Differential quadrature solution for the free vibration analysis of laminated conical shells with variable stiffness

The free vibration analysis of laminated conical shells with variable stiff ness is presented using the method of differential quadrature (DQ). The sti ffness coefficients are assumed to be functions of the circumferential coor dinate that may be more close to the realistic applications. The first-orde r shear deformation shell theory is used to account for the effects of tran sverse shear deformations. In the DQ method, the governing equations and th e corresponding boundary conditions are replaced by a system of simultaneou sly algebraic equations in terms of the function values of all the sampling points in the whole domain. These equations constitute a well-posed eigenv alue problem where the total number of equations is identical to that of un knowns and they can be solved readily. By vanishing the semivertex angle (a lpha) of the conical shell, we can reduce the formulation of laminated coni cal shells to that of laminated cylindrical shells of which stiffness coeff icients are the constants. Besides, the present formulation is also applica ble to the analysis of annular plates by letting alpha = pi /2. Illustrativ e examples are given to demonstrate the performance of the present DQ metho d for the analysis of various structures (annular plates, cylindrical shell s and conical shells). The discrepancies between the analyses of laminated conical shells considering the constant stiffness and the variable stiffnes s are mainly concerned. (C) 2001 Elsevier Science Ltd. All rights reserved.