Transverse Vibration of Sandwich Beams with Thermal-Induced Nonuniform Sectional Properties
Publication: Journal of Aerospace Engineering
Volume 32, Issue 3
Abstract
This paper presents an analytical study of the transverse vibration of sandwich beams considering the thermal-induced nonuniform cross-sectional properties. Free vibration frequency formulas of sandwich beams, under linearly varied nonuniform temperature distribution scenarios, with and without considering the effect of transverse shear deformation, were derived. The effects of transverse shear deformation of the middle part of the sandwich beam and of the reduction of Young’s modulus in the bottom layer and of the shear modulus in the middle part near the bottom layer on the transverse vibration of the sandwich beam were discussed. The results highlight the importance of considering nonuniform cross-sectional properties and associated shear effects in the dynamic analysis of sandwich beams.
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Acknowledgments
The first author acknowledges the K. C. Wong Magna Fund at Ningbo University for their financial support.
References
Avsec, J., and M. Oblak. 2007. “Thermal vibrational analysis for simply supported beam and clamped beam.” J. Sound Vib. 308 (3–5): 514–525. https://doi.org/10.1016/j.jsv.2007.04.002.
Blandino, J. R., and E. A. Thornton. 2001. “Thermally induced vibration of an internally heated beam.” J. Vib. Acoust. 123 (1): 67–75. https://doi.org/10.1115/1.1320446.
Chen, J. K., B. Kim, and L. Y. Li. 2014. “Analytical approach for transverse vibration analysis of castellated beams.” Int. J. Struct. Stab. Dyn. 14 (3): 1350071. https://doi.org/10.1142/S0219455413500715.
Chen, J. K., and L. Y. Li. 2013. “Elastic axially compressed buckling of battened columns.” Int. J. Mech. Sci. 77: 1–7. https://doi.org/10.1016/j.ijmecsci.2013.09.016.
Cheng, S. S., Q. W. Yan, L. Y. Li, and B. Kim. 2015. “Thermal buckling analysis of axially loaded columns of thin-walled open section with non-uniform sectional properties.” Int. J. Struct. Stab. Dyn. 15 (6): 1450088. https://doi.org/10.1142/S0219455414500886.
Elishakoff, I., J. Kaplunov, and E. Nolde. 2015. “Celebrating the centenary of Timoshenko’s study on effects of shear deformation and rotary inertia.” ASME Appl. Mech. Rev. 67 (6): 060802. https://doi.org/10.1115/1.4031965.
Ergun, E., and V. Alkan. 2014. “Assessment of thermal effects on the free vibration characteristics of composite beams.” Mater. Test. 56 (1): 59–64. https://doi.org/10.3139/120.110525.
Gu, J. Z. 2014. “Free vibration of castellated beams with web shear and rotary inertia effects.” Int. J. Struct. Stab. Dyn. 14 (6): 1450011. https://doi.org/10.1142/S0219455414500114.
Gu, L., Z. Qin, and F. Chu. 2015. “Analytical analysis of the thermal effect on vibrations of a damped Timoshenko beam.” Mech. Syst. Sig. Process. 60: 619–643. https://doi.org/10.1016/j.ymssp.2014.11.014.
Hajianmaleki, M., and M. S. Qatu. 2013. “Vibrations of straight and curved composite beams: A review.” Compos. Struct. 100: 218–232. https://doi.org/10.1016/j.compstruct.2013.01.001.
Lei, J. S., W. B. Yuan, and L. Y. Li. 2017. “Axial compression buckling of castellated columns at elevated temperatures.” Int. J. Struct. Stab. Dyn. 17 (3): 1750034. https://doi.org/10.1142/S0219455417500341.
Li, J., L. Jiang, and X. B. Li. 2017. “A spectral element model for thermal effect on vibration and buckling of laminated beams based on trigonometric shear deformation theory.” Int. J. Mech. Sci. 133: 100–111. https://doi.org/10.1016/j.ijmecsci.2017.07.059.
Li, W., Z. Xiang, L. Chen, and M. Xue. 2007. “Thermal flutter analysis of large-scale space structures based on finite element method.” Int. J. Numer. Methods Eng. 69 (5): 887–907. https://doi.org/10.1002/nme.1793.
Marakala, N., A. Kuttan, and K. R. Kadoli. 2010. “Thermally induced vibration a simply supported beam using finite element method.” Int. J. Eng. Sci. Technol. 2 (12): 7874–7879.
Na, S., L. Librescu, and H. Jung. 2004. “Dynamics and active bending vibration control of turbomachinery rotating blades featuring temperature-dependent material problems.” J. Thermal Stress 27 (7): 625–644. https://doi.org/10.1080/01495730490466219.
Nguyen, N. D., T. K. Nguyen, T. N. Nguyen, and H. T. Thai. 2018. “New Ritz-solution shape functions for analysis of thermo-mechanical buckling and vibration of laminated composite beams.” Compos. Struct. 184: 452–460. https://doi.org/10.1016/j.compstruct.2017.10.003.
Nguyen, Q. H., M. Hjiaj, and P. L. Grognec. 2012. “Analytical approach for free vibration analysis of two-layer Timoshenko beams with interlayer slip.” J. Sound Vib. 331 (12): 2949–2961. https://doi.org/10.1016/j.jsv.2012.01.034.
Sayyad, A. S., and Y. M. Ghugal. 2017. “Bending, buckling and free vibration of laminated composite and sandwich beams: A critical review of literature.” Compos. Struct. 171: 486–504. https://doi.org/10.1016/j.compstruct.2017.03.053.
Silverman, I. K. 1995. “Natural frequencies of sandwich beams including shear and rotary effects.” J. Sound Vib. 183 (3): 547–561. https://doi.org/10.1006/jsvi.1995.0270.
Timoshenko, S. P. 1921. “On the correction for shear of the differential equation for transverse vibration of prismatic bars.” Philos. Mag. Ser. 41 (245): 744–746. https://doi.org/10.1080/14786442108636264.
Tomar, J. S., and R. Jain. 1984. “Thermal effect on frequencies of coupled vibrations of a rotating beam of linearly varying semi-circular cross-section.” J. Sound Vib. 95 (1): 1–7. https://doi.org/10.1016/0022-460X(84)90253-0.
Tomar, J. S., and R. Jain. 1985. “Thermal effect on frequencies of coupled vibrations of pre-twisted rotating beams.” AIAA J. 23 (8): 1293–1296. https://doi.org/10.2514/3.9083.
Yuan, W. B., B. Kim, and L. Y. Li. 2014. “Buckling of axially loaded castellated steel columns.” J. Constr. Steel Res. 92: 40–45. https://doi.org/10.1016/j.jcsr.2013.10.013.
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Published In
Journal of Aerospace Engineering
Volume 32 • Issue 3 • May 2019
Copyright
©2019 American Society of Civil Engineers.
History
Received: Jun 28, 2018
Accepted: Nov 13, 2018
Published online: Mar 14, 2019
Published in print: May 1, 2019
Discussion open until: Aug 14, 2019
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