Simple static and dynamic models for the cracked elastic beam. <em>International Journal of Fracture</em>, <strong>17</strong>, (1981), pp. R71–R76. <a href="https://doi.org/10.1007/bf00036201">https://doi.org/10.1007/bf00036201</a>.</p>

<p>[30] J. Lemaitre. <em>Handbook of materials behavior models</em>, Vol. 1-3. Academic Press, (2001).</p>

<p>[31] N. T. Khiem and T. V. Lien. A simplified method for natural frequency analysis of a multiple cracked beam. <em>Journal of Sound and Vibration</em>, <strong>245</strong>, (2001), pp. 737–751. <a href="https://doi.org/10.1006/jsvi.2001.3585">https://doi.org/10.1006/jsvi.2001.3585</a>.</p>

<p>[32] S. P. Lele and S. K. Maiti. Modelling of transverse vibration of short beams for crack detection and measurement of crack extension. <em>Journal of Sound and Vibration</em>, <strong>257</strong>, (2002), pp. 559–583. <a href="https://doi.org/10.1006/jsvi.2002.5059">https://doi.org/10.1006/jsvi.2002.5059</a>.</p>

<p>[33] E. Viola, L. Federici, and L. Nobile. Detection of crack location using cracked beam element method for structural analysis. <em>Theoretical and Applied Fracture Mechanics</em>, <strong>36</strong>, (2001), pp. 23– 35. <a href="https://doi.org/10.1016/s0167-8442(01)00053-2">https://doi.org/10.1016/s0167-8442(01)00053-2</a>.</p>

<p>[34] S. H. S. Carneiro and D. J. Inman. Continuous model for the transverse vibration of cracked Timoshenko beams. <em>Journal of Vibration and Acoustics</em>, <strong>124</strong>, (2), (2002), pp. 310–320. <a href="https://doi.org/10.1115/1.1452744">https://doi.org/10.1115/1.1452744</a>.</p>

<p>[35] J. L. Hearndon, G. P. Potirniche, D. Parker, P. M. Cuevas, H. Rinehart, P. T. Wang, and M. F. Horstemeyer. Monitoring structural damage of components using an effective modulus approach. <em>Theoretical and Applied Fracture Mechanics</em>, <strong>50</strong>, (2008), pp. 23–29. <a href="https://doi.org/10.1016/j.tafmec.2008.04.002">https://doi.org/10.1016/j.tafmec.2008.04.002</a>.</p>

<p>[36] A. C. Batihan and F. S. Kadioglu. Vibration analysis of a racked beam on an elastic foundation. <em>International Journal of Structural Stability and Dynamics</em>, <strong>16</strong>, (05), (2016). <a href="https://doi.org/10.1142/s0219455415500066">https://doi.org/10.1142/s0219455415500066</a>.</p>

<p>[37] H. Darban, R. Luciano, and M. Basista. Free transverse vibrations of nanobeams with multiple cracks. <em>International Journal of Engineering Science</em>, <strong>177</strong>, (2022). <a href="https://doi.org/10.1016/j.ijengsci.2022.103703">https://doi.org/10.1016/j.ijengsci.2022.103703</a>.</p>

<p>[38] J. A. Loya, L. Rubio, and J. Fernández-Sáez. Natural frequencies for bending vibrations of Timoshenko cracked beams. <em>Journal of Sound and Vibration</em>, <strong>290</strong>, (2006), pp. 640–653. <a href="https://doi.org/10.1016/j.jsv.2005.04.005">https://doi.org/10.1016/j.jsv.2005.04.005</a>.</p>

<p>[39] J. A. Loya, J. Aranda-Ruiz, and R. Zaera. Natural frequencies of vibration in cracked Timoshenko beams within an elastic medium. <em>Theoretical and Applied Fracture Mechanics</em>, <strong>118</strong>, (2022). <a href="https://doi.org/10.1016/j.tafmec.2022.103257">https://doi.org/10.1016/j.tafmec.2022.103257</a>.</p>

<p>[40] T.-S. Pham, T. Hoang, D. Duhamel, G. Foreˆt, F. Schmidt, F.-B. Cartiaux, and V. Le Corvec. Dynamic response of a cracked multi-span continuous beam subjected to a moving multi-axle vehicle load. In <em>International Conference on Structural Health Monitoring of Intelligent Infrastructure</em>, (2021).</p>

<p>[41] T. Yan, S. Kitipornchai, J. Yang, and X. Q. He. Dynamic behaviour of edge-cracked shear deformable functionally graded beams on an elastic foundation under a moving load. <em>Composite Structures</em>, <strong>93</strong>, (2011), pp. 2992–3001. <a href="https://doi.org/10.1016/j.compstruct.2011.05.003">https://doi.org/10.1016/j.compstruct.2011.05.003</a>.</p>

<p>[42] M. Rezaiee-Pajand and N. Gharaei-Moghaddam. A force-based rectangular cracked element. <em>International Journal of Applied Mechanics</em>, <strong>13</strong>, (2021). <a href="https://doi.org/10.1142/s1758825121500472">https://doi.org/10.1142/s1758825121500472</a>.</p>

<p>[43] S. Zheng, R. Huang, R. Lin, and Z. Liu. A phase field solution for modelling hyperelastic material and hydrogel fracture in ABAQUS. <em>Engineering Fracture Mechanics</em>, <strong>276</strong>, (2022). <a href="https://doi.org/10.1016/j.engfracmech.2022.108894">https://doi.org/10.1016/j.engfracmech.2022.108894</a>.</p>

<p>[44] T. Hoang, D. Duhamel, G. Foret, H. Yin, P. Joyez, and R. Caby. Calculation of force distribution for a periodically supported beam subjected to moving loads. <em>Journal of Sound and Vibration</em>, <strong>388</strong>, (2017), pp. 327–338. <a href="https://doi.org/10.1016/j.jsv.2016.10.031">https://doi.org/10.1016/j.jsv.2016.10.031</a>.</p>

<p>[45] T. S. Azoh, W. Nzie, B. Djeumako, and B. S. Fotsing. Modeling of train track vibrations for maintenance perspectives: Application. <em>European Scientific Journal</em>, <strong>10</strong>, (21), (2014), pp. 260–275.</p>

<p>[46] E. L. Fichoux. <em>Presentation et utilisation de Cast3M</em>. Support of CEA, (2011).</p>

<p>[47] J. Fernandez-Saez, L. Rubio, and C. Navarro. Approximate calculation of the fundamental frequency for bending vibrations of cracked beams. <em>Journal of Sound and Vibration</em>, <strong>225</strong>, (1999), pp. 345–352. <a href="https://doi.org/10.1006/jsvi.1999.2251">https://doi.org/10.1006/jsvi.1999.2251</a>.</p>

<p>[48] T. G. Chondros and A. D. Dimarogonas. Vibration of a cracked cantilever beam. <em>Journal of Vibration and Acoustics</em>, <strong>120</strong>, (1998), pp. 742–746. <a href="https://doi.org/10.1115/1.2893892">https://doi.org/10.1115/1.2893892</a>.</p>

<p>[49] X. Zhao, Y. R. Zhao, X. Z. Gao, X. Y. Li, and Y. H. Li. Greens functions for the forced vibrations of cracked Euler-Bernoulli beams. <em>Mechanical Systems and Signal Processing</em>, <strong>68–69</strong>, (2016), pp. 155–175. <a href="https://doi.org/10.1016/j.ymssp.2015.06.023">https://doi.org/10.1016/j.ymssp.2015.06.023</a>.</p>