Page 308 - Introduction to Naval Architecture

VIBRATION, NOISE AND SHOCK 293

diverge with successive iterations. This is due to the profile containing
a component of the two-node profile which becomes dominant. Whilst
ways have been developed to deal with this, one would today choose to
carry out a finite element analysis.

Approximate formulae

It has been seen that the mass and stiffness distributions in the ship are
important in deriving vibration frequencies. Such data is not available
in the early design stages when the designer needs some idea of the
frequencies for the ship. Hence there has always been a need for simple
empirical formulae. The Schlick formula had severe limitations and
various authorities have proposed modifications to it.
7
Burrill suggested one allowing for added mass and shear deflection.
The frequency was given as:

where r s is the deflection correction factor.
2 2
With A in tonf, dimensions in ft and / in in ft the constant had a
value of about 200000 for a number of different ship types if L is
between perpendiculars. For length overall the constant became about
220000.
Todd adapted Schlick to allow for added mass, the total virtual
displacement being given by:

He concluded that /should allow for superstructures in excess of 40 per
cent of the ship length. For ships with and without superstructure the
results for the two-node vibration generally obeyed the rule:

4
The constant would become 238 660 if / is in m , dimensions in m and
Ay is in MN.