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Free vibration of cross-ply laminated plates with variable thickness based on shear deformation theory. (English) Zbl 1359.74160

Summary: Free vibration of laminated cross-ply plates of variable thickness including transverse problem is solved numerically to obtain eigenvalues as frequency parameter and associated eigenvectors which are spline coefficients. The variation of frequency parameters with respect to the aspect ratio, side-to-thickness ratio, ply-angle, number of layer and thickness variations for two different materials under simply supported boundary conditions are analyzed.

MSC:

74H45 Vibrations in dynamical problems in solid mechanics
74S30 Other numerical methods in solid mechanics (MSC2010)
65N25 Numerical methods for eigenvalue problems for boundary value problems involving PDEs
74K20 Plates
Full Text: DOI

References:

[1] Aydogdu, M. and Timarci, T. [2003] ” Vibration analysis of cross-ply laminated square plates with general boundary conditions,” Compos. Sci. Technol.63, 1061-1070. genRefLink(16, ’S021987621650016XBIB001’, ’10.1016
[2] Aydogdu, M. [2005] ” Vibration analysis of cross-ply laminated beams with general boundary conditions by Ritz method,” Int. J. Mech. Sci.47, 1740-1755. genRefLink(16, ’S021987621650016XBIB002’, ’10.1016 · Zbl 1192.74158
[3] Bert, C. W. [1973] ” Simplified analysis of static shear factors for beams of nonhomogeneous cross section,” J. Compos. Mater.7, 525. genRefLink(16, ’S021987621650016XBIB003’, ’10.1177
[4] Bhimaraddi, A. [1993] ” Large amplitude vibrations of imperfect antisymmetric angly-ply laminated plates,” J. Sound Vib.162, 457-470. genRefLink(16, ’S021987621650016XBIB004’, ’10.1006 · Zbl 0959.74506
[5] Bousahla, A. A., Houari, M. S. A., Tounsi, A. and Bedia, E. A. A. [2014] ” A novel higher order shear and normal deformation theory based on neutral surface position for bending analysis of advanced composite plates,” Int. J. Comput. Methods11(6), 1-18. [Abstract] genRefLink(128, ’S021987621650016XBIB005’, ’000345855100003’); · Zbl 1359.74084
[6] Ferreira, A. J. M. and Fasshauer, G. E. [2007] ” Computational of static deformations and natural frequencies of shear deformable plates by an RBF-Pseudospectral method with an optimal shape parameter,” Adv. Meshfree Tech.5, 283-310. genRefLink(16, ’S021987621650016XBIB006’, ’10.1007 · Zbl 1323.74106
[7] Ghosh, A. K. and Dey, S. S. [1994] ” Free vibration of laminated composite plates – A simple finite element based on higher order theory,” Comput. Struct.52, 397-404. genRefLink(16, ’S021987621650016XBIB007’, ’10.1016 · Zbl 0900.73733
[8] Kim, J. S. and Cho, M. [2005] ” Enhanced first-order shear deformation theory for laminated and sandwich plates,” J. Appl. Mech.72, 809-817. genRefLink(16, ’S021987621650016XBIB008’, ’10.1115
[9] Lekhnitskii, S. G. [1968] Anisotropic Plates, 2nd Edition (Gordon and Breach, New York). Translated from Russian by Tsai, S. W. and Cheron, T.
[10] Mindlin, R. D. [1951] ” Influence of rotary inertia and shear in flexural motions of isotropic elastic plates,” J. Appl. Mech.18, 31-38. genRefLink(128, ’S021987621650016XBIB010’, ’A1951UX95300004’); · Zbl 0044.40101
[11] Owen, D. R. J. and Li, Z. H. [1987] ” A refined analysis of laminated plates by finite element displace methods – II. Vibration and stability,” Comput. Struct.26(6), 915-923. genRefLink(16, ’S021987621650016XBIB011’, ’10.1016 · Zbl 0617.73072
[12] Pai, P. F. [1995] ” A new look at the shear correction factors and warping functions of anisotropic laminates,” Int. J. Solids Struct.32, 2295-2313. genRefLink(16, ’S021987621650016XBIB012’, ’10.1016
[13] Peng, L. X., Kitipornchai, S. and Liew, K. M. [2007] ” Free vibration analysis of folded plate structures by the FSDT mesh-free method,” Comput. Mech.39, 799-814. genRefLink(16, ’S021987621650016XBIB013’, ’10.1007 · Zbl 1178.74184
[14] Qatu, S. M. [1991] ” Free vibration of laminated composite rectangular plates,” Int. J. Solids Struct.28, 941-954. genRefLink(16, ’S021987621650016XBIB014’, ’10.1016
