Journals / Teknik Dergi / 2019 / Cilt: 30 - Sayı: 4

Rotary Inertia and Higher Modes Effect on the Dynamic Response of Timoshenko Beams on Two-Parameter Elastic Foundation

Pages
9289–9308
Publication Date
2019-07-01
DOI
—
🏛️Bibliographic metadata and full text access for this article are provided via DergiPark.
DergiPark Record ↗
✨

AI Summary & Key Takeaways

AI Insight
⚡ TL;DR(Too Long; Didn't Read)

A numerical example is presented to compare the modal responses of bending moment and shear force of the beams on Winkler and Vlasov type foundations with and without the rotary inertia effect.

📌 3 Key Takeaways

🎯
Objective & Hypothesis:This study investigates the dynamic response of the axially loaded Timoshenko beams on two-parameter foundation with generalized elastic end conditions.
📊
Key Findings & Data:A simplified modal analysis procedure is presented for the vibration analysis by using the conventional separation of variables method.
💡
Conclusion & Impact:A numerical example is presented to compare the modal responses of bending moment and shear force of the beams on Winkler and Vlasov type foundations with and without the rotary inertia effect.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Rotary inertia · higher modes effect · separation of variables method

Abstract

This study investigates the dynamic response of the axially loaded Timoshenko beams on two-parameter foundation with generalized elastic end conditions. A simplified modal analysis procedure is presented for the vibration analysis by using the conventional separation of variables method. The effects of higher modes and rotary inertia on the dynamic response of the forced Timoshenko beam are highlighted. A numerical example is presented to compare the modal responses of bending moment and shear force of the beams on Winkler and Vlasov type foundations with and without the rotary inertia effect.

Özet

This study investigates the dynamic response of the axially loaded Timoshenko beams on two-parameter foundation with generalized elastic end conditions. A simplified modal analysis procedure is presented for the vibration analysis by using the conventional separation of variables method. The effects of higher modes and rotary inertia on the dynamic response of the forced Timoshenko beam are highlighted. A numerical example is presented to compare the modal responses of bending moment and shear force of the beams on Winkler and Vlasov type foundations with and without the rotary inertia effect.

🔖

Cite This Article

HIZAL, Ç., ÇATAL, H. H. (2019). Rotary Inertia and Higher Modes Effect on the Dynamic Response of Timoshenko Beams on Two-Parameter Elastic Foundation. Teknik Dergi, Cilt: 30 - Sayı: 4, 9289–9308. https://ajindex.com/articles/51240

📄 Full Text PDF Viewer

📄

PDF görüntüleyici hazırlanıyor...

References (15)

  1. Doyle, P.F. and Pavlovic, M., Vibration of beams on partial elastic foundations. Earthquake Engineering and Structural Dynamics, 10, 663–674, 1982.
  2. West, H. H. and Mafi, M., Eigenvalues for beam-columns on elastic supports. Journal of Structural Engineering, 110, 1305–1320, 1984.
  3. Çatal, H. H., Free vibration of partially supported piles with the effects of bending moment, axial and shear force. Engineering Structures, 24, 1615-1622, 2002.
  4. Çatal, H. H., Free vibration of semi-rigid connected and partially embedded piles with the effects of the bending moment, axial and shear force. Engineering Structures, 28, 1911-1918, 2006.
  5. Yeşilce, Y. and Çatal, H. H., Free vibration of piles embedded in soil having different modulus of subgrade reaction. Applied Mathematical Modelling, 32(5), 889-900.
  6. Çatal, S., Solution of free vibration equations of beam on elastic soil by using differential transform method. Applied Mathematical Modelling, 32(9), 1744-1757, 2008.
  7. Yeşilce, Y. and Çatal, S., Free vibration of axially loaded Reddy-Bickford beam on elastic soil using the differential transform method, Struct. Eng. Mech. 31(4), 453-475, 2009.
  8. Yeşilce, Y. and Çatal, H. H., Solution of free vibration equations of semi-rigid connected Reddy–Bickford beams resting on elastic soil using the differential transform method. Archive of Applied Mechanics, 81, 199-213, 2011.
  9. Sapountzakis, E. J. and Kampitsis, A. E., Nonlinear dynamic analysis of Timoshenko beam-columns partially supported on tensionless Winkler foundation, Computers and Structures, 88, 1206-1219, 2010.
  10. Çatal, S., Response of forced Euler-Bernoulli beams using differential transform method. Struct. Eng. Mech. 42(1), 95-119, 2012.
  11. Özturk, B. and Coşkun, S. B., Analytical solution for free vibration analysis of beam on elastic foundation with different support conditions. Mathematical Problems in Engineering, 2013, 1-7, 2013.
  12. Pasternak P.L., On a new method of analysis on elastic foundation by means of two constants. Gosudarstvennoe Izdatel’stvo Literaturi po Stroitel’stvu i Arkhitekture, 1954.
  13. Vlasov, V.Z. and Leont’ev, U.N.: Beams, plates and shells on elastic foundations. Israel Program for Scientific Translations, Jerusalem, 1966.
  14. Morfidis, K. and Avramidis, I. E., Formulation of a generalized beam element on a two-parameter elastic foundation with semi-rigid connections and rigid offsets. Computers and Structures, 80, 1919-1934, 2002.
  15. Yokoyama, T., Vibration analysis of Timoshenko beam-columns on two-parameter ela