Free vibrations of partially filled cylindrical tanks

Abstract

The coupled free vibration characteristics of partially or completely liquid-filled ground supported circular cylindrical tanks are investigated. Attention is given to partially filled broad tanks with a height to diameter ratio of less than one. For the vibrations of the container itself Flugge's exact equations of motion are applied and the radial liquid dynamic pressure is obtained in terms of the liquid velocity potential (φ). The complex roots of the eighth-order auxiliary equation are obtained by using four different methods. The suitability of these methods is discussed based on the relative magnitude of the various coefficients in the auxiliary equation. The contained liquid is assumed to be incompressible and inviscid. The bottom of the tank is considered to be flat. The results are compared with those obtained by Haroun and Housner and found to be in good agreement. Coupled natural frequencies in bulging modes are obtained for various parameters, i.e., (i) height to diameter ratio (λ); (ii) the liquid depth factor ( α 1); and (iii) the tank wall thickness factor ( α 2). It has been shown that Flugge's exact theory is a versatile tool which can easily be used for such problems. The results can be obtained to any desired degree of accuracy in any frequency range.