Dynamic analysis of rectangular liquid containers with elastic baffle

Abstract

In the present study, fundamental time period and the hydrodynamic pressure exerted by the fluid on walls of rectangular tanks due to sinusoidal excitations are investigated by pressure based finite element method. The fluid within the tank is considered to be water and tank walls are assumed as rigid. However, the baffle within the tanks is considered to be flexible. The fluid within the tank is considered as inviscid and fluid motion is irrotational. Galerkin approach is used for finite element formulation of wave equation. Newmark’s average integration method which is unconditionally stable is used to obtain the response of baffle-liquid coupled system. The present algorithm also includes the compressibility of water within tank. The efficacy of the present algorithm has been demonstrated through numerous examples both for free and forced vibration analysis. The time period increases with presence of elastic baffle within the tanks. The time period of baffle-liquid coupled system also increases with the increase of tank length. An increasing trend of fundamental time period of baffle-liquid coupled system is also observed with the increase of liquid height within the tanks. However, the influence of height of fluid in fundamental time period of this coupled system is greater than those for the length of tanks. The free vibration responses of this coupled system also increase with the increase of flexibility of baffle wall. Position of the baffle within the tanks also influences the free vibration response of the tank with baffle. Similar to the height of baffle, the thickness of baffle also changes the flexibility of baffle within tanks hence the increase in baffle thickness reduces the time period of the baffle-fluid coupled system. Similar to the fundamental time period of baffle-fluid coupled system, the hydrodynamic pressure within the tanks due to different excitations depends on the different parameters of tank and baffle. The hydrodynamic pressure at the bottom of tank wall increases with the increase of baffle thickness. However, this hydrodynamic pressure at free surface decreases with the increase of baffle thickness. Hydrodynamic pressure at bottom surface of tank increases with decrease in fluid height. Hydrodynamic pressure at bottom surface of tank increases with increase in tank length. However, there is no notable variation in hydrodynamic pressure at free surface due to change in tank length. The dynamic response is amplified when the system is experienced external loadings having frequency close to natural frequency of the system.