Strain energy on impact 1

• Friday at 8:32 PM

• #2

rb1957

Aerospace

Apr 15, 2005

15,994

what is the stiffness of the "ground" ?

if it is "rigid" then the force is "infinite". the stiffness controls the duration of the impact, how the bar decelerates. If the ground is infinitely rigid, then the impact is "instantaneous".

If you know the force then you can calculate the stress ... no?

 

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• Friday at 9:19 PM

• #3

Ron247

Structural

Jan 18, 2019

1,146

Is this a homework problem?

 

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• Saturday at 1:04 AM

• #4

GregLocock

Automotive

Apr 10, 2001

23,764

Conceptually think of the bar as a series of springs and masses. As the mass hits the ground the spring above it compresses, and so on and so forth up the chain of springs and masses.

As you can see there's a series of compression and rarefaction waves set up in the system.

It looks like it would be fairly easy to set up a differential equation to describe the continuous system. Whether it is analytically solvable is another matter (I am confident it is). You need E as well.

It is almost directly equivalent to the axial oscillation of a column of air.

 

Last edited: Saturday at 1:17 AM

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• Saturday at 7:13 AM

• Thread starter
• #5

Y

yashsinghla

Mechanical

Apr 25, 2025

3

rb1957 said:

what is the stiffness of the "ground" ?

if it is "rigid" then the force is "infinite". the stiffness controls the duration of the impact, how the bar decelerates. If the ground is infinitely rigid, then the impact is "instantaneous".

If you know the force then you can calculate the stress ... no?

Click to expand...

What's the difference between the ground being rigid and infinitely rigid?

 

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• Saturday at 7:27 AM

• #6

goutam_freelance

Mechanical

Jan 25, 2003

592

Assuming
1. Rigid floor
2 Elastic collision
3. Instantaneous propagation of stress (infinite speed of sound)

 

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• Saturday at 11:17 PM

• #7

GregLocock

Automotive

Apr 10, 2001

23,764

3 is a very big spherical cow. And no, that is a very horrible approximation, you've assumed it behaves like a point mass on a spring the real issue is that it is a continuous system.

 

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• Monday at 8:34 AM

• #8

goutam_freelance

Mechanical

Jan 25, 2003

592

GregLocock said:

3 is a very big spherical cow

Click to expand...

I agree. But such a theoretical analysis will be time-consuming, and I would prefer ANSYS or similar software to simulate the transients.

However, I believe that the above formula will give the order of magnitude of F.

 

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• Monday at 8:54 AM

• #9

3DDave

Aerospace

May 23, 2013

11,249

Maybe this: https://calcdevice.com/impact-of-bar-on-rigid-surface-i121.html

 

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• Monday at 9:14 AM

• Thread starter
• #10

Y

yashsinghla

Mechanical

Apr 25, 2025

3

3DDave said:

Maybe this: https://calcdevice.com/impact-of-bar-on-rigid-surface-i121.html

Click to expand...

Is there any explanation for the formulas used in the above calculator?

 

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• Yesterday at 1:19 AM

• #11

GregLocock

Automotive

Apr 10, 2001

23,764

Well yes, in your dynamics textbook or lecture notes.

Here's a long article that manages to avoid using differential equations, but only because he uses FEA to derive the correct equivalent mass.

Anatomy of a Mechanical Impact - Part 1 - Flexible Rod Impacting a Rigid Surface

Explore and verify the relationship between hand calculations and the time-dependent response of a object being dropped on to a rigid surface and what deflections and stresses occur during that impact period.

blog.ozeninc.com

 

Last edited: Yesterday at 2:19 AM

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• Yesterday at 7:59 AM

1
• #12

GregLocock

Automotive

Apr 10, 2001

23,764

So I've got 5 spring/masses in series, dropped from 1m.




SDOF approximation using Gautam's equation
m1dof = 1.0103
k1dof = 3.9898e+08
freq1dof = 3162.8
h1dof = 1.0000
Force1dof = 8.8931e+04
max force at ground from 5dof model
ans = 9.7014e+04

So this ties up reasonably well with the FEA result of 88915 N, although the SDOF calculation is closer this time.

 

Last edited: Yesterday at 8:18 AM

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