East Asian mathematical journal

  • 제37권5호
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  • Pages.619-626
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  • 2021
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  • 1226-6973(pISSN)
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  • 2287-2833(eISSN)
영남수학회 (The Youngnam Mathematical Society)
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MATHEMATICAL MODELLING FOR THE AXIALLY MOVING PLATE WITH INTERNAL TIME DELAY

  • Kim, Daewook (Department of Mathematics and Education Seowon University)
  • 투고 : 2021.09.03
  • 심사 : 2021.09.27
  • 발행 : 2021.09.30
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초록

In [1, 2], we studied the string-like system with time-varying delay. Unlike the string system, the plate system must consider both longitudinal and transverse strains. First, we consider the physical phenomenon of an axially moving plate concerning kinetic energy, potential energy, and work dones. By the energy conservation law in physics, we have a nonlinear plate-like system with internal time delay.

키워드

과제정보

We are very grateful to the anonymous Referees for the some valuable comments of this manuscript.

참고문헌

  1. Daewook Kim, Asymptotic behavior for the viscoelastic Kirchhoff type equation with an internal time-varying delay term, East Asian Mathematical Journal 34 (2016), 399412.
  2. Daewook Kim, Mathematical modelling for the axially moving membrane with internal time delay, East Asian Mathematical Journal 37 (2021), 141147. https://doi.org/10.7858/EAMJ.2021.012
  3. Daewook Kim, Exponential Decay for the Solution of the Viscoelastic Kirchhoff Type Equation with Memory Condition at the Boundary, East Asian Mathematical Journal 34 (2018), 69-84. https://doi.org/10.7858/eamj.2018.008
  4. Daewook Kim, Asymptotic behavior of a nonlinear Kirchhoff type equation with spring boundary conditions, Computers and Mathematics with Applications 62 (2011), 3004-3014. https://doi.org/10.1016/j.camwa.2011.08.011
  5. Daewook Kim, Stabilization for the Kirchhoff type equation from an axially moving heterogeneous string modeling with boundary feedback control, Nonlinear Analysis: Theory, Methods and Applications 75 (2012), 3598-3617. https://doi.org/10.1016/j.na.2012.01.018
  6. G. Kirchhoff, Vorlesungenuber Mechanik, Teubner, Leipzig, 1983.
  7. J. Limaco, H. R. Clark, and L. A. Medeiros, Vibrations of elastic string with nonhomogeneous material, Journal of Mathematical Analysis and Applications 344 (2008), 806-820. https://doi.org/10.1016/j.jmaa.2008.02.051
  8. F. Pellicano and F. Vestroni, Complex dynamics of high-speed axially moving systems, Journal of Sound and Vibration, 258 (2002), 31-44. https://doi.org/10.1006/jsvi.2002.5070
  9. S. S. Rao, Vibration of continuous systems, Wiley, Florida, 2005.
  10. A. Daz-de-Anda, J. Flores, L. Gutirrez, R.A. Mndez-Snchez, G. Monsivais, and A. Morales Experimental study of the Timoshenko beam theory predictions, Journal of Sound and Vibration 34 (2012), 57325744.