Phase Lag between Force & Displacement in Forced Vibration w/ Viscosity Damping

[d9052492]

Dear all,

Can anyone explain the the phase lag between force and displacement in single degree of freedom forced vibration with viscosity damping?

The response of phase angle derived by mechanical vibration as below ( assuming force is excited harmonically) :

Phi(ω) = arctan( C*ω / ( K - M*ω^2 ) )

Where Phi is the phase angle function, C is damping, K is stiffness, M is mass, and ω is angular frequency.

From the function above we know that as C is not zero, the phase angle varies with angular frequency, but as C is set to be zero, the phase angle will be constant until K - M*ω^2 equals to zero ( the frequency also known as resonance frequency ). My question is how to explain the phase angle varies with frequency by a physical view ?

Thanks for you to think about this problem and every suggestion will be appreciated.

 

[eljose79]

The phase lag between force and displacement in single degree of freedom forced vibration with viscosity damping can be explained by considering the physical properties of the system. Viscosity damping is a type of damping that is caused by the resistance of a fluid or gas to motion. In this case, the fluid or gas is acting as a medium through which the mass is moving and therefore, it creates a drag force that is proportional to the velocity of the mass. This drag force is in opposition to the motion of the mass and therefore, it causes a phase lag between the applied force and the resulting displacement.

As the frequency of the applied force increases, the mass will experience more cycles of motion per unit time, resulting in a higher velocity and therefore, a higher drag force. This increase in drag force causes the phase angle to increase, as seen in the function you provided. On the other hand, at resonance frequency where K - M*ω^2 equals to zero, the drag force becomes zero and there is no phase lag between force and displacement.

In summary, the phase lag in single degree of freedom forced vibration with viscosity damping can be explained by the presence of a drag force that is proportional to the velocity of the mass, which causes a delay in the response of the system. I hope this helps to clarify the physical explanation behind the phase angle function. If you have any further questions, please feel free to ask. Thank you.