Question on Dynamics of Single Degree of Freedom System

[jrm2002]

Question on Dynamics

I have been reading Structural Dynamics by Anil K. Chopra and am currently on the topic “Response of a Single Degree of Freedom System to Harmonic Excitation.

Can anyone help me with following clarifications??

1. Consider the Displacement Response Factor:
It is the ratio of dynamic deformation amplitude to static deformation amplitude. Now, when the ratio of the forcing frequency to the natural frequency of the system (Single Degree of Freedom System) is less than one (indicating a gradually varying force) then this displacement response factor is only slightly greater than one indicating that the contribution due to dynamic effects is negligible. Right?

Then when the ratio of the forcing frequency to the natural frequency of the system (Single Degree of Freedom System) is very much greater than one (indicating a rapidly varying force) then this displacement response factor approaches zero. Again there is no contribution due to dynamic effect.

Only when the ratio of the forcing frequency to the natural frequency of the system (Single Degree of Freedom System) approaches one (approaching resonance) the dynamic effect becomes dominant and damping plays a significant role? Right?

Does this mean one should worry about the dynamic response (as far as dynamic deformation is concerned) only in case of resonance (considering harmonic excitation)??

Please help (the question though may be stupid!)

 

[Navin A S]

Yes, you are correct. The dynamic response becomes significant only when the ratio of the forcing frequency to the natural frequency of the system (Single Degree of Freedom System) approaches one, which is usually referred to as resonance. At resonance, the displacement response factor will be greater than one, indicating significant contribution due to dynamic effects. Additionally, damping plays a significant role at resonance.

 

[ravenprp]

Your understanding is correct. The displacement response factor is a measure of the contribution of dynamic effects to the overall deformation of the system. When the ratio of forcing frequency to natural frequency is less than one, the dynamic effect is negligible and the displacement response factor is only slightly greater than one. This means that the system is mostly responding to the static force and the dynamic force is not significant.

Similarly, when the ratio is much greater than one, the dynamic effect is also negligible and the displacement response factor approaches zero. This indicates that the system is mostly responding to the dynamic force and the static force has little influence.

As you mentioned, when the ratio approaches one (resonance), the dynamic effect becomes dominant and damping plays a significant role. This is because at resonance, the system is most sensitive to the dynamic force and even small amounts of damping can have a significant impact on the response.

In summary, the dynamic response is only a concern in cases of resonance where the system is highly sensitive to the dynamic force. In all other cases, the static force dominates the response. I hope this helps clarify your understanding.