# MDOFs damped system: transfer function estimantion

• serbring
In summary, to calculate the transfer function of a 4 DOFs system, you need to know the system natural frequencies and the stiffness coefficients for the damping.

#### serbring

I need to calculate the transfer function of a 4 DOFs system, in particular I need to calculate the system natural frequencies. Do you know to figure out these? On books I have found how to get it in the undamped case. Thanks

I need to know how to find a transfer function for 2DOF system with damping. If anyone answers this question will be helpful to two persons...thanks, Milind.

serbring said:
I need to calculate the transfer function of a 4 DOFs system, in particular I need to calculate the system natural frequencies. Do you know to figure out these? On books I have found how to get it in the undamped case. Thanks

The answer depends on how you want to model the damping.

In the general case where you have known physical sources of damping (e.g. dashpots) in the model, you have a 4x4 quadratic eigenproblem and both the eigenvalues and vectors (mode shapes) will be complex. In other words, the motion of the different DOFs in a mode are not in phase with each other.

In practice, for small levels of damping where the physical cause of the damping is not known explicitly, you would use a modal damping model based on the undamped modes and frequencies.

AlephZero said:
The answer depends on how you want to model the damping.

In the general case where you have known physical sources of damping (e.g. dashpots) in the model, you have a 4x4 quadratic eigenproblem and both the eigenvalues and vectors (mode shapes) will be complex. In other words, the motion of the different DOFs in a mode are not in phase with each other.

In practice, for small levels of damping where the physical cause of the damping is not known explicitly, you would use a modal damping model based on the undamped modes and frequencies.

for a viscous damping on this book (pag815):

I found that from an undamped transfer function, it is necessary to substitute the stiffness coefficients (k) with k-jc, where c is the damping coefficients.

## What is a MDOFs damped system?

A MDOFs damped system refers to a multi-degree of freedom system that is subject to damping forces. This means that the system has multiple independent modes of vibration and the damping forces affect each of these modes differently.

## What is a transfer function in relation to MDOFs damped systems?

A transfer function is a mathematical representation of the relationship between the input and output of a system. In the context of MDOFs damped systems, the transfer function describes how the system responds to external forces or inputs.

## Why is it important to estimate the transfer function in MDOFs damped systems?

Estimating the transfer function allows us to understand and analyze the behavior of the system, such as its natural frequencies and damping ratios. This information is crucial for designing and controlling MDOFs damped systems in various engineering applications.

## How is the transfer function estimated in MDOFs damped systems?

The transfer function can be estimated through various methods such as experimental modal analysis, system identification techniques, or analytical modeling. These methods involve measuring the system's response to known inputs and using mathematical algorithms to estimate the transfer function.

## What are some challenges in estimating the transfer function in MDOFs damped systems?

Some challenges include dealing with noise and uncertainties in the measurements, selecting appropriate input signals, and ensuring the system is linear for accurate estimation. In addition, the complexity of MDOFs damped systems can make it challenging to accurately estimate the transfer function for all modes of vibration.