Optimization of Vibrations in Laminated Composite Cylindrical Shell with DifferentialQuadrature Method

Based on ۳-D elasticity approach, differential quadrature method (DQM) in axial direction is adoptedalong with Globalized Nelder–Mead (GNM) algorithm to optimize the stacking sequence of a laminatedcylindrical shell for obtaining maximum fundamental natural frequency. The elasticity approach,combining the state space method and DQM is used to obtain a relatively accurate objective function. Thelaminate is made of anisotropic layers. The anisotropic cylindrical shell has finite length with differentboundary conditions. Shell thickness is fixed and orientations of layers are changed in a set of angles. Thehighly coupled partial differential equations are reduced to ordinary differential equations with variablecoefficients by applying DQM to the state space formulations, then, the state equations with variables atdiscrete points are obtained. Natural frequencies of the laminated shell are attained by solving the eigenfrequencyequation, which appears by incorporating boundary conditions into the state equation. A GNMalgorithm is devised for optimizing composite lamination. This algorithm is implemented for maximizingthe lowest natural frequency of cylindrical shell with ply contiguity constraint. Accuracy and convergenceof developed formulation is verified by comparing the natural frequencies with the results obtained in theliterature. Finally, the effects of end conditions, mid-radius to thickness ratio, length to mid-radius ratioand number of layers on vibration behavior of optimized shell are investigated