FOURIER-SERIES EXPANSION METHOD FOR FREE-VIBRATION ANALYSIS OF EITHERA PARTIALLY LIQUID-FILLED OR A PARTIALLY LIQUID-SURROUNDED CIRCULAR CYLINDRICAL-SHELL

An analytical method for free vibration of either a partially liquid-f illed or a partially liquid-surrounded circular cylindrical shell with various classical boundary conditions is developed by means of the St okes' transformation and the Fourier series expansion, on the basis of Sanders' shell theory. The liquid-shell coupled system is divided int o two regions for convenient formulation. One is the empty shell regio n in which the Sanders' shell equations are formulated without the liq uid effect, the other is the wetted shell region in which the shell eq uations are formulated with consideration of the liquid dynamic effect . The shell equations for each region are combined by the geometry and the force continuities at the junction of the two regions. For the vi bration relevant to the liquid motion, the velocity potential of liqui d is assumed as a sum of linear combination of suitable harmonic funct ions in the axial direction. The unknown parameters of these are selec ted to satisfy the boundary condition along the wetted shell surface. The procedure stated in the foregoing leads to a determinantal equatio n for the natural frequencies of the liquid-shell coupled system. To c larify the validity of the analytical method, the free vibration analy ses are separately performed for a partially liquid-filled and a parti ally liquid-surrounded circular cylindrical shell with clamped-free bo undary condition, and for a partially liquid-filled circular shell wit h clamped-clamped boundary condition, which have been examined in the previous works. Excellent agreement between the results of the analyti cal method and those of the previous works is found.