Impact considerations

[Mishal0488]

TL;DR

Impact considerations with differential equations with event handling

Hi guys

I am not going to go into detail with the problem at hand just an outline. Let’s assume a spring mass system where the system acts in the vertical. The equations are simple to derive and event handling on Julia can help with decoupling the system where the mass and spring are no longer in contact. At that point the mass will move vertically up and then come down to collide with the spring again.

When the collision occurs, do extra co desperations need to be defined to account for the impact forces? My reason for the question is that in an FEA environment I do t believe anything further is considered

 

[berkeman]

Is the spring massless?

 

[A.T.]

When the collision occurs, do extra co desperations need to be defined to account for the impact forces?

What do you mean by 'impact forces'? There is only one contact force between spring and mass.

How that contact force looks like on impact depends on whether the spring is massless or has inertia. With inertia you get longitudal waves propagating in the spring.

 

[Mishal0488]

Spring is massless. By impact forces I am implying moment the spring and mass connect again, the mass will have an acceleration which will obviously cause an impulse in the system. Should that vbs taken care naturally by the direction equations or does it need to have special considerations

 

[jbriggs444]

Spring is massless. By impact forces I am implying moment the spring and mass connect again, the mass will have an acceleration which will obviously cause an impulse in the system.

Why do you think there will be an impulse? We are talking about an interaction between a mass and a massless spring. There is no instantaneous change of momentum.

Depending on the exact arrangement, there may be an instantaneous change in force. Or an instantaneous change in the rate of change of force.

Consider, for example, a captive spring that is under compression but is restrained against expansion. Suppose the spring is held upright under a falling mass. The mass arrives at the position of the spring. Prior to its arrival, it is in free fall, accelerating downward due to gravity. After arrival, the mass is deflecting the spring and is immediately subject to a finite and increasing non-zero supporting force from the spring. The vertical acceleration of the mass has instantly changed. This is a point of discontinuity for the differential equations describing the motion.

Or consider a spring that is relaxed. It is not restrained against expansion. This spring is held upright under a falling mass. The mass arrives at the position of the spring. Prior to its arrival, it is in free fall, accelerating downward due to gravity. After arrival, the mass is deflecting the spring and is immediately subject to a zero but increasing supporting force from the spring. The vertical acceleration of the mass has not changed. However, the rate of change of its vertical acceleration has instantly changed. This is a point of discontinuity for the differential equations describing the motion.