New shape function in the free-vibration analysis of antisymmetric angleply composite laminates
Authors: Milosavljević D., Radaković A., Čukanović D., Bogdanović G., Husović S.
Keywords: shape function; high order shear deformation theories; cross-ply composite laminates
Abstract:
The paper analyzes the problem of free vibrations in antisymmetric crossply laminates. A new shape function which is used in higher order shear deformation theories has been introduced. The comparative analysis was performed with the known shape functions. The procedure for obtaining dynamic equations of motion in the Matlab software package has been developed. For theoretical considerations, the module with the symbolic variable has been used. The paper shows which of the existing shape functions are applicable in the free vibration analysis of antisymmetric angleply laminates. The advantages and disadvantages of the newly developed shape function are clearly highlighted. Analytical procedures have been used to obtain the results of partial differential equations, based on Navier’s solutions. Numerical integration procedures were used as an integral part of the developed Matlab codes for those shape functions where it was necessary. The results are presented in a table and figures. The procedure itself has been verified by comparison with the reference results from the literature.
References:
[1]Akavci, S.S. (2010) Two new hyperbolic shear displacement models for orthotropic laminated composite plates. Mechanics of Composite Materials, 46(2): 215-226
[2]Ambarstumian, S.A. (1958) On the theory of bending plates. Izv otd Tech Nauk an Sssr, 5: 69-77
[3]Ambarstumyan, S.A. (1958) On the Theory of Anisotropic Shells and Plates. u: Olszak W. [ur.] Proceedings of the International Union of Theoretical and Applied Mechanics on Non-Homogeniety in Elasticity and Plasticity Symposium, Warsaw, Paper No.1:83-94
[4]Aydogdu, M. (2009) A new shear deformation theory for laminated composite plates. Compos Struct, 89(1): 94-101
[5]Belaid, M., Ismail, M., Samir, B. (2012) Analysis of thick orthotropic laminated composite plates based on higher order shear deformation theory by the new function under thermomechanical loading. Composites: Part B, 43: 1453-8
[6]Ghugal, Y.M., Shimpi, R.P. (2002) A Review of Refined Shear Deformation Theories of Isotropic and Anisotropic Laminated Plates. Journal of Reinforced Plastics and Composites, 21: 775
[7]Grover, N., Maiti, D.K., Singh, B.N. (2014) Flexural behavior of general laminated composite and sandwich plates using a secant function based shear deformation theory. Latin American Journal of Solids and Structures, 11:1275-1297
[8]Jha, D.K., Kant, T., Singh, R.K. (2013) Free vibration response of functionally graded thick plates with shear and normal deformations effects. Composite Structures, 96: 799-823
[9]Kant, T., Swaminathan, K. (2001) Analytical solutions for free vibration of laminated composite and sandwich plates based on a higher-order refined theory. Compos. Struct, 53: 73-85
[10]Karama, M., Afaq, K.S., Mistou, S. (2003) Mechanical behaviour of laminated composite beam by the new multi-layered laminated composite structures model with transverse shear stress continuity. International Journal of Solids and Structures, 40(6): 1525-1546
[11]Levi, M. (1977) Memoire sur la theorie des plaques elastiques planes. J Math Pures Appl, 219-306
[12]Lo, K.H., Christensen, R.M., Wu, E.M. (1977) A high-order theory of plate deformation, part 1: homogeneous plates. J Appl Mech, 44(4): 663-8
[13]Lo, K.H., Christensen, R.M., Wu, E.M. (1977) A High-Order Theory of Plate Deformation-Part 2: Laminated Plates. Journal of Applied Mechanics, 44(4): 669-676
[14]Mantari, J.L., Bonilla, E.M., Guedes, S.C. (2014) A new tangential-exponential higher order shear deformation theory for advanced composite plates. Compos B Eng, 60: 319-28
[15]Mantari, J.L., Guedes, S.C. (2012) Analysis of isotropic and multilayered plates and shells by using a generalized higher-order shear deformation theory. Composite Structures, 94(8): 2640-2656
[16]Mantari, J.L., Oktem, A.S., Guedes, S.C. (2012) A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates. International Journal of Solids and Structures, 49(1): 43-53
[17]Mantari, J.L., Oktem, A.S., Guedes, S.C. (2012) Bending and free vibration analysis of isotropic and multilayered plates and shells by using a new accurate higher-order shear deformation theory. Composites Part B: Engineering, 43(8): 3348-3360
[18]Meiche, N.E., et al. (2011) A new hyperbolic shear deformation theory for buckling and vibration of functionally graded sandwich plate. International Journal of Mechanical Sciences, 53:237-247
[19]Radakovic, A., Cukanovic, D., Bogdanovic, G., Blagojevic, M., Stojanovic, B., Dragovic, D., Manic, N. (2020) Thermal Buckling and Free Vibration Analysis of Functionally Graded Plate Resting on an Elastic Foundation According to High Order Shear Deformation Theory Based on New Shape Function. Applied sciences-Basel, vol. 10 num. 12
[20]Reddy, J.N. (2004) Mechanics of Laminated Composite Plates and Shells: Theory and Analysis. London: CRC Press LLC, ISBN 0-8493-1592-1
[21]Reissner, E., Stavsky, Y. (1961) Bending and Stretching of Certain Types of Heterogeneous Aeolotropic Elastic Plates. ASME Journal of Applied Mechanics, 28: 402-408
[22]Soldatos, K. (1992) A transverse shear deformation theory for homogeneous monoclinic plates. Acta Mechanica, 94(3): 195-220
[23]Viola, E., Tornabene, F., Fantuzzi, N. (2013) General higher-order shear deformation theories for the free vibration analysis of completely doubly-curved laminated shells and panels. Composite Structures, 95: 639-666
[24]Xiang, S., Kang, G., Xing, B. (2012) A nth-order shear deformation theory for the free vibration analysis on the isotropic plates. Meccanica, 47(8): 1913-1921
[25]Xiang, S., Kang, G., Yang, M., Zhao, Y. (2013) Natural frequencies of sandwich plate with functionally graded face and homogeneous core. Compos Struct, 96: 226-31
[26]Zhanga, Y.X., Yangb, C.H. (2009) Recent developments in finite element analysis for laminated composite plates. Composite Structure, 88:147-157