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Living system ad gdl

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salvatore87

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Hello everyone I am a mechanical engineering student, I am not new to the forum.I would like to ask you a question concerning the resolution of a vibrating system to a degree of freedom. the system is subject to the action of an exciting force that varies in the same time f=fmax*sin(wt), agent in the baricentro of the disk. There are also a spring and a dampener always connected to the disk, and a dotted mass that belongs to the body of the left constituted by two perpendicular rods between them and bound to a cart.the problem requires to calculate the elastic constant of the spring(k) p.s in the images have been reported the system and body in the deformed configuration.
 

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you have a beautiful toasted grana with in the middle of the pendulum...the linearization etc etc.
If you use the defomated static equlibrium to determine the boundary conditions you have all the forces at stake.

you have to write all the energies and make the equation of motion. then from there go on.

It's been a while since I've been solving these beautiful things.
 
if I impose the balance of the moments regarding the cart I find myself with: the contribution given by the force weight and the two contributions given by the components long x and y of the reaction bind in the hinge b, that sum are equal to the moment of the forces of inertia (equal to the moment of inertia of the mass dots regarding d per omega) plus the term (g-d)^m*a(d) where the acceleration of the lengthy is that of the cart. In this way I find myself with two unknowns i.e. the two components of the reaction in the hinge b. at this point I impose the balance to the translation from which I find that the fx in b is nothing. but this turns out to be wrong from the results I have. in fact in the resolution of the problem it turns out that the component fx is equal to mg*sen(fi)*cos (fi) while the fy=mg*sen (fi) where fi represents the angle of rotation of the body, therefore for small spins cos (fi)=1 while sen(fi)=fi for this fy=0 and not fx.vor balance I would understand how this result is in contradiction with that imposed
 
and just because you have a pendulum that breaks the boxes. for small oscillations you can linearize while for large oscillations the components become substantially important. if the pendulum does 20° is no smaller oscillation.
 
no but the quota you see on the drawing is not the real one was only to highlight the angle, the problem that I am studying is valid for small oscillations
 
Sorry but perhaps I didn't explain well.The problem is not to find the equation of the pendulum motion, but the binding reactions in correspondence of the zipper that connects the two rods, perpendicular between always, to the disk.the case you exposed me considers a simple pendulum without identifying the reactions.
 
salvatore87 said:
Sorry but maybe I didn't explain well.The problem is not to find the equation of the pendulum motion, but the binding reactions in correspondence of the zipper that connects the two rods, perpendicular between always, to the disk.the case you exposed me considers a simple pendulum without identifying the reactions.
Click to expand...
to find the reactions to the hinge if you make them absolute x and y is an account, if instead the terna is rotating, ie solidarity with the reference system of the two rods is different.

but then they are not two fast rods is only one l-shaped rod, so you don't have to break anything in the hinge.

or find all the balance on the right of the auctions and put the result on the rod and calculate the whole pendulum with the reactions. It is normal that you find sen(fi) and cos(fi).

but the cinematic nexes you put them all? you can have more variables and with the cinematic nexes tie them and find everything in one variable.
 
The fact is that I did not understand when considering the absolute terna or the rotating one, as regards the cinematic nexes is not a problem, I have already found the relationship that binds to the teta of the disc
 
I have always found the balances of the bodies of the deformed bodies considering the absolute terna and decomposing the reactions long x and y but in this case I do not understand why it is not okay.in fact the reaction in b is equal to mg*sen(fi)
 
salvatore87 said:
The fact is that I did not understand when considering the absolute terna or the rotating one, as regards the cinematic nexes is not a problem, I have already found the relationship that binds to the teta of the disc
Click to expand...
absolute or rotating if not imposed by the problem choose you as comfortable. If you want to analyze sitting on the terna or sitting watching all the cinema. The important thing is that everything is homogeneous.

obvious that to pass from the fixed to the relative one and since there is the rotation of half...there is the theorem to pass from the two tarps and usually explain it in rational mechanics. you are already doing dynamics and control of SMS or other upper course, so go peek there.
 
no for that there is no problem I always use the fixed terna but I do not find myself with the results
 
and then the strange thing is that if the long force x is equal to mg*sen(fi) for the balance to the translation would not be balanced by any force since it is the weight force, that the reaction of the cart is directed along y. how does this explain?
 
I'm thinking about it, but I don't think anything useful. It's actually weird. you have to try to take white sheet and resurrect us again from above
 
If I equal mg sen (fi) to the result in b I would find that the balance of moments would be satisfied however the balance to the translation no. unless the component of the weight sen(fi) force is uncompromising, but all this seems absurd, since the weight force does not have long components x even if the configuration is deformed.
 

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