2012 # Three-Dimensional Free Vibration Analysis of Cross-Ply Laminated Rectangular Plates through 2D and Exact Models

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“…Free vibration analysis of multilayered spherical shells with constant radii of curvature R α and R β has been proposed by Brischetto in [66][67][68][69] using three differential equations of equilibrium in general orthogonal curvilinear coordinates. The equations have been solved in exact form in analogy with the exponential matrix method proposed by Messina [70] and Soldatos and Ye [71] for orthogonal rectilinear coordinates and cylindrical coordinates, respectively. In the present paper, the equations in general orthogonal curvilinear coordinates are rewritten for the cylindrical case imposing an infinite value for the radius of curvature R β (see Figure 1).…”

confidence: 99%

“…Free vibration analysis of multilayered spherical shells with constant radii of curvature R α and R β has been proposed by Brischetto in [66][67][68][69] using three differential equations of equilibrium in general orthogonal curvilinear coordinates. The equations have been solved in exact form in analogy with the exponential matrix method proposed by Messina [70] and Soldatos and Ye [71] for orthogonal rectilinear coordinates and cylindrical coordinates, respectively. In the present paper, the equations in general orthogonal curvilinear coordinates are rewritten for the cylindrical case imposing an infinite value for the radius of curvature R β (see Figure 1).…”

confidence: 99%

“…Equations (20)-(22) are a system of three second order differential equations in z. This system can be reduced to a system of first order differential equations using the method already seen in [66][67][68][69][70][71]. In compact form, it can be written as:…”

confidence: 99%

“…The analysis was based on a recursive solution suitable for three-dimensional vibration analysis of simply supported plates. Comparisons between 2D-displacement-based models and exact results of the linear three-dimensional elasticity were also proposed in [25] for natural frequencies, displacement, and stress quantities in multilayered plates. Exact three-dimensional elasticity theory was investigated in [26] for isosceles triangular plates by means of a global three-dimensional Ritz formulation.…”

confidence: 99%

“…Hosseini-Hashemi et al [12] used two different displacement fields to study the in-plane and the out-of-plane vibrations of a rectangular homogeneous plate, coated by a functionally graded layer. Messina [13] used the exponential matrix method to solve the three-dimensional equations of equilibrium, written in a Cartesian coordinate system, for cross-ply laminated rectangular plates. The free vibration frequencies, stresses and deflections were presented.…”

confidence: 99%