Longitudinal Vibration of Temperature Dependent Bar with Variable Cross-Section

Öz

Vibration behavior of a bar with variable cross-section, which its material properties vary with temperature, is investigated in this study. In the analysis, not only theoretical solution but also numerical solution is performed for validation. The numerical analysis is overcome by SolidWorks program based on finite element method. Four types of effects on the bar are investigated. These are effects of temperature variation, geometric ratio, slenderness ratio and mode numbers variation. The temperature is increased from 22 °C to 250 °C. The geometric ratio is varied from 0 to -1/L at intervals of 0.25/L. The slenderness ratio is varied from 1/10 to 1/20 by increasing the length of bar from 200 mm to 400 mm. As for the mode numbers, the first three mode shapes are examined in the analysis. The boundary condition of the bar is taken as clamped-free. According to the results, the natural frequency decreases with increasing the temperature. The natural frequency also decreases with decreasing the slenderness ratio. But, it increases with decreasing the geometric ratio and also increases with increasing the mode number. When the theoretical and numerical results are examined, it is seen that the results are in harmony.

Anahtar Kelimeler

• Bar,temperature,vibration,variable cross-section

Kaynakça

1. [1] Demir E., Çallıoğlu H. and Sayer M., “Vibration analysis of sandwich beams with variable cross section on variable Winkler elastic foundation”, Science and Engineering of Composite Materials, 20(4): 359–370, (2013).
2. [2] Çallıoğlu H., Sayer M., Demir E., “Elastic-plastic stress analysis of rotating functionally graded discs”, Thin-Walled Structures, 94: 38–44, (2015).
3. [3] Li Q. S., “Free longitudinal vibration analysis of multi-step non-uniform bars based on piecewise analytical solutions”, Engineering Structures, 22(9): 1205–1215, (2000).
4. [4] Bert C. W. and Zeng H., “Analysis of axial vibration of compound bars by differential transformation method”, Journal of Sound and Vibration, 275(3-5): 641–647, (2004).
5. [5] Ma H., “Exact solutions of axial vibration problems of elastic bars”, International Journal for Numerical Methods in Engineering, 75(2): 241–252, (2008).
6. [6] Arndt M., Machado R. D. and Scremin A., “An adaptive generalized finite element method applied to free vibration analysis of straight bars and trusses”, Journal of Sound and Vibration, 329(6): 659–672, (2010).
7. [7] Velasco S., Roman F. L. and White J. A., “A simple experiment for measuring bar longitudinal and flexural vibration frequencies”, American Journal of Physics, 78(12): 1429–1432, (2010).
8. [8] Ranjbaran A., Shokrzadeh A. R. and Khosravi S., “A new finite element analysis of free axial vibration of cracked bars”, International Journal for Numerical Methods in Biomedical Engineering, 27(10): 1611–1621, (2011).

9. [9] Akgoz B., Civalek O., “Lomgitudinal vibration analysis of strain gradient bars made of functionally graded materials (FGM)”, Composites Part B-Engineering, 55: 263-268, (2013).
10. [10] Bui H. L., Tran M. T., Le M. Q. and Tran D. T., “Optimal configurations of circular bars under free torsional and longitudinal vibration based on Pontryagin’s maximum principle”, Meccanica, 51(6): 1491–1502, (2016).
11. [11] II’gamov M. A., “Longitudinal vibrations of a bar with incipient transverse cracks”, Mechanics of Solids, 52(1): 18-24, (2017).
12. [12] Lee M., Park I. and Lee U., “An approximate spectral element model for the dynamic analysis of an FGM bar in axial vibration”, Structural Engineering and Mechanics, 61(4): 551-561, (2017).
13. [13] https://en.wikipedia.org/wiki/Ti-6Al-4V, (2018).
14. [14] Shen H. S., “Functionally Graded Materials Nonlinear Analysis of Plates and Shells”, CRC Press Taylor & Francis Group, Boca Raton, Florida, Usa, (2009).
15. [15] Hagedorn P. and DasGupta A., “Vibrations and Waves in Continuous Mechanical Systems”, John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, England, (2007).