Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 32579
##### Analytical and Numerical Results for Free Vibration of Laminated Composites Plates

Abstract:

The reinforcement and repair of concrete structures by bonding composite materials have become relatively common operations. Different types of composite materials can be used: carbon fiber reinforced polymer (CFRP), glass fiber reinforced polymer (GFRP) as well as functionally graded material (FGM). The development of analytical and numerical models describing the mechanical behavior of structures in civil engineering reinforced by composite materials is necessary. These models will enable engineers to select, design, and size adequate reinforcements for the various types of damaged structures. This study focuses on the free vibration behavior of orthotropic laminated composite plates using a refined shear deformation theory. In these models, the distribution of transverse shear stresses is considered as parabolic satisfying the zero-shear stress condition on the top and bottom surfaces of the plates without using shear correction factors. In this analysis, the equation of motion for simply supported thick laminated rectangular plates is obtained by using the Hamilton’s principle. The accuracy of the developed model is demonstrated by comparing our results with solutions derived from other higher order models and with data found in the literature. Besides, a finite-element analysis is used to calculate the natural frequencies of laminated composite plates and is compared with those obtained by the analytical approach.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1340599

References:

[1] R. D. Mindlin, “Influence of rotary inertia and shear on flexural motions of isotropic, elastic plates”, J. Appl. Mech., vol. 18, pp. 31–38, 1951.
[2] J. N. Reddy, “A simple higher-order theory for laminated composite plates”, J. Appl. Mech., Trans. ASME, vol. 51, pp. 745–52, 1984.
[3] A. Bessaim, M. S. A. Houari, A. Tounsi, S. R. Mahmoud, E. A. Adda Bedia, “A new higher-order shear and normal deformation theory for the static and free vibration analysis of sandwich plates with functionally graded isotropic face sheets”, J. Sandw. Struct. Mater., vol. 15, no. 6, pp. 671–703, 2013.
[4] T. H. Daouadji, A. Tounsi, E. A. Adda Bedia., “A new higher order shear deformation model for static behavior of functionally graded plates”, Adv. Appl. Math. Mech., vol. 5, no 3, pp. 351–364, 2013.
[5] R. Benferhat, T. H. Daouadji, M. Said Mansour, “A Higher Order Shear Deformation Model for Bending Analysis of Functionally Graded Plates”, Trans. Indian Inst. Met., vol. 68, no. 1, pp. 7–16, Feb. 2015.
[6] J. L. Mantari, A. S. Oktem, C. Guedes Soares, “A new trigonometric shear deformation theory for isotropic, laminated composite and sandwich plates”, Int. J. Sol. Struct., vol. 49, no. 1, p. 43–53, 2012.
[7] T. H. Daouadji, R. Benferhat, B. Adim, “A novel higher order shear deformation theory based on the neutral surface concept of FGM plate under transverse load”, Adv. Mater. Res. Int. J., vol. 5, no. 2, pp. 107–120, 2016.
[8] K. Nedri, N. El Meiche, A. Tounsi, “Free vibration analysis of laminated composite plates resting on elastic foundations by using a refined hyperbolic shear deformation theory”, Mech. Compos. Mater., vol. 49, no. 6, pp. 629–640, 2014.
[9] M. Rastgaar Aagaah, M. Mahinfalah, G. Nakhaie Jazar, “Natural frequencies of laminated composite plates using third order shear deformation theory”, Compos. Struct., vol. 72, no. 3, pp. 273–279, 2006.
[10] B. Adim, T. H. Daouadji, B. Abbès, A. Rabahi, “Buckling and free vibration analysis of laminated composite plates using an efficient and simple higher order shear deformation theory”, Mechanics & Industry, vol. 17, no. 512, pp. 1–14, 2016.