Abstract
The focus of this study is to analyse the free vibration of cylindrical shells under third-order shear deformation theory (TSDT). The constitutive equations of the cylindrical shells are obtained using third-order shear deformation theory (TSDT). The surface and traverse displacements are expected to have cubic and quadratic variation. Spline approximation is used to approximate the displacements and transverse rotations. The resulting generalized eigenvalue problem is solved for the frequency parameter to get as many eigenfrequencies as required starting from the least. From the eigenvectors, the spline coefficients are computed from which the mode shapes are constructed. The frequency of cylindrical shells is analysed by varying circumferential node number, length dimension, layer number, and different materials. The authenticity of the present formulation is established by comparing with the available FEM results.
Highlights
Composite shell structures are source of attraction for marine structures such as submarines [1,2,3,4,5,6]
To avoid the discrepancies of the FSDT, HSDT was developed to precisely estimate the crosswise shear stresses which are significant in thick plates and shells. iHSDT plate theories suggest the expansion of displacements to required degree with respect to thickness coordinates avoiding a shear correction factor
In third-order shear deformation theory (TSDT), the displacements are extended to the power of three so that to get crosswise shear stresses and strains variation of fourth power through thickness. is neglects the requirement of shear correction coefficient [16]
Summary
Composite shell structures are source of attraction for marine structures such as submarines [1,2,3,4,5,6]. Different methods incorporating HSDT were adopted by different researchers for analysing free vibration of shells.
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