2014
DOI: 10.1155/2014/479738
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Three-Dimensional Exact Free Vibration Analysis of Spherical, Cylindrical, and Flat One-Layered Panels

Abstract: 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 ge… Show more

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Cited by 32 publications
(59 citation statements)
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“…Furthermore, these characteristics have been emphasized mostly by the use of composite materials, such as laminated composites, in order to obtain the best engineering properties with respect to conventional materials. Several applications in literature [64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80] have demonstrated the advantages that can be obtained in many dynamic problems, based especially on the free vibration analysis of beams, plates and shells. However, the heterogeneity of the material properties that characterizes the laminate and the shear stresses between the laminae can cause the phenomenon of the delamination.…”
Section: Introductionmentioning
confidence: 99%
“…Furthermore, these characteristics have been emphasized mostly by the use of composite materials, such as laminated composites, in order to obtain the best engineering properties with respect to conventional materials. Several applications in literature [64][65][66][67][68][69][70][71][72][73][74][75][76][77][78][79][80] have demonstrated the advantages that can be obtained in many dynamic problems, based especially on the free vibration analysis of beams, plates and shells. However, the heterogeneity of the material properties that characterizes the laminate and the shear stresses between the laminae can cause the phenomenon of the delamination.…”
Section: Introductionmentioning
confidence: 99%
“…A simple method of reducing its order to the first one is described in [3,31] and it may be summarized as a redoubling of the involved variables. In the first author's past works [20,21], a detailed description of this approach can be found. The compact form of the reduced system of first order partial differential equations is:…”
Section: Use Of the Exponential Matrix And Mathematical Layers In Thementioning
confidence: 99%
“…Details about their determination can be found in the first author's past works [20][21][22][23][24][25][26].…”
Section: Use Of the Exponential Matrix And Mathematical Layers In Thementioning
confidence: 99%
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“…Theories on shells have been developed a lot through the years. In particular, the physical three-dimensional (3D) problem [32][33][34][35] can be simplified using different approximations which can lead to two-dimensional (2D) models. As a function of the hypothesis of the theory under study the solutions can closely fit the original 3D shell or plate.…”
Section: Introductionmentioning
confidence: 99%