# Calculating the natural frequency of a piping system

• studentoftheg
In summary, the conversation discusses calculating the natural frequency of a piping system using a formula from a design code. The formula includes terms such as the effective axial force, Young's modulus, mass, span length, and critical buckling load. The conversation also mentions the possibility of a negative natural frequency and the interpretation of an imaginary frequency in the context of the formula's assumptions. It is suggested that the negative frequency may be due to the conservative nature of the effective force and that there may be additional factors to consider.

#### studentoftheg

I'm calculating the natural frequency of a piping system that is spanning between two points, the formula is the square route of various terms, including the effective axial force in the piping. This is taken from a design code, see below:

f = C * SQRT[(E.I/M.L^4)(1+Seff/Pcr+C.(d/D)^2]

C = Constant dependant on boundary conditions of span
E = Youngs modulus
I = Second moment of area (piping)
M = Mass
L = Span length
Seff = Axial force in piping
d = deflection
D = piping diameter

The axial force in the piping is negative, due to the temperature and pressure, and I'm trying to perform a conservative calculation assuming the piping is fully restrained. This results in a negative term in the square root. Is it possible to have a negative natural frequency?

The natural frequency is coming out as -0.5 i Hz (i being sqrt(-1)).

Any help or guidance appreciated. Thanks

Just some quick observations:

I would say that the interpretation of the result probably depends on the assumptions made when deriving that forumla.

It could be that an imaginary frequency could indicate an overdamped system which does not oscillate, but instead decays towards its equilibrium state (or diverges unphysically away from the equilibrium state, depending on the sign). It may not be possible to say just from looking at that formula.

Either you have made a mistake, or you need to study the assumptions of the derivation of that formula to understand what the imaginary frequency means in your context.

yeah I've been doing some reading over night, i think it might be due to the effective force being overly conservative. there will be 'feed in' to it, which will reduce the compressive force. thanks

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

The natural frequency of a piping system refers to the frequency at which the system would naturally vibrate if it were to be disturbed. This frequency is determined by the physical characteristics of the piping system, such as its length, material, and supports.

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

The natural frequency of a piping system can be calculated using the equation f = (1/2π) * √(K/M), where f is the natural frequency, K is the stiffness of the system, and M is the mass of the system. This equation is based on the principles of mechanical resonance.

## 3. What factors affect the natural frequency of a piping system?

The natural frequency of a piping system is primarily affected by its length and material. A longer and more rigid pipe will have a higher natural frequency, while a shorter and more flexible pipe will have a lower natural frequency. Other factors that can affect the natural frequency include the type of supports used and any external forces acting on the system.

## 4. Why is it important to calculate the natural frequency of a piping system?

Calculating the natural frequency of a piping system is important because it helps to ensure the system's stability and reliability. If the system's natural frequency is close to the frequency of any external forces acting on it, resonance can occur, leading to excessive and potentially damaging vibrations. By calculating the natural frequency, engineers can design the system to avoid resonance and prevent potential failures.

## 5. Can the natural frequency of a piping system be changed?

Yes, the natural frequency of a piping system can be changed by altering its physical characteristics. For example, the natural frequency can be increased by increasing the stiffness of the system or decreasing its mass. It can also be changed by adjusting the supports or adding damping materials to the system.