Analytical solution for free vibrations of rotating cylindrical shells having free boundary conditions. (1st February 2017)

• Record Type: Journal Article
• Authors: Alujević, N.; Campillo-Davo, N.; Kindt, P.; Desmet, W.; Pluymers, B.; Vercammen, S.
• Is Part Of: Engineering structures. Volume 132(2017:Feb. 01)
• Page Start: 152
• Page End: 171
• Publication Date: 2017-02-01
• Subjects: Vibration -- Circular cylindrical shells -- Free boundary conditions -- Rotating shells -- Elastic foundation -- Rotating modes -- Analytical methods -- Natural frequencies -- Mode shapes; Structural engineering -- Periodicals; Structural analysis (Engineering) -- Periodicals; Construction, Technique de la -- Périodiques; Génie parasismique -- Périodiques; Pression du vent -- Périodiques; Earthquake engineering; Structural engineering; Wind-pressure; Periodicals; 624.105
• DOI: 10.1016/j.engstruct.2016.11.008
• Languages: English
• ISSNs: 0141-0296

Abstract

Highlights: Free vibration problem of a rotating cylindrical shell with free ends is solved analytically. Eight different functional forms for mode shapes were identified and derived. The mode shapes are determined by the eight types of roots of the characteristic polynomial. The analytical results are compared to experimental. Excellent agreement is obtained. Abstract: In this paper free vibrations of rotating cylindrical shells with both ends free are studied. The model used also allows for considering a flexible foundation supporting the shell in the sense of a radial and circumferential distributed stiffness. Furthermore, a circumferential tension (hoop stress) which may be due to pressurisation or centrifugal forces is taken into account. Natural frequencies and mode shapes are determined exactly for both stationary shells and for shells rotating with a constant angular speed around the cylinder axis. Trigonometric functions are assumed for the circumferential mode shape profiles, and a sum of eight weighted exponential functions is assumed for the axial mode shape profiles. The functional form of the axial profiles is shown to greatly vary with the roots of a characteristic bi-quartic polynomial that occurs in the process of satisfying the equations of motion. In the previously published work it has been very often assumed that the roots are two real, two imaginary, and two pairs of complex conjugates. In the present study, a total of eight types of roots are shown to determine the whole set of mode shapes, either for stationary or for rotating shells. The results using the developed analytical model are compared with results of experimental studies and very good agreement is obtained. Also, a parametric study is carried out where effects of the elastic foundation stiffnesses and the rotation speed are examined.