Exact analysis for three-dimensional free vibrations of cross-ply cylindrical and doubly-curved laminates

Comparison of Natural Frequencies of Laminates by 3-D Theory, Part Ii: Curved Panels

“…Spherical and saddle panels: To check the e!ects of curvature in opposite directions, Table 12 presents the "rst eight modes of normalized frequencies " R W ( /E ) for the cross-ply moderately thick spherical and saddle shell panels, with a"b"10h for two to 10 layers in comparison with Huang [41] …”

“…The present work is a general survey of and comparison with the literature focused on free vibration of the various curved panels, isotropic [1}5, 7}9] and laminated composite [10}42], on simple supports. The most commonly studied geometric con"gurations are of the cylindrical and spherical types of construction, but there are a few of the hyperbolic or saddle shapes [5,41]. As to composites lamination, most are reported on cross-ply with a few on angle-ply constructions [6,14,19,23,28,40].…”

“…A layer wise analysis for free vibration of thick composite cylindrical shells was done by Huang and Dasgupta [40] by using characteristic beam functions in the in-plane directions and quadratic "nite element interpolation in the thickness direction. In the mean time, Huang [41] reported an exact analysis for three-dimensional free vibrations of cross-ply cylindrical and double curved laminates using the 3-D equations of motion and power-series method. Wu et al [42] published their re"ned asymptotic theory, in which slightly increased frequencies appeared when expanded to order four.…”

Static and vibration analysis of cross-ply laminated composite doubly curved shallow shell panels with stiffeners resting on Winkler–Pasternak elastic foundations

“…To determine the natural frequencies of simply supported cross-ply laminates cylindrical and doubly curved shells, a set of layerwise three-dimensional equations of motion in terms of displacements has been presented by Bhimaraddi (1991) and Huang (1995). Based on three-dimensional elasticity, Wu et al (1996) performed the bending and stretching problem of doubly curved laminated composite shells.…”

Convergence Investigation for the Exponential Matrix and Mathematical Layers in the Static Analysis of Multilayered Composite Structures

“…Also in these cases, several solutions have been proposed for the free vibration analysis. The free frequencies of simply supported composite mono and doubly-curved shells were found by Huang [17] using the power series method. A further example for the use of the exponential matrix method to solve the 3D equilibrium equations may be found in [18], where Soldatos and Ye wrote the equations in cylindrical coordinates, in order to calculate the free frequencies of angle-ply multilayered cylinders.…”