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Dynamic stability of liquid‐filled cylindrical shells under vertical excitation, Part II: Theoretical results
Author(s) -
Chiba M.,
Tani J.
Publication year - 1987
Publication title -
earthquake engineering and structural dynamics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.218
H-Index - 127
eISSN - 1096-9845
pISSN - 0098-8847
DOI - 10.1002/eqe.4290150104
Subject(s) - galerkin method , parametric oscillator , parametric statistics , shell (structure) , instability , resonance (particle physics) , excitation , multiple scale analysis , mechanics , equations of motion , boundary value problem , vibration , stability (learning theory) , physics , coupling (piping) , mathieu function , normal mode , mathematics , classical mechanics , mathematical analysis , materials science , finite element method , atomic physics , thermodynamics , optics , acoustics , statistics , machine learning , computer science , metallurgy , composite material , quantum mechanics
Theoretical analyses are presented for the dynamic stability of a clamped‐free cylindrical shell partially filled with liquid, under vertical excitation. In the analyses, the dynamic version of the Donnell equations and the velocity potential theory were used for the motions of the shell and the liquid, respectively. The problem was solved by using the modified Galerkin method so as to satisfy the boundary conditions. The equations of motion coupling the shell and the liquid were derived from a type of coupled Mathieu's equation. It is found that the parametric principal resonance could occur, as well as the parametric combination resonance of the sum type, involving two natural vibrations with the same circumferential wave number but with different axial mode number. The latter type of parametric resonance apparently has not been previously studied. The instability regions where parametric resonance occurs were determined by using Hsu's method. 17 To compare with the experimental results which had been stated in a companion paper, 15 detailed numerical calculations were carried out for the two test cylinders partially filled with water. Excellent agreement between theory and experiment was demonstrated for the instability regions.