[15] Reddy, J. N. [1978] ” Free vibration of antisymmetric angle-ply laminated plates including transverse shear deformation by the finite element method,” J. Sound Vib.66, 565-576. genRefLink(16, ’S021987621650016XBIB015’, ’10.1016
[16] Reddy, J. N. [1999] Theory and Analysis of Elastic Plates (Taylor & Francis, USA).
[17] Rezaiee-Pajand, M. and Karkoon, M. [2014] ” Optimal node location in triangular plate bending elements,” Int. J. Comput. Methods11(5), 1-36. [Abstract] genRefLink(128, ’S021987621650016XBIB017’, ’000344257100006’); · Zbl 1359.74276
[18] Rezaiee-Pajand, M., Shahabian, F. and Tavakoli, F. H. [2016] ” Stress analysis of free-edge laminaed composite plates by two bending elements,” Int. J. Comput. Methods13(1), 1-18. genRefLink(16, ’S021987621650016XBIB018’, ’10.1080 · Zbl 1359.74275
[19] Said, A., Ameur, M., Bousahla, A. A. and Tounsi, A. [2014] ” A new simple hyperbolic shear deformation theory for functionally graded plates resting on Winkler-Pasternak elastic foundations,” Int. J. Comput. Methods11(6), 1-18. [Abstract] genRefLink(128, ’S021987621650016XBIB019’, ’000345855100011’); · Zbl 1359.74278
[20] Singh, B. N., Yadav, D. and Iyengar, N. G. R. [2001] ” Natural frequencies of composite plates with random material properties using higher-order shear deformation theory,” Int. J. Mech. Sci.43, 2193-2214. genRefLink(16, ’S021987621650016XBIB020’, ’10.1016 · Zbl 0988.74514
[21] Shankara, C. A. and Iyengar, N. G. R. [1996] ” A C0 element for the free vibration analysis of laminated composite plates,” J. Sound Vib.191(5), 721-738. genRefLink(16, ’S021987621650016XBIB021’, ’10.1006
[22] Stavsky, Y. [1965] ” On the theory of symmetrically heterogeneous plates having the same thickness variation of the elastic moduli,” in Topics in Applied Mechanic, eds. Abir, D. et al. (American Elsevier, New York), pp. 105-166.
[23] Thai, H. T. and Kim, S. E. [2010] ” Free vibration of laminated composite plates using two variable refined plate theory,” Int. J. Mech. Sci.52, 626-633. genRefLink(16, ’S021987621650016XBIB023’, ’10.1016
[24] Viswanathan, K. K. and Lee, S. K. [2007] ” Free vibration of laminated cross-ply plates including shear deformation by spline method,” Int. J. Mech. Sci.49, 352-363. genRefLink(16, ’S021987621650016XBIB024’, ’10.1016
[25] Viswanathan, K. K. and Kim, K. S. [2008] ” Free vibration of antisymmetric angle-ply laminated plates including transverse shear deformation: Spline method,” Int. J. Mech. Sci.50, 1476-1485. genRefLink(16, ’S021987621650016XBIB025’, ’10.1016 · Zbl 1264.74105
[26] Viswanathan, K. K., Kim, K. S. and Lee, J. H. [2009] ” Asymmetric free vibrations of laminated annular cross-ply circular plates including the effects of shear deformation and rotary inertia: Spline method,” Forsch Ingenieurwes73, 205-217. genRefLink(16, ’S021987621650016XBIB026’, ’10.1007
[27] Viswanathan, K. K., Lee, J. H., Zainal, A. A. and Hossain, I. [2011] ” Free vibration of symmetric angle-ply laminated cylindrical shells of variable thickness,” Acta Mech.221, 309-319. genRefLink(16, ’S021987621650016XBIB027’, ’10.1007 · Zbl 1242.74035
[28] Viswanathan, K. K., Javed, S., Zainal, A. A. and Prabakar, K. [2015] ” Free vibration of symmetric angle-ply laminated annular circular plate of variable thickness under shear deformation theory,” Meccanica, doi: [10.1007/s11012-015-0175-3] . genRefLink(128, ’S021987621650016XBIB028’, ’000365188800010’); · Zbl 1336.74031
[29] Whitney, J. M. and Leissa, W. [1969] ” Analysis of heterogeneous anisotropic plates,” J. Appl. Mech.36, 261-266. genRefLink(16, ’S021987621650016XBIB029’, ’10.1115 · Zbl 0181.52603
[30] Whitney, J. M. and Pagano, N. J. [1970] ” Shear deformation in heterogeneous plates,” J. Appl. Mech.37, 1031-1036. genRefLink(16, ’S021987621650016XBIB030’, ’10.1115 · Zbl 0218.73078
[31] Whitney, J. M. and Sun, C. T. [1973] ” A higher order theory for extensional motion of laminated composites,” J. Sound Vib.30, 85. genRefLink(16, ’S021987621650016XBIB031’, ’10.1016
[32] Yang, P. C., Nooris, C. H. and Stavsky, Y. [1966] ” Elastic wave propagation in heterogeneous plates,” Int. J. Solids Struct.2, 665-684. genRefLink(16, ’S021987621650016XBIB032’, ’10.1016
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