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

Messina, Arcangelo

doi:10.1080/15376494.2011.642935

Cited by 28 publications

(45 citation statements)

References 10 publications

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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).…”

Section: D Exact Shell Modelmentioning

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:…”

Section: D Exact Shell Modelmentioning

confidence: 99%

“…The equilibrium equations in general orthogonal curvilinear coordinates (see [66][67][68][69]) are adapted to the case of a cylinder giving an infinite value for one of the two radii of curvature. The equilibrium equations in rectilinear orthogonal coordinates and in cylindrical coordinates were exactly solved by Messina [70] and Soldatos and Ye [71], respectively. Classical and refined two-dimensional GDQ methods for the free vibration analysis of shell structures have been developed in [72][73][74][75][76][77][78][79][80][81] where several benchmarks related to doubly-curved multilayered composite shells and higher-order theories have been proposed.…”

Section: Introductionmentioning

confidence: 99%

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Refined 2D and Exact 3D Shell Models for the Free Vibration Analysis of Single- and Double-Walled Carbon Nanotubes

et al. 2015

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The present paper talks about the free vibration analysis of simply supported Single-and Double-Walled Carbon Nanotubes (SWCNTs and DWCNTs). Refined 2D Generalized Differential Quadrature (GDQ) shell methods and an exact 3D shell model are compared. A continuum approach (based on an elastic three-dimensional shell model) is used for natural frequency investigation of SWCNTs and DWCNTs. SWCNTs are defined as isotropic cylinders with an equivalent thickness and Young modulus. DWCNTs are defined as two concentric isotropic cylinders (with an equivalent thickness and Young modulus) which can be linked by means of the interlaminar continuity conditions or by means of van der Waals interactions. Layer wise approaches are mandatory for the analysis of van der Waals forces in DWCNTs. The effect of van der Waals interaction between the two cylinders is shown for different DWCNT lengths, diameters and vibration modes. The accuracy of beam models and classical 2D shell models in the free vibration analysis of SWCNTs and DWCNTs is also investigated.

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Section: D Exact Shell Modelmentioning

confidence: 99%

Section: D Exact Shell Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Refined 2D and Exact 3D Shell Models for the Free Vibration Analysis of Single- and Double-Walled Carbon Nanotubes

et al. 2015

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“…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.…”

Section: Introductionmentioning

confidence: 99%

Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels

Brischetto

2014

Shock and Vibration

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The paper proposes a three-dimensional elastic analysis of the free vibration problem of one-layered spherical, cylindrical, and flat panels. The exact solution is developed for the differential equations of equilibrium written in orthogonal curvilinear coordinates for the free vibrations of simply supported structures. These equations consider an exact geometry for shells without simplifications. The main novelty is the possibility of a general formulation for different geometries. The equations written in general orthogonal curvilinear coordinates allow the analysis of spherical shell panels and they automatically degenerate into cylindrical shell panel, cylindrical closed shell, and plate cases. Results are proposed for isotropic and orthotropic structures. An exhaustive overview is given of the vibration modes for a number of thickness ratios, imposed wave numbers, geometries, embedded materials, and angles of orthotropy. These results can also be used as reference solutions to validate two-dimensional models for plates and shells in both analytical and numerical form (e.g., closed solutions, finite element method, differential quadrature method, and global collocation method).

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“…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.…”

Section: Introductionmentioning

confidence: 99%

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

Brischetto

Torre

2017

J. Compos. Sci.

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Abstract:The exact three-dimensional analysis of a large group of geometries is accomplished here using the same formulation written in orthogonal mixed curvilinear coordinates. This solution is valid for plates, cylindrical shells, cylinders and spherical shells. It does not need specialized equations for each proposed geometry. It makes use of a formulation that is valid for spherical shells and automatically degenerates in the simpler geometries. Second order differential equations are reduced of an order redoubling the number of variables, and then they are solved via the exponential matrix method. Coefficients of equations vary through the thickness when shells are considered. M mathematical layers must be introduced into each physical layer to approximate the curvature. The correlation between M and the order of expansion N for the exponential matrix is analyzed in this paper in order to find their opportune combined values to obtain the exact results. As their effects may depend on different parameters, several geometries, lamination sequences, thickness ratios and imposed half-wave numbers are taken into consideration.

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

Cited by 28 publications

References 10 publications

Refined 2D and Exact 3D Shell Models for the Free Vibration Analysis of Single- and Double-Walled Carbon Nanotubes

Refined 2D and Exact 3D Shell Models for the Free Vibration Analysis of Single- and Double-Walled Carbon Nanotubes

Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels

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

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