4 жыл бұрын
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@oa213 2 күн бұрын
Thank you for the series. It was very helpful for studying dynamics 2 :)
@aztatzirubioisaac8863 2 ай бұрын
Tks for sharing this course. :)
@nikolaskatsantonis827 2 ай бұрын
I hope to get 11/10 in 2 months, amazing videos!
@muhammadyasir7671 4 ай бұрын
Where does Ic=1/2mR^2 came from for homogeneous mass for the disc?
@erayyildiz9562 4 ай бұрын
I very like these introductory lectures before the detailed lectures of each different concepts. Great way to motivate the students, and make the concept more intuitive during learning process. Thank you.
@diegocastro1666 5 ай бұрын
Thank you so much
@lfolfollfolfol5976 5 ай бұрын
hello is this beam subjected to a force or not if yes give me the value of this force
@PereswindsurfchannelIT 6 ай бұрын
Great video! Thank you for explanation! Anyway, I didn't understand why the fourth deivative of Vi is canceled. Shouldn't it be replace with a terms that in some steps gives you the modal mass? Or maybe I just missed some assumptions. Sorry I'm trying to figure out the meeaning of modal mass on the beam
@cgr3955 6 ай бұрын
thanks, very clearly explained:)
@trueislam2170 6 ай бұрын
Valuable videos🎉🎉
@trueislam2170 7 ай бұрын
Great... Very helpful ❤❤
@liamthedevastator 7 ай бұрын
Thank you for sharing your knowledge on this subject! The explanations are clear and concise and very cleanly illustrated on the paper.
@alibaashi3956 7 ай бұрын
This is the best vedio I have seen on KZfaq. Thank you for your demonstration and thank you for your time👏
@HayatMJaber 8 ай бұрын
can you explain more the chain rule of calculus in this case please?
@menglimarrero4296 8 ай бұрын
Natural frequency isnt it 1 over time? , 1/t=f
@modernbabylonacademy8788 8 ай бұрын
Can I know the program that u use to write like this plz
@anglophilemurad 9 ай бұрын
Which book do you follow sir
@anglophilemurad 9 ай бұрын
Which book do you follow
@Marco-px5nf 9 ай бұрын
Hi Juran, Heel duidelijk uitgelegd. Top
@alifarshad-wu8wl 10 ай бұрын
Tanks a lot sir for making this course public. Is there any possible way to make the lecture notes available too? It can be so helpful to review the contents...
@user-sj1nx6pl1v 10 ай бұрын
If the masses and sping constants are same in 1st problem, how the expression of kinetic and potential energy will vary? Please answer
@fsgf902 11 ай бұрын
Hi! Prof. Schilder, I am glad to learn about your mechanic vibration lesson, these lesson hello me a lot. to reduce the vibration amplitude of a centrifugal fan whose motor support bracket like a spider, I optimize the structure of the spider, which is like a cantilever system. I change the leg of spider structure from one beam to a trusswork, and the vibration amplitude was reduced. and I can't understand the relationship between the stability of structure and vibration amplitude. could you share me some know-how about this issue? may you have a nice day.
@songotenks7531 11 ай бұрын
thank you for all the hard work you have put in.
@gregorytierney3274 Жыл бұрын
Do you have MATLAB code to solve this?
@motivecrew138 Жыл бұрын
Life saver
@tomasgustainis6607 Жыл бұрын
Thank you for the videos. They were very enjoyable and clear.
@gijs6560 Жыл бұрын
at 9:35 , why do you say that B^4 = (n^4pi^2/L^4) _times_ rhoA ..., should it not be *equal* to rhoA ...?
@JurnanSchilder Жыл бұрын
You are absolutely right!
@gijs6560 Жыл бұрын
So, if I understand correctly, when integrating the delta function from 0 to L, we can always say it is equal to 1? Is that like saying you integrate from 0 to (L- to L+) as it is such a small piece of L? I am confused, as when evaluating the integral you get delta(L - L) - delta (0 - L) = 0 - delta (-L) , where -delta(-L) = infinite.
@gijs6560 Жыл бұрын
and if that is the case, then I don't quite understand what's the use of this delta function..
@gijs6560 Жыл бұрын
It causes the sin integral to stay a sin, and I do not get why
@gijs6560 Жыл бұрын
If i is j, why still write down Vj Vi, and not just Vi^2 or something like that?
@noahsinnema3348 Жыл бұрын
What a ride! This whole course had its highs and its twits and turns, with me not getting it, but in the end the whole plot fell together wonderfully. Jokes aside, many thanks Professor Schilder for these lectures, a great series!
@DeadbeatJeff Жыл бұрын
(Possibly stupid question) Shouldn't there be some sort of coefficients in from of each term U(x)\eta(t) so that the sum converges? I'm modeling some vibrations in a beam in MATLAB, and, without these coefficients in front, the first 10 terms appear not to capture ~99% of the variability, which, I would think the first 4 or 5 terms would ordinarily do so. TIA
@gijs6560 Жыл бұрын
So for X1, do you multiply the function by (1/m) / (1/m^2)?
@DeadbeatJeff Жыл бұрын
Wonderful video series, sir! Thank you so much for your lovely exposition.
@gijs6560 Жыл бұрын
Do we just assume its an exponential? So choose e^(st) every time? or because it would be logical is the bullet was to slow down exponentially?
@JurnanSchilder Жыл бұрын
So, in fact I show in this video that for a 1st order linear ODE with constant coefficients we van DERIVE that the solution is an e-power. This leads us to TRY and e-power for any other linear ODE with constant coefficients as well. If we do try this, we see that this will always work indeed.
