Natural frequencies of clamped orthotropic skew plates
TL;DR: In this article, an approximate formula for the isotropic and orthotropic skew plates with clamped sides is proposed. But the accuracy of the proposed approximate formulae is limited by comparing numerical and experimental results.
About: This article is published in Journal of Sound and Vibration.The article was published on 1982-03-22. It has received 12 citations till now. The article focuses on the topics: Orthotropic material & Skew.
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TL;DR: A review of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations is presented in this paper, where a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials.
Abstract: A summary of the recent developments in the analysis of laminated beams and plates with an emphasis on vibrations and wave propagations in presented. First, a review of the recent studies on the free-vibration analysis of symmetrically laminated plates is given. These studies have been conducted for various geometric shapes and edge conditions. Both analytical (closed-form, Galerkin, Rayleigh-Ritz) and numerical methods have been used. Because of the importance of unsymmetrically laminated structural components in many applications, a detailed review of the various developments in the analysis of unsymmetrical ly laminated beams and plates also is given. A survey of the nonlinear vibrations of the perfect and geometrically laminated plates is presented next. It is seen that due to the bending-stretching coupling, the nonlinear behavior of the unsymmetrically laminated perfect and imperfect plates, depending upon the boundary conditions, may be hardening or softening type. Similar behavior also is observed for imperfect isotropic and laminated plates. Lastly, the developments in studying the wave propagation in laminated materials are reviewed. It is seen that a significant effort has been spent on developing appropriate continuum theories for modeling the composite materials. Some recent studies on the linear and nonlinear transient response of laminated materials also are described.
288 citations
01 Jan 2014
TL;DR: In this article, the size effect on orthotropic Kirchhoff-type skew micro-plates is investigated based on a modified couplestresstheory, where the 2D couple stress state of the orthotropic 12 micro-plate is described solely by only one material length scale parameter in accordance with the in-plane 13 shear modulus.
Abstract: 8 Abstract The size effect on orthotropic Kirchhoff-type skew micro-plates is investigated based on a modified 9 couplestresstheory.Forathree-dimensionalorthotropicbody,threeadditionalmateriallengthscaleparameters 10 should be involved in the modified couple stress theory ( with respect to the three shear moduli ) . However, in 11 this study and without restricting the generality, we assume that the 2D couple stress state of the orthotropic 12 micro-plate is described solely by only one material length scale parameter in accordance with the in-plane 13 shear modulus. Furthermore, this reasonable assumption allows us to compare qualitatively the results with 14 those obtained by the nonlocal elasticity theory, which also uses only one material length scale parameter to 15
62 citations
TL;DR: In this article, the size effect on orthotropic Kirchhoff-type skew micro-plates is investigated based on a modified couple stress theory and the resulting initial boundary value problem is of fourth order, and it is solved employing the analog equation method.
Abstract: The size effect on orthotropic Kirchhoff-type skew micro-plates is investigated based on a modified couple stress theory. For a three-dimensional orthotropic body, three additional material length scale parameters should be involved in the modified couple stress theory (with respect to the three shear moduli). However, in this study and without restricting the generality, we assume that the 2D couple stress state of the orthotropic micro-plate is described solely by only one material length scale parameter in accordance with the in-plane shear modulus. Furthermore, this reasonable assumption allows us to compare qualitatively the results with those obtained by the nonlocal elasticity theory, which also uses only one material length scale parameter to capture the size effect. Using Hamilton’s principle, the governing equilibrium equation of the micro-plate and the associated general boundary conditions are derived in terms of the deflection. The resulting initial boundary value problem is of fourth order, and it is solved employing the analog equation method. Example problems are presented for orthotropic skew micro-plates, and useful conclusions are drawn from the investigation of their micron-scale response. Some of the findings detected in studying the microstructure vibratory response of orthotropic skew micro-plates, based on the modified couple stress theory, are also verified by those obtained by the nonlocal elasticity theory. Nevertheless, a new important finding is that both the frequency and critical load parameters increase by increasing the material length scale parameter of the modified couple stress theory, which is in direct contradiction to that of the nonlocal elasticity theory where these parameters decrease by increasing the nonlocal parameter.
60 citations
TL;DR: In this paper, a differential quadrature method is applied for static, free vibration, and stability analysis of skewed and trapezoidal composite thin plates, and a general transformation scheme is employed to transfer the variation of the variables in the computational to the physical domain and vice versa.
45 citations
TL;DR: In this article, the effects of skew angle and lamination scheme on natural frequencies were studied for skew laminated composite plates with simply supported and clamped edges, and results were tabulated for different lamination schemes and compared to available studies in the literature.
30 citations
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TL;DR: The fundamental equation of classical plate theory can be found in this article, where anisotropic and variable-thickness versions of the classical plates are considered, as well as other considerations.
Abstract: : Contents: Fundamental Equations of Classical Plate Theory; Circular Plates; Elliptical Plates; Rectangular Plates; Parallelogram Plates; Other Quadrilateral Plates; Triangular Plates; Plates of Other Shapes; Anisotropic Plates; Plates With Inplane Forces; Plates With Variable Thickness; and Other Considerations.
2,137 citations
202 citations
TL;DR: In this article, the free vibration of skew plates by the Rayleigh-Ritz method with B-spline functions as co-ordinate functions was investigated and convergence of the solutions was investigated in a few typical cases and was found to be satisfactory.
102 citations
TL;DR: In this paper, the vibration problems of skew plates with different edge conditions involving simple support and clamping have been considered by using the variational method of Ritz, a double series of beam characteristic functions being employed appropriate to the combination of the edge conditions.
74 citations
64 citations