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research-article

A Finite strip for vibration analysis of rotating toroidal shell under internal pressure

[+] Author and Article Information
Ivo Senjanovic

University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, Croatia
ivo.senjanovic@fsb.hr

Ivan Catipovic

University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, Croatia
ivan.catipovic@fsb.hr

Neven Alujevic

University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, Croatia
nalujevic@fsb.hr

Damjan Cakmak

University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, Croatia
damjan.cakmak@fsb.hr

Nikola Vladimir

University of Zagreb, Faculty of Mechanical Engineering and Naval Architecture, Zagreb, Croatia
nikola.vladimir@fsb.hr

1Corresponding author.

ASME doi:10.1115/1.4041734 History: Received July 20, 2018; Revised October 07, 2018

Abstract

In this paper, a finite strip for vibration analysis of rotating toroidal shells subjected to internal pressure is developed. The expressions for strain and kinetic energies are formulated in a previous paper, in which vibrations of a toroidal shell with a closed cross-section are analysed using the Rayleigh-Ritz method and Fourier series. In this paper, however, the variation of displacements u, v and w with the meridional coordinate is modelled through a discretisation with a number of finite strips. The variation of the displacements with the circumferential coordinate is taken into account exactly, by using simple sine and cosine functions of the circumferential coordinate. A unique argument is used in order to be able to capture travelling modes due to the shell rotation. The finite strip properties, i.e. the stiffness matrix, the geometric stiffness matrix and the mass matrices are defined by employing bar and beam shape functions, and by minimizing the strain and kinetic energies. In order to improve the convergence of the results, also a strip of a higher order is developed. The application of the finite strip method is illustrated in cases of toroidal shells with closed and open cross-sections. The obtained results are compared with those determined by the Rayleigh-Ritz method and the finite element method.

Copyright (c) 2018 by ASME
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