Natural frequency and bending analysis of heterogeneous polar orthotropic-faced sandwich panels in the existence of in-p
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(2020) 20:111
ORIGINAL ARTICLE
Natural frequency and bending analysis of heterogeneous polar orthotropic‑faced sandwich panels in the existence of in‑plane pre‑stress M. M. Alipour1 · M. Shaban2 Received: 13 April 2020 / Revised: 19 July 2020 / Accepted: 24 August 2020 © Wroclaw University of Science and Technology 2020
Abstract In this paper, the effects of plane pre-stresses on the free vibration and static analyses of circular and annular sandwich panels are examined based on an accurate formulation, as first time. It is assumed that initially pre-stresses consist of in-plane normal (tensile/compressive) and pure bending stresses. New first-order shear deformation theory together with a layerwise approach for sandwich panel is utilized. The sandwich panels are made up of either orthotropic or heterogeneous polar orthotropic materials. Furthermore, piecewise-defined linear local in-plane displacements are adopted based on zigzag theory. The governing partial differential equations are extracted by implementing principle of minimum total potential energy. A unified analytical solution procedure is developed based on power series method for the analysis of heterogeneous initially stressed annular and circular sandwich panels with arbitrary boundary conditions. The transverse shear stress is precisely calculated by considering three-dimensional theory of elasticity. To validate the proposed formulation, the obtained results are compared with those of finite element method. After numerically demonstrating the accuracy of the method, the effects of different geometrical and material parameters, boundary conditions and in-plane pre-stresses on the free vibration and static behavior of circular and annular sandwich panels are investigated. Keywords Pre-stress · Sandwich panel · Unified analytical solution · Heterogeneous orthotropic facing · Natural frequency · Bending
1 Introduction Heterogeneous orthotropic materials have been used extensively in various and modern marine, nuclear and military industries. Nowadays, in some industries, heterogeneous functionally graded (FG) materials are just now becoming a primary choice for material. On the other hand, due to manufacturing process, initial stresses are presented in the structures which cannot be neglected. The initial stress may have some advantageous or disadvantages for some applications * M. Shaban [email protected]; [email protected]
M. M. Alipour [email protected]; [email protected]
1
Department of Mechanical Engineering, University of Mazandaran, 47416‑13534 Babolsar, Iran
Mechanical Engineering Department, Faculty of Engineering, Bu-Ali Sina University, Hamadan, Iran
2
of laminated composite and/or sandwich panel. As a result, it is important to consider the effect of initial stress on the static and vibration behavior of laminated composite and sandwich panels. Most of the presented studies on the initially stressed structures were carried out using equivalent single layer theories. Based on the first-order shear deformati
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