An analytical solution for cross-ply laminates under cylindrical bending based on through-the-thickness inextensibility. Part II—Vibrations

Tbe dynamic behavior of cross-ply laminated plates under cylindrical and/or planar bending is considered. The methodology introduced in Part I is extended for treating the transverse vibration of laminated plates. The solution for a simply-supported plate at two ends is obtained. Natural frequencies and the corresponding stress distribution for several cases ~ presented. Also, we employed a new procedure for finding the exact natural frequencies and the corresponding stresses based on the elasticity solution presented by JOnes (1970). The proposed procedure significantly increases the capability of the elasticity solution and eliminates most of the problems experienced by the previous researchers in the application of the solution for higher modes and multi-layer laminates. The comparison of the results obtained by the introduced method and the elasticity solution validates the integrity of the introduced method. The results are also obtained by finite element method and one of the higher-order laminated plate theories. The investigation shows the inadequacy of the higher-order theory in predicting the stresses. Also the results obtained by finite element method shoW, that by increasing the mode number of vibration, to obtain a satisfactory result, a finer mesh is necessary. Furthermore, the. shear stresses at the interface at two adjacent layers are more likely to be inaccurate. © 1998 Elsevier Science Ltd