How can I solve a dynamic vibration problem?

In summary, if you want to find the effective inertia and effective stiffness for a system in equilibrium, you should determine the condition for equilibrium and then use the effective inertia and effective stiffness from that.
  • #1
deuel18
34
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.
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  • #2
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.
 
  • #3
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?
 
  • #4
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.
 
  • #5
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)?
 
  • #6
Well, what is the condition for equilibrium?
 
  • #7
Ah i see. So the equilibrium cancels the mg with the kdelta.
 
  • #8
Sounds like you've got it.
 
  • #9
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.
 

1. What is a dynamic vibration problem?

A dynamic vibration problem is a phenomenon in which an object or structure experiences vibrations or oscillations due to external forces or disturbances. These vibrations can be harmful and affect the performance or stability of the object.

2. What are the causes of dynamic vibration problems?

The main causes of dynamic vibration problems include unbalanced forces, resonance, and external disturbances such as wind or earthquakes. These forces can cause the object to vibrate at its natural frequency, leading to potential damage.

3. How can dynamic vibration problems be prevented?

Dynamic vibration problems can be prevented by using proper design and engineering techniques. This may include using materials with high damping properties, implementing vibration isolation methods, and avoiding resonance conditions.

4. What are the consequences of ignoring dynamic vibration problems?

Ignoring dynamic vibration problems can result in structural damage, reduced performance, and even safety hazards. The vibrations can also cause fatigue and wear on the object, leading to costly repairs or replacements.

5. How can dynamic vibration problems be solved?

To solve dynamic vibration problems, it is important to first identify the root cause. This may involve conducting vibration analysis and using tools such as finite element analysis. Once the cause is determined, appropriate measures can be taken to mitigate or eliminate the vibrations.

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