Fundamental frequencies of bidirectional functionally graded sandwich beams partially supported by foundation using different beam theories
Email:
vuthianninh@utc.edu.vn
Từ khóa:
BFGSW beam, partial foundation support, frequency, finite element method.
Tóm tắt
Investigation on the influence of beam theory and partial foundation support on natural frequencies play an important role in design of structures. In this paper, fundamental frequencies of a bidirectional functionally graded sandwich (BFGSW) beam partially supported by an elastic foundation are evaluated using various beam theories. The core of the sandwich beam is homogeneous while its two face sheets are made from three distinct materials with material properties varying in both the length and thickness directions by power gradation laws. The finite element method is employed to derive equation of motion and to compute the frequencies of the beam. The effects of the material gradation, the foundation parameters and the span to height ratio on the frequencies are studied in detail and highlighted. The difference of the frequencies obtained by different beam theories is also examined and discussed. The numerical results of the paper are useful in designing BFGSW beams with desired fundamantal frequencies.Tài liệu tham khảo
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[11] P. Tossapanon, N. Wattanasakulpong, Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation, Composite structures, 142 (2016) 215-225. https://doi.org/10.1016/j.compstruct.2016.01.085
[12] Z. Su et al., A general Fourier formulation for vibration analysis of functionally graded sandwich beams with arbitrary boundary condition and resting on elastic foundations, Acta mech, 227 (2016) 1493-1514. https://doi.org/10.1007/s00707-016-1575-8
[13] A. S. Sayyad, Y. M. Ghugal, On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results, Composite structures, 129 (2015) 177-201. https://doi.org/10.1016/j.compstruct.2015.04.007
[14] M. Aydogdu, V. Taskin, Free vibration analysis of functionally graded beams with simply supported edges, Materials and design, 28 (2007) 1651-1656. https://doi.org/10.1016/j.matdes.2006.02.007
[15] M. Şimșek, Vibration analysis of a functionally graded beam under a moving mass by using different beam theories, Composite structures, 92 (2010) 904-917. https://doi.org/10.1016/j.compstruct.2009.09.030
[16] A. Mahi et al., An analytical method for temperature-dependent free vibration analysis of functionally graded beams with general boundary conditions, Composite structures, 92 (2010) 1877-1887. https://doi.org/10.1016/j.compstruct.2010.01.010
[17] H-T. Thai, T. P. Vo, Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories, International journal of mechanical sciences, 62 (2012) 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014
[18] M. Şimșek, Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load, Composite Structures, 92 (2010) 2532-2546. https://doi.org/10.1016/j.compstruct.2010.02.008
[19] G. N. Praveen, J. N. Reddy, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, International journal of solids and structures, 35 (1998) 4457-4476. https://doi.org/10.1016/s0020-7683(97)00253-9
[2] N. A. Apetre, B. V. Sankar, D. R. Ambur, Analytical modeling of sandwich beams with functionally graded core, Journal of sandwich structures and materials, 10 (2008) 53-74. https://doi.org/10.1177/1099636207081111
[3] M. C. Amirani, S. M. R. Khalili, N. Nemati, Free vibration analysis of sandwich beam with FG core using the element free Galerkin method, Composite structures, 90 (2009) 373-379. https://doi.org/10.1016/j.compstruct.2009.03.023
[4] T. P. Vo et al., Finite element model for vibration and buckling of functionally graded sandwich beams based on a refined shear deformation theory, Engineering structures, 64 (2014) 12-22. https://doi.org/10.2016/j.engstruct.2014.01.029
[5] A. Karamanli, Bending behaviour of two directional functionally graded sandwich beams by using a quasi-3d shear deformation theory, Composite structures, 174 (2017) 70-86. https://doi.org/10.1016/j.compstruct.2017.04.046
[6] V. T. A. Ninh, L. T. N. Anh, N. D. Kien, Free vibration of a 2D-FGSW beam based on a shear deformation theory, Vietnam journal of mechanics, VAST, 42 (2020) 189-205. https://doi.org/10.15625/0866-7136/14817
[7] D. K. Nguyen et al., Dynamic behavior of a bidirectional functionally graded sandwich beam under nonuniform motion of a moving load, Shock and vibration, 2020 (2020) 15. https://doi.org/10.1155/2020/8854076
[8] M. Eisenberger, D. Z. Yankelevsky, M. A. Adin, Vibrations of beams fully or partially supported on elastic foundations, Earthquake engineering and structural dynamics, 13 (1985) 651-660. https://doi.org/10.1002/eqe.4290130507
[9] W. Q. Chen, C. F. Lu, Z. G. Bian, A mixed method for bending and free vibration of beams resting on a Pasternak elastic foundation, Applied mathematical modelling, 28 (2004) 877–890. https://doi.org/10.1016/j.apm.2004.04.001
[10] A. M. Zenkour, M. N. M. Allam, M. Sobhy, Bending analysis of FG viscoelastic sandwich beams with elastic cores resting on Pasternak’s elastic foundations, Acta mech, 212 (2010) 233–252. https://doi.org/10.1007/s00707-009-0252-6
[11] P. Tossapanon, N. Wattanasakulpong, Stability and free vibration of functionally graded sandwich beams resting on two-parameter elastic foundation, Composite structures, 142 (2016) 215-225. https://doi.org/10.1016/j.compstruct.2016.01.085
[12] Z. Su et al., A general Fourier formulation for vibration analysis of functionally graded sandwich beams with arbitrary boundary condition and resting on elastic foundations, Acta mech, 227 (2016) 1493-1514. https://doi.org/10.1007/s00707-016-1575-8
[13] A. S. Sayyad, Y. M. Ghugal, On the free vibration analysis of laminated composite and sandwich plates: A review of recent literature with some numerical results, Composite structures, 129 (2015) 177-201. https://doi.org/10.1016/j.compstruct.2015.04.007
[14] M. Aydogdu, V. Taskin, Free vibration analysis of functionally graded beams with simply supported edges, Materials and design, 28 (2007) 1651-1656. https://doi.org/10.1016/j.matdes.2006.02.007
[15] M. Şimșek, Vibration analysis of a functionally graded beam under a moving mass by using different beam theories, Composite structures, 92 (2010) 904-917. https://doi.org/10.1016/j.compstruct.2009.09.030
[16] A. Mahi et al., An analytical method for temperature-dependent free vibration analysis of functionally graded beams with general boundary conditions, Composite structures, 92 (2010) 1877-1887. https://doi.org/10.1016/j.compstruct.2010.01.010
[17] H-T. Thai, T. P. Vo, Bending and free vibration of functionally graded beams using various higher-order shear deformation beam theories, International journal of mechanical sciences, 62 (2012) 57-66. https://doi.org/10.1016/j.ijmecsci.2012.05.014
[18] M. Şimșek, Non-linear vibration analysis of a functionally graded Timoshenko beam under action of a moving harmonic load, Composite Structures, 92 (2010) 2532-2546. https://doi.org/10.1016/j.compstruct.2010.02.008
[19] G. N. Praveen, J. N. Reddy, Nonlinear transient thermoelastic analysis of functionally graded ceramic-metal plates, International journal of solids and structures, 35 (1998) 4457-4476. https://doi.org/10.1016/s0020-7683(97)00253-9
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27/12/2020
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03/03/2021
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08/03/2021
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27/05/2021
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Kiểu trích dẫn
Vu Thi An, N. (1622048400). Fundamental frequencies of bidirectional functionally graded sandwich beams partially supported by foundation using different beam theories. Tạp Chí Khoa Học Giao Thông Vận Tải, 72(4), 452-467. https://doi.org/10.47869/tcsj.72.4.5
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