Vibration of an Offshore Structure Having the Form of a Hollow Column Partially Filled with Multiple Fluids and Immersed in Water

Table 1

The lowest four natural frequencies of a fixedly supported immersed beam carrying an eccentric tip mass and two intermediate lumped masses.

Methods	Parameters						Natural frequencies (rad/sec)
	𝑥2	𝑥3	𝐽^∗2	𝐽^∗3	𝑀^∗2	𝑀^∗3	𝜔1	𝜔2	𝜔3	𝜔4
Present	13	14	0.1	0.1	0.1	0.1	2.5978	10.0440	42.3158	109.7077
[9]	13	14	0.1	0.1	0.1	0.1	2.5978	10.0441	42.3158	109.7078