Natural frequency calculation of open laminated conical and cylindrical shells by a meshless method
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Natural frequency calculation of open laminated conical and cylindrical shells by a meshless method Songhun Kwak1, Kwanghun Kim2,a
, Yonguk Ri2 , Gwangil Jong1, Hyonil Ri2
1 College of Mechanical Science and Technology, Kim Chaek University of Technology, Pyongyang 999093,
Democratic People’s Republic of Korea
2 Department of Engineering Machine, Pyongyang University of Mechanical Engineering, Pyongyang 999093,
Democratic People’s Republic of Korea Received: 10 December 2019 / Accepted: 11 May 2020 © Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract In this paper, a new and an efficient solution method based on local gradient smoothing method has been applied to free vibration problem of open composite laminated cylindrical and conical shells with elastic boundary conditions. The theoretical model is formulated by the first-order shear deformation theory, and the motion equation is obtained by the Hamilton’s principle. The motion equation is discretized by meshless shape function; in this process, the derivatives of the shape function are approximated by local gradient smoothing method. The accuracy, applicability and efficiency of this method are demonstrated for free vibrations of open composite laminated cylindrical and conical shells with different geometric, material parameters and boundary condition. The numerical results show good convergence characteristics and good agreement between the present method and the existing literature. And through several numerical examples, some useful results for free vibration results of open composite laminated cylindrical and conical shells are obtained, which may serve as a benchmark solutions for researchers to check their analytical and numerical methods.
1 Introduction As the rapid development of science and technology, new processes for manufacturing composite materials are used in variety of engineering fields such as aerospace, high-speed train and ship engineering and are developing rapidly. With the development of new composite materials manufacturing processes, the cost of materials has reduced and application fields of composite materials are extending more widely. The study on free vibration of shells, one of the structural elements widely used in engineering, has attracted of attention many researchers. So far, for analyzing the dynamic characteristics of shell, classical shell theory (CST) [1–5], first-order shear deformation theory (FSDT) [6–9] and HSDT (higher-order shear deformation theory) [10–15] have been developed and used. Since transverse normal and shear deformations are neglected in the CST, the FSDT was developed to correct these defects.
a e-mail: [email protected] (corresponding author)
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Eur. Phys. J. Plus
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HSDT is a theory developed to avoid the use of shear correction coefficient introduced in FSDT and to predict more accurate vibration behavior. However, as pointed out by Qu et al. [7], somewhat complex formulas and bounda
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