How Can Vibrations of a Thin Plate in Space Be Analyzed and Modeled?

[tmn]

Hi,
I'm triyng to model electric drive with a load in simulink.
The load is a thin plate of a known dimensions, axis of rotation is passes through the center of mass parallel to the lower and upper edges. The motor is direct drive and moves the plate on a known angle with a known acceleration, then stops.
The plate is elastic and start to vibrate. Important thing that the force of gravity isn't considering as the whole thing is working in Space.

My question is - how to find an amplitude, frequency and time period before vibrations will subside?
I've read some stuff about D'Alembert's principle, generalized equations of motion etc (it seems that I studied this things, but forgot completely), but still far from the solution.
I would be very grateful if you could advise how this things can be calculated and/or modeled, which methods can be used, some related readings etc, any help will be appreciated.
Thanks!

 

[Achy47]

Hello,

Thank you for reaching out about your project. Modeling electric drives with a load in Simulink can be a complex task, but with the right approach, it can be done successfully.

First, to calculate the amplitude, frequency, and time period of the vibrations, you will need to determine the natural frequency of the plate. This can be done using the equation:

f = (1/2π) * √(k/m)

Where f is the natural frequency, k is the stiffness of the plate, and m is the mass of the plate. You can also use D'Alembert's principle to calculate the natural frequency.

Once you have the natural frequency, you can use the equation:

ω = 2πf

Where ω is the angular frequency, to calculate the frequency in radians per second.

To determine the amplitude of the vibrations, you will need to consider the initial displacement and velocity of the plate when the motor starts and stops. This can be done by setting up a system of equations using the generalized equations of motion and solving for the amplitude.

As for modeling the vibrations in Simulink, you can use a transfer function block to represent the dynamics of the plate. The input to the transfer function would be the force from the motor, and the output would be the displacement of the plate. You can then use a scope block to visualize the displacement over time and determine when the vibrations subside.

I would recommend exploring more resources on modeling vibrations and dynamic systems in Simulink, such as tutorials and examples provided by MathWorks. Additionally, you can also consult with a colleague or a mentor who has experience in this area for guidance and support.

Best of luck with your project!