Abstract
The main purpose of this paper is to investigate the effect of bidirectional continuously graded nanocomposite materials on free vibration of thick shell panels rested on elastic foundations. The elastic foundation is considered as a Pasternak model after adding a shear layer to the Winkler model. The panels reinforced by randomly oriented straight single-walled carbon nanotubes are considered. The volume fractions of SWCNTs are assumed to be graded not only in the radial direction, but also in axial direction of the curved panel. This study presents a 2-D six-parameter power-law distribution for CNTs volume fraction of 2-D continuously graded nanocomposite that gives designers a powerful tool for flexible designing of structures under multi-functional requirements. The benefit of using generalized power-law distribution is to illustrate and present useful results arising from symmetric, asymmetric and classic profiles. The material properties are determined in terms of local volume fractions and material properties by Mori–Tanaka scheme. The 2-D differential quadrature method as an efficient numerical tool is used to discretize governing equations and to implement boundary conditions. The fast rate of convergence of the method is shown and results are compared against existing results in literature. Some new results for natural frequencies of the shell are prepared, which include the effects of elastic coefficients of foundation, boundary conditions, material and geometrical parameters. The interesting results indicate that a graded nanocomposite volume fraction in two directions has a higher capability to reduce the natural frequency than conventional 1-D functionally graded nanocomposite materials.
Highlights
IntroductionDue to their thermal and mechanical merits compared to single-composed materials, have been widely used for a variety of engineering applications
Layered composite materials, due to their thermal and mechanical merits compared to single-composed materials, have been widely used for a variety of engineering applications
This paper is motivated by the lack of studies in the technical literature concerning to the three-dimensional vibration analysis of thick bidirectional nanocomposite curved panels resting on a two-parameter elastic foundation reinforced by randomly oriented straight single-walled carbon nanotubes Carbon nanotubes (CNTs)
Summary
Due to their thermal and mechanical merits compared to single-composed materials, have been widely used for a variety of engineering applications. Farid et al (2010) presented free vibration analysis of initially stressed thick supported functionally graded curved panel resting on twoparameter elastic foundation (Pasternak model), subjected in thermal environment was studied using the three-dimensional elasticity formulation. Carbon nanotubes (CNTs) have demonstrated exceptional mechanical, thermal and electrical properties These materials are considered as one of the most promising reinforcement materials for high performance structural and multi-functional composites with vast application potentials (Esawi and Farag 2007; Thostenson et al 2001). In order to investigate 3-D dynamic response of thick bidirectional nanocomposite curved panels resting on a two-parameter elastic foundation, it is assumed that the volume fraction of the CNTs follows a 2-D six-parameter power-law distribution:. The mechanical constitutive relation that relates the stresses to the strains is as follows: 32 3 rr
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