Affiliation:
1. Department of Civil Engineering , Bursa Uludag University, Engineering Faculty , Görükle Campus, 16059 , Bursa , Türkiye
Abstract
Abstract
In this study, two different general eigenvalue problems for nanobeams made of functionally graded material with pores in their sections according to Rayleigh beam theory using modified couple stress theory are established. Fourier sine series and Stokes transformation are used for the solution. First, the partial differential equation of motion of the problem is discretized into an ordinary differential equation. Then, the Fourier sine series of infinite series is substituted into this ordinary differential equation to determine the Fourier coefficient. Using the force boundary conditions of the system, Stokes’ transformation is performed at both ends to include elastic spring parameters. The unknown displacement terms are discretized to form two eigenvalue problems. By solving these eigenvalue problems, vibration frequencies for different boundary conditions can be found analytically. The variations of some parameters are discussed in a series of graphs.
Subject
Physical and Theoretical Chemistry,General Physics and Astronomy,Mathematical Physics
Reference65 articles.
1. S. K. Bohidar, R. Sharma, and P. R. Mishra, “Functionally graded materials: a critical review,” Int. J. Res., vol. 1, no. 4, pp. 289–301, 2014.
2. R. M. Mahamood, E. T. Akinlabi, M. Shukla, and S. L. Pityana, Functionally Graded Material: An Overview in Proc. World Congress Eng., WCE, Vol III, July 4–6, 2012, London, UK.
3. F. F. Calim, “Vibration analysis of functionally graded Timoshenko beams on Winkler–Pasternak elastic foundation,” Iran. J. Sci. Technol., Trans. Civ. Eng., vol. 44, no. 3, pp. 901–920, 2020. https://doi.org/10.1007/s40996-019-00283-x.
4. H. Deng and W. Cheng, “Dynamic characteristics analysis of bi-directional functionally graded Timoshenko beams,” Compos. Struct., vol. 141, pp. 253–263, 2016. https://doi.org/10.1016/j.compstruct.2016.01.051.
5. Y. Huang and Z. Y. Ouyang, “Exact solution for bending analysis of two-directional functionally graded Timoshenko beams,” Arch. Appl. Mech., vol. 90, no. 5, pp. 1005–1023, 2020. https://doi.org/10.1007/s00419-019-01655-5.
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