Abstract
In this paper, for the free vibration analysis of an open laminated cylindrical shell with elliptical section (OLCSES), under different elastic boundary conditions (BCs), a new meshfree Tchebychev-radial point interpolation method (TRPIM) shape function using the basis function consisted of radial basis and Tchebychev polynomial basis, is proposed. With the help of the first-order shear deformation theory, the local weak-forms of the governing equation and BC of OLCSES are derived. Its BC is modelled as a general BC via an artificial elastic spring technique, and the displacement functions are all approximated by TRPIM shape function in two directions (x, θ) regardless of the BC. The natural frequency of OLCSES is obtained by solving its governing equation and BC equation discretized by TRPIM shape function. The numerical results are in good agreement with those of preceding literatures and finite element method (FEM). The natural frequencies of OLCSES under different BCs including classical and elastic BCs are newly obtained and the effect of some parameters such as its material property and geometry on them is studied. The results can be used as reference data for researchers studying dynamic characteristics of shell structures with elliptical section.
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