Response to a forced 2 DOF system

In summary, the speaker is trying to find the steady state responses of a forced 2 degree of freedom system. They have determined the equations of motion and have matrices for mass, stiffness, damping, and forcing. However, they are unable to use eigen analysis to decouple the equations and are seeking other methods, mentioning the possibility of using matrix inversion. They are using Matlab for this analysis. Another person asks about the possibility of decoupling and the speaker responds that it may not be possible due to a non-symmetric stiffness matrix.
  • #1
castwerks
2
0
I have a forced 2 degree of freedom system that I am trying to find the steady state responses to. I have determined the two equations of motions and found the [m], [k], [c], and {f} matrixes.

However when i try to use eigen analysis ( q=phi'*[m]*phi ) I am unable to uncouple the two equation of motion to allow me to solve the system as two independ. single degree of freedom systems.

I believe I have correctly set up the EOMs... what other methods can I use to solve for the x and y steady state responses.

PS i am using matlab.
 
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  • #2
What is your system? Are you sure it is possible to decouple the two equations?

-Kerry
 
  • #3
i guess it is impossible to uncouple the system (non symetric striffness matrix)... i think i figured it out by matrix inversion method
 

1. What is a forced 2 DOF (degree of freedom) system?

A forced 2 DOF system is a mechanical system that has two independent degrees of freedom and is subject to an external force or excitation. This means that the system can move in two different directions and is influenced by an external input, such as a vibrating motor or a periodic force.

2. How is the response of a forced 2 DOF system calculated?

The response of a forced 2 DOF system is typically calculated using mathematical models and equations, such as the equations of motion or transfer functions. These equations take into account the system's physical properties, external forces, and initial conditions to determine the system's response over time.

3. What factors affect the response of a forced 2 DOF system?

The response of a forced 2 DOF system can be affected by a variety of factors, including the system's natural frequencies, damping ratios, and the characteristics of the external force. Additionally, the initial conditions, such as the system's initial displacement and velocity, can also impact the response.

4. What are the different types of response in a forced 2 DOF system?

The response of a forced 2 DOF system can be classified into three main types: transient response, steady-state response, and forced response. The transient response is the initial behavior of the system before reaching a steady-state. The steady-state response is the behavior of the system once it has reached a stable equilibrium. The forced response is the response of the system to the external force or excitation.

5. How is the damping ratio of a forced 2 DOF system related to its response?

The damping ratio of a forced 2 DOF system is a measure of the system's ability to dissipate energy and resist oscillations. A higher damping ratio results in a faster decay of the system's response, while a lower damping ratio can lead to persistent oscillations. Therefore, the damping ratio can greatly influence the behavior of a forced 2 DOF system and its response to external forces.

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