An approach to free vibration analysis of axially graded beams

• Autorzy: Kukla S. , Rychlewska J.

Identyfikatory

DOI

10.15632/jtam-pl.54.3.859

• Języki publikacji: EN

Abstrakty

EN

In this study, the solution to the free vibration problem of axially graded beams with a non-uniform cross-section has been presented. The proposed approach relies on replacing functions characterizing functionally graded beams by piecewise exponential functions. The frequency equation has been derived for axially graded beams divided into an arbitrary number of subintervals. Numerical examples show the influence of the parameters of the functionally graded beams on the free vibration frequencies for different boundary conditions.

Słowa kluczowe

EN

axially graded beam; non-uniform beam; free vibration

• Wydawca: Polskie Towarzystwo Mechaniki Teoretycznej i Stosowanej
• Czasopismo: Journal of Theoretical and Applied Mechanics
• Rocznik: 2016
• Tom: Vol. 54 nr 3
• Strony: 859--870
• Opis fizyczny: Bibliogr. 18 poz., rys., tab.

Twórcy

autor

Kukla S.

• Czestochowa University of Technology, Institute of Mathematics, Czestochowa, Poland

autor

Rychlewska J.

• Czestochowa University of Technology, Institute of Mathematics, Czestochowa, Poland

Bibliografia

• 1. Alshorbagy A.E., Eltaher M.A., Mahmoud F.F., 2011, Free vibration characteristics of a functionally graded beam by finite element method, Applied Mathematical Modelling, 35, 412-425
• 2. Anandrao K.S., Gupta R.K., Ramachandran P., Rao G.V., 2012, Free vibration analysis of functionally graded beams, Defence Science Journal, 62, 3, 139-146
• 3. Chauhan P.K., Khan I.A., 2014, Review on analysis of functionally graded material beam type structure, International Journal of Advanced Mechanical Engineering, 4, 3, 299-306
• 4. Hein H., Feklistova L., 2011, Free vibrations of non-uniform and axially functionally graded beams using Haar wavelets, Engineering Structures, 33, 3696-3701
• 5. Huang Y., Li X.-F., 2010, A new approach for free vibration of axially functionally graded beams with non-uniform cross-section, Journal of Sound and Vibration, 329, 2291-2303
• 6. Huang Y., Yang L.-E., Luo Q.-Z., 2013, Free vibration of axially functionally graded Timoshenko beams with non-uniform cross-section, Composites: Part B, 45, 1493-1498
• 7. Kukla S., Rychlewska J., 2014, Free vibration of axially functionally graded Euler-Bernoulli beams, Journal of Applied Mathematics and Computational Mechanics, 13, 1, 39-44
• 8. Lebed O.I., Karnovsky I.A., 2000, Formulas for Structural Dynamics, Mc Graw-Hill
• 9. Li X.-F., Kang Y.-A., Wu J.-X., 2013, Exact frequency equations of free vibration of exponentially functionally graded beams, Applied Acoustics, 74, 413-420
• 10. Liu Y., Shu D.W., 2014, Free vibrations analysis of exponential functionally graded beams with a single delamination, Composites: Part B, 59, 166-172
• 11. Matbuly M.S., Ragb O., Nassar M., 2009, Natural frequencies of a functionally graded cracked beam using the differential quadrature method, Applied Mathematics and Computation, 215, 2307-2316
• 12. Pradhan K.K., Chakraverty S., 2013, Free vibration of Euler and Timoshenko functionally graded beams by Rayleigh-Ritz method, Composites: Part B, 51, 175-184
• 13. Shahba A., Attarnejad R., Zarrinzadeh H., 2013, Free vibration analysis of centrifugally stiffened tapered functionally graded beams, Mechanics of Advanced Materials and Structures, 20, 331-338
• 14. Shahba A., Rajasekaran S., 2012, Free vibration and stability of tapered Euler-Bernoulli beams made of axially functionally graded materials, Applied Mathematical Modelling, 36, 3094-3111
• 15. Sina S.A., Navazi H.M., Haddadpour H., 2009, An analytical method for free vibration analysis of functionally graded beams, Materials and Design, 30, 741-747
• 16. Tang A.-Y., Wu J.-X., Li X.-F., Lee K.Y., 2014, Exact frequency equations of free vibration of exponentially non-uniform functionally graded Timoshenko beams, International Journal of Mechanical Sciences, 89, 1-11
• 17. Wattanasakulpong N., Ungbhakorn V., 2012, Free vibration analysis of functionally graded beams with general elastically end constraints by DTM, World Journal of Mechanics, 2, 297-310
• 18. Wu L., Wang Q., Elishakoff I., 2005, Semi-inverse method for axially functionally graded beams with an anti-symmetric vibration mode, Journal of Sound and Vibration, 284, 1190-1202

Uwagi

PL

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniajacą naukę.