Semi-Definite (Unrestrained) Two Degree of Freedom (2DOF) Problem

[@GauravKumar-np2qm]

Wonderfully delivered lecture. Thanks for uploading this video.

[@AJ-et3vf]

Thank you very much for this sir! Very useful! I wish I saw this back in Vibrations class so I would've known that a natural frequency for one of the masses isn't weird or wrong. We were given a problem like this involving a train car. So it was definitely like this one, a semi-definite unconstrained problem.

[@donray5973]

Amazing boss

[@michacichowski6206]

Maybe I am wrong, but I see one in consequence - since omega_1^2=0, then we have two repeated roots of omega=0. Then, we should have another solution of ODE based on this root, which is same as you given, but multiplied by t. Then, this solution would show that we can have motion at constant velocity - what, according to Newton's First Law makes sense. Moreover, in first equation there are two constants in one term - C_1 and Phi_1 - and they can be simplified to one one constant. So, we still have one more equation, that could be used for another constant - maybe in the term with t. By the way, I really like this series - as I am mechanical engineer, it is perfect way of reminding a lot of very useful fundamentals, and also learn something new! (I hope that there are more materials regarding aeroelasticity). I really appreciate the effort you put in this videos. Thank you!

[@Freeball99]

What you have said is correct. Because of the repeated root, we need to multiply the solution by t to get the second solution. And, yes, this is what produces the rigid-body motion.

[@Iris0555]

Sir....what will happen if three masses are connected to this system......???

[@Freeball99]

You would end up with and extra degree of freedom, so you would now have a third mode, which would be higher frequency than the first two. Plus each of the mode shapes would look different from before because they now involve 3 masses. The first mode (the lowest frequency mode) would be symmetric and the other two modes would be anti-symmetric whereby one of the masses will move in exactly the opposite direction as the other two.

[@Iris0555]

@@Freeball99 sir is there any derivation for it.....i found this on my question paper but i didn't found solution on my book and internet..,....if u have time plz make vedio on this s topic👍thanks for the reply.......🙏

[@Freeball99]

​@@Iris0555​You can use exactly the same method I used here to derive this. The only thing that is slightly more difficult is taking the determinant of a 3x3 matrix. I can make a video on this. Also, as a correction to my previous comment, because this is a semi-definite problem, the first mode will be a rigid body mode (as before) , the 2nd mode and the 3rd mode anti-symmetric. I will likely make a video on this eventually, but I have a few others to make first.

[@Iris0555]

@@Freeball99 sir one more doubt that ......what is expression flexural vibration of beam and thanks for ur kind help it will help many of us over long period of time ❤️

[@HEG-Z]

epic vids, cheers, my lecturer for structural dynamics this semester is useless #Textbooks #youtube #Engineering