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

✍ Scribed by Chih-Ping Wu; Chia-Ying Lee

• Publisher: Elsevier Science
• Year: 2001
• Tongue: English
• Weight: 139 KB
• Volume: 43
• Category: Article
• ISSN: 0020-7403
• DOI: 10.1016/s0020-7403(01)00010-8

✦ Synopsis

The free vibration analysis of laminated conical shells with variable sti ness is presented using the method of di erential quadrature (DQ). The sti ness coe cients are assumed to be functions of the circumferential coordinate that may be more close to the realistic applications. The ÿrst-order shear deformation shell theory is used to account for the e ects of transverse shear deformations. In the DQ method, the governing equations and the corresponding boundary conditions are replaced by a system of simultaneously algebraic equations in terms of the function values of all the sampling points in the whole domain. These equations constitute a well-posed eigenvalue problem where the total number of equations is identical to that of unknowns and they can be solved readily. By vanishing the semivertex angle ( ) of the conical shell, we can reduce the formulation of laminated conical shells to that of laminated cylindrical shells of which sti ness coe cients are the constants. Besides, the present formulation is also applicable to the analysis of annular plates by letting = =2. Illustrative examples are given to demonstrate the performance of the present DQ method for the analysis of various structures (annular plates, cylindrical shells and conical shells). The discrepancies between the analyses of laminated conical shells considering the constant sti ness and the variable sti ness are mainly concerned.