@DeadbeatJeff Жыл бұрын
1) It looks like you are using the fact that the "differential equation operator" is self-adjoint (Sturm-Liouville theory), so eigenvectors corresponding to distinct eigenvalues are orthogonal (really a consequence of The Spectral Theorem) kzfaq.info/get/bejne/Z5iUZJinrpuWkmw.html 2) "The Gram-Schmidt process is A Good Thing" (TM).
@JurnanSchilder Жыл бұрын
You are absolutely right Jeff and thanks for sharing the interesting link. Since this lecture series is intended for mechanical engineering students, I try to keep the mathematical background to a minimum. At our university, a math course on Theory of PDEs is offered only in the master phase and this is mentioned there.
@DeadbeatJeff Жыл бұрын
[OT] How, if at all, can all of this be simplified/streamlined by Laplace/Fourier transforms?
@JurnanSchilder Жыл бұрын
Thanks for all your nice comments Jeff. The equations of motion of a vibrating string, bar and shaft are in fact all examples of the Wave Equation. The general solution can be written as a Fourier series in space. So in this case, trying a Fourier series will not just be a good approximation, but actually result in the exact solution as presented here. For other continuous problems though, like a vibrating beam, the equation of motion is fourth order in space. Using a Fourier series as general solution will not be able to satisfy all boundary conditions and therefore only approximate the solution. The general solution contains a sine/cosine combo and a sinh/cosh combo. You will see this in the videos about vibrating bars. I hope that once you have arrived there, this will become clear. If not, please ask me again at that time.
@DeadbeatJeff Жыл бұрын
@@JurnanSchilder Very good; that absolutely and thoroughly answers the question - thank you.
@DeadbeatJeff Жыл бұрын
1) Super-great video series! Thank you so much. 2) I guess I'm used to seeing k as the symbol for the wave number, not \beta, but, if this is common usage, I'll get used to it.
@JurnanSchilder Жыл бұрын
Indeed k is also used a lot. Since we use k also for a spring's stiffness, we sometimes use \beta instead. Feel free to change it to k if you prefer it though!
@DeadbeatJeff Жыл бұрын
@@JurnanSchilder Right, spring stiffness; I just wasn't thinking - keep your notation.
@saeedmekdachi4300 Жыл бұрын
watching this 3 years after you posted them and I have to say they are the best I've seen. please consider doing videos on other subjects. Thanks a lot!
@behzadtaghipour6394 Жыл бұрын
thanks a lot! great!
@behzadtaghipour6394 Жыл бұрын
thanks that is very helpful, really appriciate it
@behzadtaghipour6394 Жыл бұрын
thanks a lot
@carbonarameca414 Жыл бұрын
Great Lectuve, thank you, but why do you take the second Partial derivative of v(x,t) with respect to t, for the acceleration term ? I would have take the total second derivative of v(x,t) with respect to t, for the acceleration, and develop this term using the chain rule. Would i find the same result if i do this ? I do not know if my question/probleme is clear.
@VikiJoker1924 Жыл бұрын
I didn't get how the solution part works at 10:26 How did the quadratic eqn with s^2 + ... gets multiplied to the exponent and equated?
@robbybos1999 Жыл бұрын
It is an homogeneous second ODE. Using x(t)= exp(st) then differentiate twice gives x(t)' = s*exp(st) and x(t)"= s^2*exp(st). Substituting this in x" + d/m*x' + k/m*x=0 gives --> s^2*exp(st) + d/m*(s*exp(st)) + k/m*exp(st) = 0 . Now we take exp(st) common as its a common factor in all terms. This results in (s^2 + d/m*s + k/m)*exp(st). The natural frequency is given as wn=sqrt(k/m) --> wn^2=k/m. Damping factor is given as J=d/2mwn. rewrite this in d/m gives d/m=2Jwn. Substituting wn^2 and d/m in (s^2 + d/m*s + k/m)*exp(st) gives --> (s^2 +2JwnS + wn^2)exp(st)=0. As exp(st) will never reach zero, the terms in the brackets must equal 0 in order for the equation to be true. I hope my explanations helps and makes sense:)
@VikiJoker1924 Жыл бұрын
@@robbybos1999 wow, got it now! thanks so much buddy! That was a very clear explanation!
@VikiJoker1924 Жыл бұрын
How are the forces on left side for mass 2 acting towards the mass? Shouldn't it be the other way?
@VikiJoker1924 Жыл бұрын
Is it because when M1 moves to the right, it compresses the k2 and d2, which causes the spring and damper to exert a force on both the sides, ie force on the left and right?
@jakobsime4190 4 ай бұрын
Right??? Thats what makes sense to me.
@VikiJoker1924 Жыл бұрын
why do we use x,y, and theta rather than x,y,z?
@JurnanSchilder Жыл бұрын
This course is restricted to 2D problems.
@VikiJoker1924 Жыл бұрын
@@JurnanSchilder I understand, sir. Thanks for the reply!
@cbkt35 Жыл бұрын
you are the goat. THE GOAT.
@sethmiano4019 Жыл бұрын
This lecture series is so good for anyone student of vibration study! It lays out and teach the first principles and foundations required then moves on towards its physical applications.
@onelenqwena7135 Жыл бұрын
Do you release your notes online?
@lindachen685 Жыл бұрын
Excelent thank you very much!
@lindachen685 Жыл бұрын
Thank you very much God bless you😊