Timeline for Two-directional vibration of Euler–Bernoulli beam with Lagrange multiplier
Current License: CC BY-SA 4.0
18 events
| when toggle format | what | by | license | comment | |
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| Oct 26 at 12:10 | comment | added | rnotlnglgq | I was struggling with DAE, PDE projection, Lagrange multiplier. At last I gave up. | |
| Sep 15 at 19:24 | history | edited | Michael E2 |
edited tags
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| Mar 28 at 13:20 | comment | added | Alex Trounev | @rnotlnglgq Have you any progress in this problem solution? | |
| Jan 25 at 2:44 | answer | added | Alex Trounev | timeline score: 8 | |
| Jan 18 at 8:59 | history | edited | rnotlnglgq | CC BY-SA 4.0 |
formular and text typo
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| Jan 18 at 8:57 | comment | added | rnotlnglgq | 1. The desired end time is not determinated yet. For observing some mode instability, I guess I'll need dozens of periods. | |
| Jan 18 at 8:55 | comment | added | rnotlnglgq | @xzczd 4. Yes. I'm aware that I introduced the $s$ dependence blindly, possibly be inspired by the author writing the $\lambda$ inside derivative operators, while I didn't note that obtaining (A1) implies its independence. It sounds like that $\lambda$ is independent of $s$, so it may be directly solved from given equations. I'll try to figure it out later. | |
| Jan 18 at 8:04 | comment | added | xzczd♦ | 4. …After taking a closer look at the paper, I'm afraid you've made a severe mistake: equation (3) should not be included in the system, it's used for deducing (8) and (9). And the $\lambda$ is not a function of $s$. Just read the paragraph below equation (A2). | |
| Jan 18 at 4:44 | comment | added | xzczd♦ |
1. What's the desired end time? 2. There's a typo in bcrhs, you've missed a ^2 in the end. 3. I suggest using With to rewrite the system so it'll be easier to check.
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| Jan 18 at 1:21 | history | edited | rnotlnglgq | CC BY-SA 4.0 |
fix typo
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| Jan 18 at 1:20 | comment | added | rnotlnglgq |
@AlexTrounev Thanks. I'll edit, though fixing it does not change any complaint of NDSolve.
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| Jan 18 at 1:14 | comment | added | Alex Trounev |
There is a typo in constraint, it should be (1+Derivative[0,1][u][t,s])^2+Derivative[0,1][v][t,s]^2==1 - see equation (3) in the paper.
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| Jan 18 at 1:05 | history | edited | rnotlnglgq | CC BY-SA 4.0 |
typo
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| Jan 18 at 0:23 | comment | added | rnotlnglgq | @Hugh I've uploaded two main pages of that paper. | |
| Jan 18 at 0:23 | history | edited | rnotlnglgq | CC BY-SA 4.0 |
upload parts of paper
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| Jan 18 at 0:08 | comment | added | rnotlnglgq | @Hugh 4th derivative can be found in the equation for v (where there're two nested $\partial^2$). The beam axis is horizontal, and gravity is ignored and we only care for the horizontal dimensions. There's a linear damping. The equation is a Euler-Lagrange equation of a Lagrangian. | |
| Jan 17 at 20:18 | comment | added | Hugh | The paper is behind a pay wall so I can't read it. The Bernoulli Euler beam has forth derivatives of the displacement for the PDE. I can't immediately see those. Is this a beam that has its axis horizontal? Have you also got damping in there? Is your equation for the Lagrangian or the equation of motion? | |
| Jan 17 at 17:41 | history | asked | rnotlnglgq | CC BY-SA 4.0 |