How can I solve a dynamic vibration problem?

  • Thread starter Thread starter deuel18
  • Start date Start date
  • Tags Tags
    Dynamic Vibration
Click For Summary
SUMMARY

The discussion focuses on solving a dynamic vibration problem involving a suspended bar and its effective inertia and stiffness. Participants emphasize the importance of considering the weight of the bar and the preload on the spring to derive the equation of motion accurately. The consensus is that, when properly accounted for, the preload and weight terms will cancel out, simplifying the analysis for small displacements from equilibrium. The use of the sum of moments method at pivot A is also highlighted as a valid approach to establish equilibrium conditions.

PREREQUISITES
  • Understanding of dynamic systems and vibrations
  • Familiarity with equations of motion in mechanical systems
  • Knowledge of effective inertia and effective stiffness concepts
  • Experience with static equilibrium and moment calculations
NEXT STEPS
  • Study the derivation of equations of motion for dynamic systems
  • Learn about effective stiffness and inertia in mechanical vibrations
  • Explore the sum of moments method for analyzing static equilibrium
  • Investigate preload effects in spring systems and their impact on dynamics
USEFUL FOR

Mechanical engineers, students studying dynamics, and anyone involved in analyzing vibration problems in mechanical systems will benefit from this discussion.

deuel18
Messages
34
Reaction score
1
Thread moved from the technical forums, so no Homework Template is shown
Hello. I need some help for my HW. I've been trying this particular problem but I don't know if I am on the right track. The problem and my progress in answering the problem is down below.
IMAG0366%7E2.jpg

IMAG0368.jpg
 
Physics news on Phys.org
I cannot read your work (I'm an old man with poor eyesight), but this is not a hard problem. Simply write the equation of motion and pull out the effective inertia and the effective stiffness from there.
 
Dr.D said:
I cannot read your work (I'm an old man with poor eyesight), but this is not a hard problem. Simply write the equation of motion and pull out the effective inertia and the effective stiffness from there.
I see. I guess my specific question is, if the bar as shown in number 7 is placed as is, should i take into account the weight? Like a suspended mass with spring, the weight is not considered. Is the same applies for this particular problem?
 
For your own learning, you should definitely take the weight into account. The implication seems to be that the bar is in equilibrium in the horizontal position shown, so that means that the weight is supported on compression in the spring. Determine the amount of preload on the spring, and then take that and the weight of the bar into account. If done properly, the prelaod and the weight terms should all cancel, leaving you with an equation for small displacements away from equilibrium.
 
Dr.D said:
For your own learning, you should definitely take the weight into account. The implication seems to be that the bar is in equilibrium in the horizontal position shown, so that means that the weight is supported on compression in the spring. Determine the amount of preload on the spring, and then take that and the weight of the bar into account. If done properly, the prelaod and the weight terms should all cancel, leaving you with an equation for small displacements away from equilibrium.
I got those in mind but if I choose sum of the moment method at pivot A, it gives mg(L/2) - k(delta)(L) - k(y)(L) = I(alpha). Does that mean mg(L/2) is equal to k(delta)(L)?
 
Well, what is the condition for equilibrium?
 
Ah i see. So the equilibrium cancels the mg with the kdelta.
 
Sounds like you've got it.
 
I do. I was able to do it on other problems. I am just having hard time crunching the numbers right. So i looked for guidance.
 

Similar threads

Beam boundary condition problem
  • · Replies 12 ·
Replies
12
Views
3K
Dynamics of Machines - Forced Vibration
  • · Replies 2 ·
Replies
2
Views
1K
Engineering How to Combine Signals for High Dynamic Range?
  • · Replies 1 ·
Replies
1
Views
2K
Engineering Bucket supported by wood frame and tension wire
  • · Replies 1 ·
Replies
1
Views
2K
Where can I study this type of problem? (fluid dynamics)
  • · Replies 1 ·
Replies
1
Views
1K
Spec'ing the power of heater for an atypical heat exchanger problem
  • · Replies 22 ·
Replies
22
Views
4K
Engineering Dynamics of Rigid Bodies: The Concept of Law of Gravitation
  • · Replies 1 ·
Replies
1
Views
2K
Engineering Struggling with a Structural Analysis Problem?
  • · Replies 1 ·
Replies
1
Views
2K
How to set up this problem with driven torsional oscillator?
  • · Replies 5 ·
Replies
5
Views
1K
Engineering Dynamics: relative-motion analysis using rotating axis
  • · Replies 1 ·
Replies
1
Views
2K