Forced vibration with decreasing force amplitude

• abrandt
In summary, the problem at hand deals with a mining skip that experiences forced vibration due to the impact of material being emptied. The force of impact decreases each time due to the decreasing mass of material. This is a general transient dynamics problem and can be solved by finding the response to an impulsive load and using linear superposition to find the response to a series of impulses. A "worst case" analysis may also be necessary due to the randomness of the impacts in real life. As an engineering student working on a project with an external company, you may need to consider this approach for solving the problem.

abrandt

I'm working on a problem that has forced vibration. The force, every time it is applied, is less than the previous impact. For clarity, the problem is dealing with a mining skip that is emptying. The inside of the skip is separated in sections using ribs but the top blocks still exert a force on the lower blocks. The impact of the material hitting the bottom of the skip (a 50 degree angle) is causing the skip to vibrate. This impact happens at distinct intervals with the time between impacts remaining roughly constant. The impact force is decreasing due to the decreasing total mass of the material inside the skip. I was wondering if you could point me in the right direction. Most of the problems i have dealt with deal specifically with a periodic force that is constant each time it is applied. I thought about adding a dampening force to diminish the force each time it is applied but wouldn't that just act to dampen the free vibration component? For background i am an engineering student who is working on a project with an external company.

You are right that the usual type of "forced response" analysis (modeled in the frequency domain) is about constant-amplitude response to a steady force.

Your situation seems more like a general transient dynamics problem. You could find the response of the system to an impulsive load (i.e. one impact). The response will be the sum of exponentially decaying vibrations in each of the structural modes that are excited. It's not obvious from your description whether the response would be mainly one vibration mode, or a combination of several modes.

If the system is linear, you can then find the response to a series of impulses of different sizes by linear superposition. That would be straightforward to do numerically, even with a spreadsheet if you don't want to do any programming.

You may want to do some sort of "worst case" analysis here, varying the times of the impulses in your model, since I'm guessing that what happens in real life is partly random.

1. What is forced vibration with decreasing force amplitude?

Forced vibration with decreasing force amplitude is a phenomenon where a system experiences vibrations due to an external force, but the amplitude of the force decreases over time. This can occur in various systems such as mechanical, electrical, and structural systems.

2. What causes forced vibration with decreasing force amplitude?

Forced vibration with decreasing force amplitude can be caused by various factors such as friction, damping, or energy dissipation within the system. These factors can gradually decrease the amplitude of the external force and lead to forced vibration with decreasing force amplitude.

3. How does forced vibration with decreasing force amplitude affect a system?

Forced vibration with decreasing force amplitude can have different effects on a system depending on its characteristics. In some cases, it can cause the system to reach a steady-state vibration, while in others it can lead to system failure or damage. It is important to understand the properties of the system to predict the effects of forced vibration with decreasing force amplitude.

4. Can forced vibration with decreasing force amplitude be controlled?

Yes, forced vibration with decreasing force amplitude can be controlled to some extent by adjusting the properties of the system, such as damping and stiffness. Additionally, using vibration isolation techniques can also reduce the effects of forced vibration with decreasing force amplitude on the system.

5. How is forced vibration with decreasing force amplitude studied?

Forced vibration with decreasing force amplitude is studied through various techniques such as mathematical modeling, experimental testing, and simulation. These methods help to understand the behavior of the system and predict its response to forced vibration with decreasing force amplitude in different scenarios.