Natural frequency

I am having difficulty in finding the heave, roll and pitch natural frequency of my model. I want to know the natural frequency so that I could predict the wave period and wavelength that is going to make my model have maximum motion in the seakeeping experiment. In order to find it, i need to know the virtual mass and restoring constant. to get added mass, i need to know the wavelength. My target is to know the wavelength,but to get it, I need to have the value of the wavelength first. This is so confusing,I am currently reading "Dynamics of Marine Vehicle" by Rameswar Bhattacharya. Can anyone help me?

 

It is a rather complicated issue. The natural frequency of the boat is not a constant. It varies according to conditions. For example, the direction of wind and waves will affect it. also, the trim and heel. There are basic design features that also contribute. For example, a flared or clipper bow will change the curve of acceleration, and therefore the natural frequency, of pitching. Sometimes is easier and better to conduct the experiment and then calculate backwards.

 

Thanx a million gonzo....but my final year project supervisor asked me to find the natural frequency first before i can conduct the experiment...is there any typical natural frequency that i can refer to?...say,if a displacement hull,what is the range for its heave,pitch n roll natural frequency?

 

To find the heave, roll and pitch is a relatively straight forward exercise. I assume when you say ‘model’ you mean a mathematical model rather than a physical model? Since if you have a physical model it is very easy to perform.


Heave

The period is given by 2.pi.[Kzz/(g.Aw.rho)]^0.5

Kzz includes the ‘added mass’
Aw waterplane area


Roll

The period is given by 2.pi.Kxx/(g.GM)^0.5

Where Kxx includes added mass

Pitch

The period is given by 2.pi.Kyy/(g.GML)^0.5

Again, Kyy is displacement plus added mass.

The added mass is related to an oscillating circular cylinder. Thus added mass = rho.constant.XSA

However the constant varies considerably depending upon hull form and various tables for different hull forms have been produced. You’ll need to find the closest table to the hull form you are investigating in your model. But its often very close to double the displacement.

Wind and waves do not affect the natural frequency of the ship; wind and waves are a forcing moment or function and the equations above become a bit more complex, drifting into non linear. This just affects the behaviour but does not alter the natural frequency. Since the equations are then not = 0 but = M.cos.wt

Thus you would get only need the displacement and underwater XSA (cross sectional area) that affect the added mass term. The rest as can be seen is directly proportional to the GMT and GML.

In other words, KMT and KML. Which is of course a simple matter to calculate.

<edited: typo>

 

Mmmmm, beautiful, all necessary info boiled down to 13 rows; here some "moral points" AH!

 

The K is found by experimentation. Unless you are calculating a design type that has been tested, it would be hard to guess what value to use.

 

Thanks Ad Hoc and to the rest for replying..... : )