دانلود رایگان مقاله ارتعاشات آزاد FG-CNT تقویت شده ورق های مورب کامپوزیت

Abstract

Present study deals with the free vibration analysis of skew plates made from functionally graded carbon nanotube reinforced composites. Carbon nanotubes as reinforcements are distributed across the thickness of the plate. Distribution pattern may be uniform or functionally graded. The developed formulation from a Cartesian coordinate system is transformed to an oblique coordinate system to satisfy the boundary conditions. The virtual strain and kinetic energies of the plate are obtained using the first order shear deformation plate theory. Ritz method whose shape functions are developed according to the Gram–Schmidt process is implemented to construct an eigenvalue problem associated to the natural frequencies of the plate. The developed solution method is general and may be used for arbitrary boundary conditions of the plate. Results are compared for isotropic homogeneous and composite laminated plates in skew shape with the available data in the open literature. Afterwards numerical results are provided for skew plates reinforced with carbon nanotubes. It is shown that volume fraction of carbon nanotubes and their distribution pattern are both influential of natural frequencies of the carbon nanotube reinforced plates. Generally, the higher the volume fraction of carbon nanotubes, the higher the natural frequencies of the skew plate. Keywords

7. Conclusion

Free vibration response of carbon nanotube reinforced composite plates in a skew shape is investigated in the present research. Distribution of reinforcement through the thickness of the matrix may be uniform or functionally graded. Properties of the composite media are estimated according to a modified rule of mixtures approach with introduction of efficiency parameters. The components of displacement field are transformed from an orthogonal coordinate system to an oblique one. The total strain and kinetic energies of the skew plate are obtained. The conventional Ritz formulation is used to deduce the matrix representation of the equations of motion associated to the free vibration motion. Shape functions are estimated according to the orthogonal polynomials developed according to the Gram–Schmidt process. The resulting eigenvalue problem is established. Comparison and convergence studies are carried out to assure the correctness and efficiency of the proposed method. Afterwards parametric studies are given to obtain the frequencies of carbon nanotube reinforced skew plates. It is shown that, increasing the volume fraction of carbon nan-