Free vibration of the Timoshenko beam interacting with the Winkler foundation

• Autorzy: Noga S. , Bogacz R.
• Języki publikacji: EN

Abstrakty

EN

In the study a free transverse vibration analysis of the simply supported Timoshenko beam on an arbitrary variable Winkler foundation is presented. The analysis is based on the use of the analytical method compared with numerical simulation. The elastic foundation is composed of two arbitrary variable, massless, regions of the Winkler type. At first the general solution of free vibration is derived by the separation of variable method. The natural frequencies of the system under consideration are determined. Then the models of the system formulated by using finite element technique are prepared and eigenvalue problem is solved. Achieved results of calculation are discussed and compared for these models. All needed finite element models are formulated by using ANSYS FE code. It is important to note that the data presented in the article is yielded the practical advice to design engineers.

Słowa kluczowe

EN

free vibration; Timoshenko beam; Winkler foundation; finite element model

PL

drgania swobodne; belka Timoshenki; podłoże typu Winklera; model MES

• Wydawca: Polskie Towarzystwo Symulacji Komputerowej
• Czasopismo: Symulacja w Badaniach i Rozwoju
• Rocznik: 2011
• Tom: Vol. 2, nr 4
• Strony: 209--223
• Opis fizyczny: Bibliogr. 9 poz., rys., tab.

Twórcy

autor

Noga S.

• Politechnika Rzeszowska

autor

Bogacz R.

• Politechnika Krakowska

Bibliografia

• 1. R. Bogacz, On dynamics and stability of continuous systems subjected to a distributed moving load, Ingenieur – Archiv 53 (1983) 243–255.
• 2. R. Bogacz, S. Nowakowski, K. Popp, On the stability of a Timoshenko beam on an elastic foundation under a moving spring – mass system, Acta Mechanica 61 (1986) 117–127.
• 3. R. Bogacz, W. Czyczuła, Response of beam on visco – elastic foundation to moving distributed load, Journal of Theoretical and Applied Mechanics 46 (2008) 763–775.
• 4. K. T. Chan, X. Q. Wang, Free vibration of a Timoshenko beam partially loaded with distributed mass, Journal of Sound and Vibration 206 (1997) 353–369.
• 5. C. de Silva, Vibration and Shock Handbook, Taylor & Francis, Boca Raton, 2005.
• 6. S. Noga, Free transverse vibration analysis of an elastically connected annular and circular double – membrane compound system, Journal of Sound and Vibration 329 (2010) 1507–1522.
• 7. S. Noga, Free vibrations of an annular membrane attached to Winkler foundation, Vibrations in Physical Systems, vol. XXIV (2010) 295–300.
• 8. S. S. Rao, Vibration of Continuous Systems, Wiley, Hoboken, 2007.
• 9. T. Wang, L. Gagnon, Vibrations of continuous Timoshenko beams on Winkler – Pasternak foundations, Journal of Sound and Vibration 59 (1978) 211–220.