Analytical layerwise free vibration analysis of circular/annular composite sandwich plates with auxetic cores
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Analytical layerwise free vibration analysis of circular/ annular composite sandwich plates with auxetic cores M. M. Alipour . M. Shariyat
Received: 11 June 2015 / Accepted: 31 August 2015 Springer Science+Business Media Dordrecht 2015
Abstract In the present research, free vibration of circular and annular sandwich plates with auxetic (negative Poisson’s ratio) cores and isotropic/orthotropic face sheets is investigated for different combinations of the boundary conditions. To ensure that the results are accurate and reliable, a global–local layerwise plate theory is employed instead of the traditional equivalent single-layer theories. The governing equations are derived based on Hamilton’s principle and solved using a Taylor transform whose center is located at the outer radius of the plate. Due to this hint, the resulting semi-analytical solution can be employed for both circular and annular sandwich plates. After investigation of vibration behavior of a single-layer annular auxetic plate, a comprehensive parametric study including evaluation of effects of the auxeticity for sandwich plates with isotropic and orthotropic face sheets, symmetric and asymmetric
layups, different core to sheet thickness, radius to thickness, and inner to outer radius ratios, and various boundary conditions, is carried out. Results show that unlike the single-layer auxetic plates that exhibit a transition state, the auxeticity may considerably increase the natural frequencies and rigidities of the circular/annular sandwich plates, especially when the boundary conditions induce higher rigidity in the plate or when the fibers are along the radial direction. Accuracy of results of the employed layerwise theory and the proposed semi-analytical solution is verified by comparing the results with those of the threedimensional theory of elasticity extracted from the ABAQUS software. Keywords Free vibration Auxetic core Layerwise theory Composite annular sandwich plate Differential transform
1 Introduction M. M. Alipour Department of Mechanical Engineering, University of Mazandaran, Babolsar 47416-13534, Iran e-mail: [email protected]; [email protected] M. Shariyat (&) Faculty of Mechanical Engineering, K.N. Toosi University of Technology, Tehran 19991-43344, Iran e-mail: [email protected]; [email protected] URL: http://wp.kntu.ac.ir/shariyat/publications.html
While rectangular plates have commonly been used for relatively fixed structural components, plates with circular or annular configurations have been the most appropriate choice for plates with continuous (e.g., power train transmission plates or discs) or partial (e.g., supporting or rotating tables) rotations or when less energy dissipation (e.g., heat transfer) is of concern. These types of plates may be fabricated in three-layer sandwich constructions with different
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layer material properties to satisfy a diversity of purposes; so that depending on the design requirements, the core may be either more rigid or more compl
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