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Include spring in Modal Analysis

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Hi,

I have a complicated model on hand that includes a flexsure bearing. The bearing actually works a torsional spring, that is, has stiffness in rotational direction.

Since the model is too complicated, I would like to simplify the bearing part to reduce the size of mesh result. Right now I am thinking of model it as a very simple geometry (like a beam or a set of beams) and assign them with translational and torsional stiffness character that matches the original bearing.

I am new to COMSOL, so I really don't know whether it is feasible in COMSOL. I would appreciate if anyone could offer me some ideas. Thank you.

6 Replies Last Post 25.03.2010, 23:44 GMT-4
Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 25.03.2010, 03:05 GMT-4
Hi

Feasible certainly, but its slightly tricky, you must write your eqations yourself and for rotations its the most complex.

Take a look at the hierarchy of structural elements in V3.5a: you have trusses (y,v,w but no rotations), beams (u,v,w,thx,thy,thz), shells (u,v,w,thx,thy,thz), and solids (u,v,w,p but no rotations).

Trusses can only take axial forces, beams can, in addition to axial forces, bend with moments (hence the rotation), shells the same, while solids take all cases, but loads are expressed as pressure (force over area). The rotation are not expressed as such in the solid structural case, but they are there, at least for small rigid body rotation through the antiysymmetric part of the global strain tensor (thx=0.5*(wy-vx), thy=0.5*(uz-wx), and thz=0.5*(vx-uy) PLS check carefully the order and signs as I might have mistyped one or the other, compare them with the strain values).

Now, to link beams and 3D solid you need to link the extra rotation DoF's too, and this must be done without overstiffening the structure. It's out of the scope what I manage to write here, but try it out wih a short 3D solid cylinder attached to a 3D beam of cylindrical shape.

If you look carefully at the beam equations, when you add ponctual masses you can see how to add lumped elements also in 3D solids.

Finally, if you want to add a linear spring to a 3D solid part, if the spring is attached to a fixed reference, you select i.e. a surface/boundary and you add a load of the type kx*u ky*v kz*w , where kx, ky, kz are the string stiffness in x,y,z respectively (to be distributed over your reference coordinates correctly). If your spring is attahing bewteen two elements, you need the differential of the displacements u1-u2 etc. Good emaple ofrintegration coupling variables

This holds for a static or time dependent calculations, for eigenmodes or harmonics you must take into account the Fourier development, as forces are not considered, you need to add the lambda "multipliers".

For rotations you must define a cylindrical coordinate via a workplane (there is an example in the structural toolbox documentation torque load, it has been discussed on the forum a couple of times too) and add rotational stiffness corresponding to moments that are to be translated into forces over areas =(pressure) on the 3D structural domain.

So even if all this looks slightly tough it is not that difficult, once you get the hold on it, and its an excellent exercice for 3D mechanics.

Good luck
Ivar
Hi Feasible certainly, but its slightly tricky, you must write your eqations yourself and for rotations its the most complex. Take a look at the hierarchy of structural elements in V3.5a: you have trusses (y,v,w but no rotations), beams (u,v,w,thx,thy,thz), shells (u,v,w,thx,thy,thz), and solids (u,v,w,p but no rotations). Trusses can only take axial forces, beams can, in addition to axial forces, bend with moments (hence the rotation), shells the same, while solids take all cases, but loads are expressed as pressure (force over area). The rotation are not expressed as such in the solid structural case, but they are there, at least for small rigid body rotation through the antiysymmetric part of the global strain tensor (thx=0.5*(wy-vx), thy=0.5*(uz-wx), and thz=0.5*(vx-uy) PLS check carefully the order and signs as I might have mistyped one or the other, compare them with the strain values). Now, to link beams and 3D solid you need to link the extra rotation DoF's too, and this must be done without overstiffening the structure. It's out of the scope what I manage to write here, but try it out wih a short 3D solid cylinder attached to a 3D beam of cylindrical shape. If you look carefully at the beam equations, when you add ponctual masses you can see how to add lumped elements also in 3D solids. Finally, if you want to add a linear spring to a 3D solid part, if the spring is attached to a fixed reference, you select i.e. a surface/boundary and you add a load of the type kx*u ky*v kz*w , where kx, ky, kz are the string stiffness in x,y,z respectively (to be distributed over your reference coordinates correctly). If your spring is attahing bewteen two elements, you need the differential of the displacements u1-u2 etc. Good emaple ofrintegration coupling variables This holds for a static or time dependent calculations, for eigenmodes or harmonics you must take into account the Fourier development, as forces are not considered, you need to add the lambda "multipliers". For rotations you must define a cylindrical coordinate via a workplane (there is an example in the structural toolbox documentation torque load, it has been discussed on the forum a couple of times too) and add rotational stiffness corresponding to moments that are to be translated into forces over areas =(pressure) on the 3D structural domain. So even if all this looks slightly tough it is not that difficult, once you get the hold on it, and its an excellent exercice for 3D mechanics. Good luck Ivar

