# Computing Natural Frequency of a Torus System: 3D vs. 2D Added Mass

• Fluidman117
In summary, the conversation discusses the computation of natural frequency for a system with a torus object in heaving motion and the need to add an added mass term to the equation. The speaker found a paper with formulas for both 3D and 2D added mass, but is unsure which one to use and when. They also mention the specificity of the question and the need for a reference to the paper or more information about the torus' motion.

#### Fluidman117

Hi!

I am trying to compute the natural frequency of a system and I also need to add the added mass term to my equation. The object I have is a torus and is basically in heaving motion. I found a good paper, which gives a formula for 3d added mass and 2d added mass.

I would figure that I have to use the 3d added mass formula, correct? But when and why do you need to use the 2D added mass?

Thanks!

anyone?

Just give it a little time. Your question is very specific and not general knowledge to most of us.

A reference to the paper would help as well - or at least some clues about what you mean by "heaving motion of a torus".

Hi there,

I would suggest carefully considering the specific parameters and conditions of your torus system before deciding whether to use the 3D or 2D added mass formula. The added mass term represents the effect of the surrounding fluid on the motion of the object, and it can vary based on factors such as the shape and size of the object, the fluid density, and the type of motion being analyzed.

In general, the 3D added mass formula should be used for objects with a more complex geometry and a significant three-dimensional motion component, such as the torus in your case. This formula takes into account the added mass in all three dimensions (x, y, and z) and can provide a more accurate result for systems with a larger range of motion.

On the other hand, the 2D added mass formula is typically used for simpler geometries and motions that are primarily in one direction (such as heaving motion). It only considers the added mass in the direction of motion (z-axis), and therefore may not accurately capture the effects of the surrounding fluid in more complex systems.

In summary, it is important to carefully evaluate the specific characteristics of your torus system and the type of motion being analyzed in order to determine which added mass formula would be most appropriate for your calculations. Additionally, it is always recommended to compare and validate results using both formulas to ensure the accuracy of your findings. I hope this helps. Best of luck with your research!

## 1. What is the natural frequency of a torus system?

The natural frequency of a torus system refers to the frequency at which the system naturally oscillates without any external forces acting upon it. This frequency is determined by the system's physical properties, such as mass and stiffness.

## 2. How is the natural frequency of a torus system calculated?

The natural frequency of a torus system can be calculated using the equation f = √(k/m), where f is the natural frequency, k is the system's stiffness, and m is its mass. In the case of a torus system, this calculation also takes into account the added mass of the water surrounding the torus.

## 3. What is the difference between 3D and 2D added mass in a torus system?

In a 3D added mass calculation, the entire volume of the torus is considered when determining the added mass, while in a 2D calculation, only the surface area of the torus is taken into account. This can result in different natural frequencies for the same torus system.

## 4. Why is it important to consider both 3D and 2D added mass in a torus system?

It is important to consider both 3D and 2D added mass in a torus system because the added mass can significantly affect the natural frequency of the system. Neglecting one of these calculations can result in an inaccurate natural frequency, which can have consequences in the system's performance and stability.

## 5. How does the natural frequency of a torus system impact its stability?

The natural frequency of a torus system is directly related to its stability. If the natural frequency of the system matches the frequency of external forces, resonance can occur, resulting in large and potentially damaging oscillations. Therefore, understanding and accurately computing the natural frequency is crucial for ensuring the stability of a torus system.