Free Vibrations of a Laminated Composite Circular Cylindrical Shell Partially Filled with Liquid

Abstract

The present paper deals with a free vibration analysis of the circular cylindrical shell partially filled with liquid. On the assumption that the shell is made of the double-ply laminated CFRP composite material and the liquid is incompressible and inviscid, the linear responses of the shell vibration are theoretically analyzed. Displacements of the shell wall vibrated under a clamped-free condition are expanded into a Fourier series for circumferential coordinates. The buldging in shell under the condition is simulated on the concept of the finite element method (FEM) using isoparametric elements. The equation of continuity and the linearized Bernoulli's theorem are applied to analyze the motion of liquid free surface. The natural frequencies of vibration are determined in relation with the ply-angles of laminates for given parameters. There are some differences in the trend of frequency curves between the (φ/φ) laminate and the (-φ/φ) one, where φ is ply-angle. In the ratio greater than 0.5 of liquid level to shell height, the frequencies of the cross-ply laminated shell increase first with increasing the angle φ and then show plateaus in the higher ply-angle regions over 60° of curves, while for the angle-ply laminated one they gradually decrease after reaching the maximum values. In the ratio less than 0.5, however, the both laminated shells show the maximum value in frequencies at a paticular ply-angle. When circumferential wave number or mode of vibration is considered as a parameter, for the both laminated composite materials the curve is the same as stated above.