Mechanical Engineering
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# Energy level of multi-degree of freedom system

## Question

hi
i want to calculate the energy level of 2-degree of freedom system like sth that i attacked. i read many things but i don't find any thing that say the point clearly!

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Looks to me like the kinetic energy of your systems is

T=(1/2)*m1*xdot^2+(1/2)*m2*ydot^2

and the potential energy is

V=(1/2)*K1*(x-xc)^2+(1/2)*K2*(y-x)^2+(1/2)*K3*y^2

if we understand that all springs are relaxed when xc=x=y=0.

All of this raises a question for me. Why do you want this if you did not know how to develop it in the first place?

DrD

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Posted (edited)
12 hours ago, DrD said:

Looks to me like the kinetic energy of your systems is

T=(1/2)*m1*xdot^2+(1/2)*m2*ydot^2﻿﻿

and the potential energy is

V=(1/2)*K1*(x-xc)^2+(1/2)*K2*(y-x)^2+(1/2)*K3*y^2

if we understand that all springs are relaxed when xc=x﻿=y=0.

All of this raises a question for ﻿me. Why do you want this if you did not know how to develop it in th﻿e first place? ﻿

DrD

thank you for helping.

in fact i know this type of calculating energy and I'm sorry for didn't say it. actually it wasn't in my mind at the time.

this is a Nonlinear Energy Sink (NES) system and we have K4 as nonlinear spring. in the papers someone use Runge-Kutta algorithm to obtain the energy level of the system and the result is in Integral form that is close to the form that you said. (I attached the example!)

after all i,m not professional in vibration and I maybe don't understand  sth or be in a wrong way!!

Edited by ash7
i forget the pic

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Runge-Kutta is for solving differential equations. All that is needed here is simple quadrature, such as the trapezoidal rule.

DrD

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