Response of Thin Plates Subjected to Inertia Distributed Loads Moving with Variable Velocity in Opposite Directions

  • M. S. Dada Department of Mathematics, University of Ilorin, Ilorin, Nigeria
  • K. O. Adedeji Department of Mathematics, University of Ilorin, Ilorin, Nigeria
Keywords: inertia loads, distributed loads, variable velocity, Chebyshev collocation method

Abstract

The study examined the dynamic deflection characteristic of a plate which is subjected to a pair of inertia distributed loads, moving with variable velocities and in opposite direction was investigated. The model was formulated based on the thin plate theory. The governing equation obtained for the behavior of the model was reduced from a partial differential equation to an ordinary differential equation using a series solution for the dynamic deflection in terms of the normal modes. The reduced ODE was solved using chebyshev collocation method, result obtained was presented in graphical form.

References

Amiri, J. V., Nikkhoo, A., Davoodi, M. R., & Hassanabadi, M. E. (2013). Vibration analysis of a Mindlin elastic plate under a moving mass excitation by eigenfunction expansion method. Thin-Walled Structures, 62, 53–64. https://doi.org/10.1016/j.tws.2012.07.014

Boyd, J. P. (2001). Chebyshev and Fourier spectral methods. Courier Corporation.

Canuto, C., Hussaini, M. Y., Quarteroni, A., & Zang, T. A. (2007). Spectral methods: Evolution to complex geometries and applications to fluid dynamics. Springer. https://doi.org/10.1007/978-3-540-30728-0

De Faria, A. R., & Oguamanam, C. D. (2004). Finite element analysis of the dynamic response of plates under traversing loads using adaptive meshes. Thin-Walled Structures, 42, 1481–1493. https://doi.org/10.1016/j.tws.2004.03.012

Dyniewicz, B., Pisarski, D., & Bajer, C. I. (2017). Vibrations of a Mindlin plate subjected to a pair of inertial loads moving in opposite directions. Journal of Sound and Vibration, 386, 265–282. https://doi.org/10.1016/j.jsv.2016.09.027

Eftekhari, S. A., & Jafari, A. A. (2014). A mixed modal-differential quadrature method for free and forced vibration of beams in contact with fluid. Meccanica, 49(3), 535–564. https://doi.org/10.1007/s11012-013-9810-z

Esen, I. (2013). A new finite element for transverse vibration of rectangular thin plates under a moving mass. Finite Elements in Analysis and Design, 66, 26–35. https://doi.org/10.1016/j.finel.2012.11.005

Esen, I. (2015). A new FEM procedure for transverse and longitudinal vibration analysis of thin rectangular plates subjected to a variable velocity moving load along an arbitrary trajectory. Latin American Journal of Solids and Structures, 12(4), 808–830. https://doi.org/10.1590/1679-78251525

Gbadeyan, J. A., & Oni, S. T. (1995). Dynamic behaviour of beams and rectangular plates under moving loads. Journal of Sound and Vibration, 185(3), 677–695. https://doi.org/10.1006/jsvi.1995.0226

Gbadeyan, J. A., & Dada, M. S. (2006). Dynamic response of a Mindlin elastic rectangular plate under a distributed moving mass. International Journal of Mechanical Sciences, 48, 323–340. https://doi.org/10.1016/j.ijmecsci.2005.09.005

Mamandi, A., Kargarnovin, M. H., & Farsi, S. (2010). An investigation on effects of travelling mass with variable velocity on nonlinear dynamic response of an inclined Timoshenko beam with different boundary conditions. International Journal of Mechanical Sciences, 52(12), 1694–1708. https://doi.org/10.1016/j.ijmecsci.2010.09.003

Marchesiello, S., Fasana, A., & Garibaldi, L. (1999). Dynamics of multi-span continuous straight bridges subject to multi-degrees of freedom moving vehicle excitation. Journal of Sound and Vibration, 224(3), 541–561. https://doi.org/10.1006/jsvi.1999.2197

Nikkhoo, A., Banihashemi, S., & Kiani, K. (2022). Parametric investigations on dynamics of cracked thin rectangular plates excited by a moving mass. Scientia Iranica, 29(2), 789–802. https://doi.org/10.24200/sci.2022.58345.5686

Nikkhoo, A., Banihashemi, S., & Kiani, K. (2023). On non-stationary response of cracked thin rectangular plates acted upon by a moving random force. Scientia Iranica, 30(3), Article SCI.61247.7220. https://doi.org/10.24200/sci.2023.61247.7220

Nikkhoo, A., Hassanabadi, M. E., & Azam, S. E. (2014). Vibration of a thin rectangular plate subjected to a series of moving inertial loads. Mechanics Research Communications, 55, 105–113. https://doi.org/10.1016/j.mechrescom.2013.10.009

Pi, Y., Yu, R., Li, C., Yang, B., & Luo, J. (2023). Vibration control of a thin rectangular plate subjected to moving masses using an adaptive sliding mode control method. International Journal of Robust and Nonlinear Control, 33(10), 6835–6856. https://doi.org/10.1002/rnc.6835

Song, Q., Shi, J., Liu, Z., & Wan, Y. (2016). Dynamic analysis of rectangular thin plates of arbitrary boundary conditions under moving loads. International Journal of Mechanical Sciences, 117, 16–29. https://doi.org/10.1016/j.ijmecsci.2016.08.005

Sorrentino, S., & Catania, G. (2017). Dynamic analysis of rectangular plates crossed by distributed moving loads. Mathematics and Mechanics of Solids, 23(9), 1291–1302. https://doi.org/10.1177/1081286517719120

Wu, J. J. (2005). Dynamic analysis of a rectangular plate under a moving line load using scale beams and scaling laws. Computers & Structures, 83(19–20), 1646–1658. https://doi.org/10.1016/j.compstruc.2004.11.022

Wu, J. J. (2007). Vibration analyses of an inclined flat plate subjected to moving loads. Journal of Sound and Vibration, 299(1–2), 373–387. https://doi.org/10.1016/j.jsv.2006.07.002

Yao, S. J., Chen, Y., Sun, C., Zhao, N., Wang, Z., & Zhang, D. (2024). Dynamic response mechanism of thin-walled plate under confined and unconfined blast loads. Journal of Marine Science and Engineering, 12(2), Article 224. https://doi.org/10.3390/jmse12020224

Published
2025-08-28
How to Cite
Dada, M. S., & Adedeji, K. O. (2025). Response of Thin Plates Subjected to Inertia Distributed Loads Moving with Variable Velocity in Opposite Directions. Earthline Journal of Mathematical Sciences, 15(5), 905-925. https://doi.org/10.34198/ejms.15525.905925
Section
Articles