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 analyzed using the Rayleigh–Ritz method (RRM) and Fourier series. In this paper, however, the variation of displacements u, v, and w with the meridional coordinate is modeled through a discretization 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 traveling 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 RRM and the finite element method (FEM).
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April 2019
Research-Article
A Finite Strip for the Vibration Analysis of Rotating Toroidal Shell Under Internal Pressure
Ivo Senjanović,
Ivo Senjanović
Faculty of Mechanical Engineering and Naval
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
e-mail: [email protected]
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
e-mail: [email protected]
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Ivan Áatipović,
Ivan Áatipović
Faculty of Mechanical Engineering and Naval
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
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Neven Alujević,
Neven Alujević
Faculty of Mechanical Engineering and Naval
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
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Damjan Čakmak,
Damjan Čakmak
Faculty of Mechanical Engineering and Naval
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
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Nikola Vladimir
Nikola Vladimir
Faculty of Mechanical Engineering and Naval
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Search for other works by this author on:
Ivo Senjanović
Faculty of Mechanical Engineering and Naval
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
e-mail: [email protected]
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
e-mail: [email protected]
Ivan Áatipović
Faculty of Mechanical Engineering and Naval
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Neven Alujević
Faculty of Mechanical Engineering and Naval
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Damjan Čakmak
Faculty of Mechanical Engineering and Naval
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Nikola Vladimir
Faculty of Mechanical Engineering and Naval
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Architecture,
University of Zagreb,
Ivana Lučića 5,
Zagreb 10000, Croatia
Contributed by the Technical Committee on Vibration and Sound of ASME for publication in the JOURNAL OF VIBRATION AND ACOUSTICS. Manuscript received July 20, 2018; final manuscript received October 7, 2018; published online November 19, 2018. Assoc. Editor: Stefano Lenci.
J. Vib. Acoust. Apr 2019, 141(2): 021013 (17 pages)
Published Online: November 19, 2018
Article history
Received:
July 20, 2018
Revised:
October 7, 2018
Citation
Senjanović, I., Áatipović, I., Alujević, N., Čakmak, D., and Vladimir, N. (November 19, 2018). "A Finite Strip for the Vibration Analysis of Rotating Toroidal Shell Under Internal Pressure." ASME. J. Vib. Acoust. April 2019; 141(2): 021013. https://doi.org/10.1115/1.4041734
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