In this paper, a novel meshfree approach for three-dimensional free vibration analysis of thick laminated composite conical, cylindrical shells and annular plates is presented. The theoretical model for free vibration analysis of thick shells and plates is formulated by applying the three-dimensional theory of elasticity, and all displacement components are approximated by a novel meshfree Tchebychev-point interpolation method (TPIM) shape function using Tchebychev polynomials as a basis. After deriving the governing equations and boundary conditions for individual layers of the laminated shell, the governing equations and boundary conditions of the entire system are derived by combining them according to the order of layers. The boundary and combination conditions are generalized by introducing the artificial spring technique, and the type of conditions is selected by the spring stiffness values. The accuracy and reliability of the proposed method are verified by comparison with the results of literatures and finite element software ABAQUS. The free vibration characteristics such as the natural frequency and mode shape of laminated conical, cylindrical shells and annular plates under different boundary conditions are presented through some numerical examples.
This paper presents a unified solution method to investigate the free vibration behaviors of laminated composite conical shell, cylindrical shell and annular plate with variable thickness and arbitrary boundary conditions using the Haar wavelet discretization method (HWDM). Theoretical formulation is established based on the first order shear deformation theory(FSDT) and displacement components are extended Haar wavelet series in the axis direction and trigonometric series in the circumferential direction. The constants generating by the integrating process are disposed by boundary conditions, and thus the equations of motion of total system including the boundary condition are transformed into an algebraic equations. Then natural frequencies of the laminated composite structures are directly obtained by solving these algebraic equations. Stability and accuracy of the present method are verified through convergence and validation studies. Effects of some material properties and geometric parameters on the free vibration of laminated composite shells are discussed and some related mode shapes are given. Some new results for laminated composite conical shell, cylindrical shell and annular plate with variable thickness and arbitrary boundary conditions are presented, which may serve as benchmark solutions.
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