Recent content by aerowenn

Good deal, thanks! There doesn't seem to be a lot on this problem, I think because it may not have many practical uses. I'm looking into the feasibility of an attitude control system for small satellites with these piezoelectric beams. But yes, the scenario you described with spring steel is...

To extend on my point. At neutral, if you take position x along the beam, the distance of x from the mounting location is simply x. However, if you take x at full deflection, according to the equation I posted above, it now has a position (x, y) or (x, w) in the case of that equation. Since x...

Thanks! What I'm trying to do is develop an equation that will give me the torque the beam exerts on object to which it is mounted in the cantilever setup. It's easy enough to make this a time dependent function by making P a sinusoid, and thus, the acceleration isn't hard to get after that...

I'm trying to model a Euler-Bernoulli beam to gather the total angular torque it will provide on a hub on which it is anchored. The beam is a cantilever, and I'm using the standard deflection equations which represent behavior to an applied force on the tip. You can solve for the force needed...

Terribly sorry about that, you are correct. All of that is equal to 0. As for the other response, I thought of that, but I'm not sure the general solution to second order differential equations applies here. Both functions are dependent on "t".

Let's say I have the equation: ##\ddot {\theta}(t)(J + y(t)^2) + 2 \dot {\theta}(t) y(t) \dot y(t) + \ddot y(t)Jn## It's the general form of an equation I'm working with to describe the motion of a beam. As you can see both ##{\theta}(t)## and y(t) are equations of t. J and Jn are just...

Ok, I'm missing something critical here, it seems like I've solved a similar problem before but I just can't get it or find examples anywhere. How would I take the equation for the beam, having it's components theta and r both with second derivatives and solve for something like angular...

I like that, thanks for the suggestion, it would make it easier to model I think. First though I need to prove mathematically that it can't be done without changing the diameter (or length of arms). I would prefer to take the equations of motion and show this, because I'm going to need them...

Well to illustrate a bit further, this research is for an attitude control mechanism for small satellites. There will be feedback control in the end, but you are correct in thinking it will not be very complex. There shouldn't be a need for complexity as long as the motion of the device is...

I see that we can't create an angular velocity without morphing the shape of the arms. But I need to be able to bring this before my advisor and explain it well. I might have simply misunderstood his reasoning behind using this paper to begin with. With the equation of motion as you posted...

I should note that (zeta) on the right hand side is equal to zero for my purpose, as there are no outside torques present. I'm trying to create one.

Sorry, I've been away. Yes, what I am working asks the question on whether or not a long term change in angular position of the hub can be created by some motion of the arms. They would move in the same direction (both CCW or CW when they move). The arms would consist of a piezoelectric...

Sorry, all that is equal to the external torque. I was trying to take this equation equal to zero and produce a rotation. But it didn't make sense.

I didn't think so. I believe I'm misreading or misunderstanding the source document. It discusses a satellite performing planar motions to defeat an external torque. Perhaps disturbance torque or something, the source doesn't really matter. Neglecting the modes of the flexible arm, the...

While I'm here, let me pose a conceptual question: If these arms were to have a motion profile in which they move much faster in one direction than the other, translating to a higher acceleration in one direction (but for a shorter time) in one direction, can this result in an overall...