Dynamic Stability of Fluid-Coupled Coaxial Cylindrical Shells under Vertical Excitation

• Published in: Nihon Kikai Gakkai ronbunshū. C Vol. 55; no. 512; pp. 870 - 877
• Main Authors: TANI, Junji, SAKAI, Tatsuyoshi, CHIBA, Masakatsu
• Format: Journal Article
• Language: Japanese
• Published: The Japan Society of Mechanical Engineers 1989
• Subjects: Dynamic Stability; Fluid-Coupled Coaxial Cylinders; Theoretical Analysis; Vertical Excitation; Vibration
• ISSN: 0387-5024; 1884-8354
• DOI: 10.1299/kikaic.55.870

Theoretical analyses are presented for the dynamic stability of a free-clamped coaxial cylindrical shell partially filled in the annular gap with incompressible, inviscid liquid and subjected to vertical excitation. The dynamic version of the Donnell equations and the velocity potential theory are used for the motions of the shell and the liquid, respectively. The problem is solved by using the modified Galerkin method so as to satisfy the boundary conditions, and the governing equation is reduced to a type of coupled Mathieu's equation. The instability boundaries where parametric resonance occurs are determined by using Hsu's method. It is found that a principal instability resonance and a combination instability resonance of the sum type of two natural vibrations, each of which has the same circumferential wave number and different axial mode of vibration, are likely to occur. Further, the interactive effect of the coaxial cylinders is found to become small with an increase in the wave number and the annular gap.