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Posted: 1 decade ago 25.03.2010, 05:03 GMT-4
hi

i quote
"This holds for a static or time dependent calculations, for eigenmodes or harmonics you must take into account the Fourier development, as forces are not considered, you need to add the lambda "multipliers".

what do you mean by lambda "multipliers" and fourier developpement? could you explain more theoritically the point here?
indeed, i implement myself mass loading effect in the following form in eigen analysis

-(lambda^2)*cte*(u )



hi i quote "This holds for a static or time dependent calculations, for eigenmodes or harmonics you must take into account the Fourier development, as forces are not considered, you need to add the lambda "multipliers". what do you mean by lambda "multipliers" and fourier developpement? could you explain more theoritically the point here? indeed, i implement myself mass loading effect in the following form in eigen analysis -(lambda^2)*cte*(u )

Ivar KJELBERG COMSOL Multiphysics(r) fan, retired, former "Senior Expert" at CSEM SA (CH)

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Posted: 1 decade ago 25.03.2010, 08:56 GMT-4
Hi

exactly:
for a mass M loading atached to a solid you typically add (for eigenmodes) a force/pressure load of the type:

Px[N/m^2] = - (lambda[1/s])^2*(M[kg])*u[m]/(Area[m^2])

if have gravity and an acceleration load its something l

Fz = - lambda^2*w*M - M*g0

to be normalised over a length or an area depending on what you apply it too, and where i.e. g0 = 1[lbf/lb] a constant of the earth gravity acceleration (9.81m/s^2).

I use lambda instead of "-jomega_whatever", as "lambda" seems to be always defined and I can keep my load case when I switch forth and back between eigenfrequency and static for which "lambda = 0" hence cancels out nicely, while "-jomega_..." is no longer defined when changing modes, and I must edit each time my load line or add it as a constant = 0)

This is similar/the same as the Fourier/Laplace developments of the time equation, or for those used to control and electricity lambda is the "s^2" you have, or the w^2 omega square

Ivar

Hi exactly: for a mass M loading atached to a solid you typically add (for eigenmodes) a force/pressure load of the type: Px[N/m^2] = - (lambda[1/s])^2*(M[kg])*u[m]/(Area[m^2]) if have gravity and an acceleration load its something l Fz = - lambda^2*w*M - M*g0 to be normalised over a length or an area depending on what you apply it too, and where i.e. g0 = 1[lbf/lb] a constant of the earth gravity acceleration (9.81m/s^2). I use lambda instead of "-jomega_whatever", as "lambda" seems to be always defined and I can keep my load case when I switch forth and back between eigenfrequency and static for which "lambda = 0" hence cancels out nicely, while "-jomega_..." is no longer defined when changing modes, and I must edit each time my load line or add it as a constant = 0) This is similar/the same as the Fourier/Laplace developments of the time equation, or for those used to control and electricity lambda is the "s^2" you have, or the w^2 omega square Ivar

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Posted: 1 decade ago 25.03.2010, 09:27 GMT-4
merci Ivar,
by the way ,i would like to implement a boundary condition form of traction
this traction come from a boundary equation of the form :

ui(x1)= int(g(x1-xprim1)tij(xprim1)dxprim1)

do you that i can use the weak boundary mode to model this kind of fredholm equation and reinject the value in the boundary condition of the 3D simulation of the domain.
Indeed,i try to model a elastic radiation condition (special type of the spring)

Ps: j'ai vu que vous aviez écrit en français dans certains post ; bravo pour votre excellente maitrise de notre langue
merci Ivar, by the way ,i would like to implement a boundary condition form of traction this traction come from a boundary equation of the form : ui(x1)= int(g(x1-xprim1)tij(xprim1)dxprim1) do you that i can use the weak boundary mode to model this kind of fredholm equation and reinject the value in the boundary condition of the 3D simulation of the domain. Indeed,i try to model a elastic radiation condition (special type of the spring) Ps: j'ai vu que vous aviez écrit en français dans certains post ; bravo pour votre excellente maitrise de notre langue

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Posted: 1 decade ago 25.03.2010, 09:30 GMT-4
in the mean time i post the kind of special model i want to implement

best regard
in the mean time i post the kind of special model i want to implement best regard


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Posted: 1 decade ago 25.03.2010, 23:44 GMT-4
Ivar,

Thanks so much for such an comprehensive response. I am gonna study on this a little more and try to work it out. Thanks again.
Ivar, Thanks so much for such an comprehensive response. I am gonna study on this a little more and try to work it out. Thanks again.

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