Gravitational potential energy from vertical deformation

[Lysandros]

Hi community,

I have coded an FE program in order to study the behaviour of rotating machines on an elastic structure, where I have used Timoshenko beams. Now I am calculating the total energies of the system. For the potential deformation energy U_def, it is U_def=1/2*x'*K*x, where x is the deformation vector and K the stiffness matrix. But is there a way to calculate also the gravitational potential energy due to a vertical displacement, like U_grav=m*g*h for a point mass? The mass is distributed throughout the beams, so I am not sure, what I should multiply.

Thank you, best wishes
Lysandros

 

[rb1957]

is the CG moving ? This could be the CG of the entire mass, or the CG of an element.

you are no doubt accounting for the structural dynamics too, eh?

another day in paradise, or is paradise one day closer ?

 

[Lysandros]

Thanks rb1957 for the response. I guess you are right, it would be the CG shift Δh of the entire mass, multipled by m*g. I thought it should be calculated with sort of a sum or an integral along the entire structure. For now I have taken care for the kinetic part, so yes indeed it is a structural dynamics problem.

 

[rb1957]

you can use CG (and mass) of the entire, or CG of each element (and the mass associated with each element) or any combination inbetween.

another day in paradise, or is paradise one day closer ?