Инд. авторы:	Morozov E.V., Lopatin A.V.
Заглавие:	Fundamental frequency of fully clamped antisymmetric angle-ply laminated plates with structural anisotropy
Библ. ссылка:	Morozov E.V., Lopatin A.V. Fundamental frequency of fully clamped antisymmetric angle-ply laminated plates with structural anisotropy // Composite Structures. - 2018. - Vol.187. - P.530-538. - ISSN 0263-8223. - EISSN 1879-1085.
Внешние системы:	DOI: 10.1016/j.compstruct.2018.02.084; РИНЦ: 35717510; SCOPUS: 2-s2.0-85043287208; WoS: 000443821700058;
Реферат:	eng: An analytical solution determining the fundamental frequency of a fully clamped composite anisotropic laminated plate is presented in the paper. The plate is composed of unidirectional composite plies oriented at some angle to one of the plate sides. The plies alternating over the plate thickness differ from each other by only the sign of the angle of orientation. Such a plate is characterised by the structural anisotropy with the extension-twisting and bending-shear coupling effects which are taken into account in the appropriate constitutive equations. The governing equations model the coupled in-plane and out-of-plane plate motions. The vibration problem is solved using the Galerkin method. The beam functions corresponding to the first vibration mode of a beam with clamped ends are employed as the approximating functions. The problem is reduced to a solution of cubic algebraic equation. Based on this solution, effects of the angle of reinforcement orientation and number of plies on the fundamental frequency of the plate with structural anisotropy are investigated. The results are verified using finite element method. An assessment of the anisotropy effect on the frequency value has been performed by comparison with the results obtained based on the orthotropic model of the plate. The formula providing the number of plies for a plate with structural anisotropy is derived for the prescribed fundamental frequency.
Ключевые слова:	NATURAL FREQUENCIES; RECTANGULAR-PLATES; Finite-element analysis; Galerkin method; BOUNDS; Extension-twisting coupling effect; Structural anisotropy; Laminated plate with clamped edges; Fundamental frequency; FREE-VIBRATION;
Издано:	2018
Физ. характеристика:	с.530-538
Цитирование:	1. Comer, A.J., Ray, D., Obande, W.O., Jones, D., Lyons, J., Rosca, I., et al. Mechanical characterisation of carbon fibre–PEEK manufactured by laser-assisted automated-tape-placement and autoclave. Compos A 69 (2015), 10–20. 2. Jones, R.M., Mechanics of composite materials. 1999, Taylor & Francis, London. 3. Vinson, J.R., Sierakowski, R.L., The behavior of structures composed of composite materials. 2004, Kluwer Academic Publishers, Hingham MA. 4. Vasiliev, V.V., Morozov, E.V., Advanced mechanics of composite materials and structural elements. 3rd ed., 2013, Elsevier, Amsterdam. 5. Kollar, L.P., Springer, G.S., Mechanics of composite structures. 2003, Cambridge University Press. 6. Dhurvey, P., Mittal, N.D., Review on various studies of composite laminates with ply drop-off. J Eng Appl Sci 8:8 (2013), 595–605. 7. Tsai S. Weight and cost reduction by using unbalanced and unsymmetric laminates. In: Proc18th international conference on composite materials. Jeju, Korea; 2011. 8. Herencia, J.E., Weaver, P.M., Friswell, M.I., Closed-form solutions for buckling of long anisotropic plates with various boundary conditions under axial compression. J Eng Mech 136 (2010), 1105–1114. 9. York CB. Weaver PM. Balanced and symmetric laminates – new perspectives on an old design rule. In: Proc 51st AIAA/ASME/ASCE/AHS/ASC structures, structural dynamics, and materials conference, Paper No. AIAA-2010-2775, Orlando, Florida; 2010. 10. Li, D., York, C.B., Bounds on the natural frequencies of laminated rectangular plates with extension-bending coupling. Compos Struct 133 (2015), 863–870. 11. Li, D., York, C.B., Bounds on the natural frequencies of laminated rectangular plates with extension–twisting (and shearing–bending) coupling. Compos Struct 131 (2015), 37–46. 12. York, C.B., On tapered warp-free laminates with single-ply terminations. Compos A 72 (2015), 127–138. 13. York, C.B., On extension-shearing coupled laminates. Compos Struct 120 (2015), 472–482. 14. York, C.B., On bending-twisting coupled laminates. Compos Struct 160 (2017), 887–900. 15. York, C.B., Almeida, S.F.M., On extension-shearing bending-twisting coupled laminates. Compos Struct 164 (2017), 10–22. 16. Gorman, D.J., Ding, W., Accurate free vibration analysis of clamped antisymmetric angle-ply laminated rectangular plates by the Superposition-Galerkin method. Compos Struct 34 (1996), 387–395. 17. Qatu, M., Vibration of laminated shells and plates. 2004, Academic Press/Elsevier. 18. Aygodu, M., Timarci, T., Vibration analysis of cross-ply laminate square with general boundary conditions. Compos Sci Technol 63:7 (2003), 1061–1070. 19. Wei, Shi Jian, Nakatani, A., Kitagawa, H., Vibration analysis of fully clamped arbitrarily laminated plate. Compos Struct 63 (2004), 115–122. 20. Viswanathan, K.K., Karthik, K., Sanyasiraju, Y.V.S.S., Aziz, Z.A., Free vibration study of anti-symmetric angle-ply laminated plates under clamped boundary conditions. Curved Layer Struct 3:1 (2016), 265–275. 21. Javed, S., Viswanathan, K.K., Aziz, Z.A., Prabakar, K., Free vibration of anti-symmetric angle-ply plates with variable thickness. Compos Struct 137 (2016), 56–69. 22. Reddy, J.N., Mechanics of laminated composite plates and shells. Theory and analysis. 2nd ed., 2004, CRC Press, Boca Raton. 23. Blevins, R.D., Formulas for natural frequency and mode shape. 2001, Krieger Publishing Company, Malabar, FL. 24. Nastran, M.S.C., Quick reference guide's: MSC. 2011, Software Corporation.