1,721,105 research outputs found
Exact Free Vibration Analysis of Lévy FGM Plates with Higher-Order Shear and Normal Deformation Theories
Full text linkFirst-known exact solutions are derived for free vibration of thick and moderately thick functionally graded rectangular plates with at least one pair of opposite edges simply-supported on the basis of a family of two-dimensional shear and normal deformation theories with variable order. The boundary-value problem is first expressed in a compact unified form which is invariant with respect to the order of the kinematic theory. The Lévy method applied to this compact form yields a set of governing equations written in terms of invariant matrices, which are then appropriately expanded according to the order of the plate model. The resulting equations are put into a state-space representation and the frequency values are finally obtained by substituting the general solution of the state equation into the set of boundary conditions and solving the related homogeneous system. After discussing the way of recovering the through-the-thickness modal displacement and stress distribution at any point of the plate and how the effective elastic properties of the graded plate are computed, some numerical results are presented using various higher-order theories. Comparisons with exact three-dimensional and other two-dimensional approaches are provided for two-constituents metal-ceramic plates. New exact results for functionally graded plates with six combinations of boundary conditions are also obtained. They can be useful as valuable sources for validating other approaches and approximate methods
Refined 2-D Theories for Free Vibration Analysis of Annular Plates: Unified Ritz Formulation and Numerical Assessment
Full text linkThis paper presents a unified Ritz-based method for the computation of modal properties of both thick and thin, circular and annular isotropic plates with different boundary conditions. The solution is based on an appropriate and simple formulation capable of handling in an unified way a large variety of two-dimensional higher-order plate theories. The formulation is also invariant with respect to the set of Ritz admissible functions. In this work, accurate upper-bound vibration solutions are presented by using kinematic models up to sixth order and products of Chebyshev polynomials and boundary-compliant functions. Considering the circumferential symmetry of annular plates and the 2-D nature of underlying theories, the present method is also computationally efficient since only single series of trial functions in the radial direction are required
Computation of Eigenvalues for Thick and Thin Circular and Annular Plates Using a Unified Ritz-Based Formulation
No full textExact Vibration Solutions for Cross-Ply Laminated Plates with Two Opposite Edges Simply Supported Using Refined Theories of Variable Order
Full text linkThis paper presents exact solutions for free vibration of rectangular cross-ply laminated plates with at least one pair of opposite edges simply supported using refined kinematic theories of variable order. Exact natural frequencies are obtained using an efficient and unified formulation where the solving set of second-order differential equations of motion and related boundary conditions are expressed at layer level in terms of so-called fundamental nuclei having invariant properties with respect to the order of the plate theory. The nuclei are then appropriately expanded according to the number of layers and the order of the theory and the resulting equations are transformed into a first-order model whose solution is obtained by using the state space concept. In this way, the mathematical effort needed to derive analytical solutions is highly reduced. Both higher-order equivalent single-layer and layer-wise theories are considered in this study. Comparisons with other exact solutions are presented and useful benchmark frequency results for symmetric and un-symmetric cross-ply laminates are provided
Exact Vibration Solutions of Refined Theories of Variable Order for Laminated and FGM Plates and Shells
No full textLevy-Type Vibration Solutions of Cross-Ply Laminated Plates Based on Refined Variable-Kinematic Theories
No full textNatural Frequencies of Sandwich Plates with FGM Core Via Variable-Kinematic 2-D Ritz Models
No full textThis paper deals with the formulation of advanced two-dimensional Ritz-based models for accurate prediction of natural frequencies of thin and thick sandwich plates with core made of functionally graded material (FGM). The formulation is rather general due to its invariant properties with respect to the underlying plate kinematic theory and the admissible set of Ritz functions. Convergence and accuracy of the method are investigated in this work using an entire family of higher-order layerwise and equivalent single-layer theories, whose corresponding displacement variables are approximated by series of Chebyshev polynomials multiplied by appropriate boundary functions. Results are presented for rectangular sandwich FGM plates with various thickness-to-length ratios and combinations of clamped, free and simply-supported edges
A hierarchical formulation of the state-space Levy's method for vibration analysis of thin and thick multilayered shells
Full text linkThe state-space approach in conjunction with the Levy's method is used to solve exactly the free vibration problem of specially orthotropic multilayered cylindrical and spherical panels. A hierarchical formulation is presented to build the matrices of the method from small elementary blocks which are invariant with respect to the order and typology of the kinematic shell theory. As a result, the analytical effort to derive the governing equations is minimized and a large number of Levy-type solution based on low to high order, equivalent single-layer or layerwise theories, can be generated within the same mathematical framework. Thereby, the refinement of the two-dimensional shell model can be tailored according to the thickness ratio and the degree of anisotropy of the problem under study and the desired accuracy. Some illustrative results on both thin and thick, laminated and sandwich panels with various boundary conditions are presented and discussed to show the potential of the formulation
A Variable-Kinematic Ritz Formulation based on Higher-Order Zig-Zag Theories for Vibration Analysis of Sandwich Plates
No full textFormulation and Validation of Variable-Kinematic 2-D Ritz-based Models for Vibration Analysis of FGM Sandwich Plates
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