Discussion Forum

Hi

it sounds easy: cantilever + a spring + a mass, but once you start to think of it becomes slightly more complex.

What you need to tell us is your model a 3D, a 2D or a 1D model ?
Because if its a 3D model you must tell us more, the underlying hypothesis, for you cantilever it's straightforward: a density, a Young modulus and a Poisson coefficient, a fixed boundary condition, and the geometric extend in X,Y,Z. For the mass I assume you are thinking about a point mass, but then is it free in 3D ? restrained in some direction, and what about the rotations ?
For the spring again 3D, 2D or 1D if so along which axis, and the rotations, ? is it expressed by a simple stiffness or a full stiffness matrix?

COMSOL has only the "Spring Foundation" built in to link a boundary to an inertia reference frame (INF mass) via an isotropic or anisotropic spring stiffness. For the rest you must build the items yourself via the equations.
OR maybe you have the MDB module, then you can attach the free end of the cantilever to an "attachment" and continue in MDB for the spring and mass point.
But still you must have a reply to all the questions addressed above, and probably a few I have forgotten...

Do not give up, once you have sorted out these questions of DoF (Degrees of Freedom) then the model often rather quickly written out and you can get suggestive models running

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Good luck Ivar

Thank for your reply.

The model is in 3D, but using a single beam element simply fixed at both ends, not a cantilever.

Yes, I am envisioning a point mass attached to the beam through a spring of some sort; for the first attempt, I am just assuming vertical (i.e. the direction of gravity) components of displacement, no rotations. For the spring I guess I am assuming a vertical (soft) and lateral (very stiff) stiffness. So at the contact point (or area) of the beam, the displacements would have a quasi-static part due to the weight of the mass and a dynamic part due the beam-mass interaction. The mass travels at constant speed (and slow relative to sqrt(E/rho) of the beam).

Thanks!
-CNL

Or it can be done in 2D, doesn't matter. Attached is a diagram of what I am thinking.

Thank for your reply.

The model is in 3D, but using a single beam element simply fixed at both ends, not a cantilever.

Yes, I am envisioning a point mass attached to the beam through a spring of some sort; for the first attempt, I am just assuming vertical (i.e. the direction of gravity) components of displacement, no rotations. For the spring I guess I am assuming a vertical (soft) and lateral (very stiff) stiffness. So at the contact point (or area) of the beam, the displacements would have a quasi-static part due to the weight of the mass and a dynamic part due the beam-mass interaction. The mass travels at constant speed (and slow relative to sqrt(E/rho) of the beam).

Thanks!
-CNL

Hi

you image looks more like a 2D beam problem, with a pinned - rolling BC for the beam, the material and beam, parameters defined E, nu, rho and L & I, and a moving mass M of velocity v with a spring Ky on a rolling point in contact to the beam.

So most of the physics is described, a few hypothesis are missing or considered implicit, I understand them as: the horizontal velocity of the mass M is NOT influenced by the spring, only the vertical Y axis motion of the mass.
A point remains open: should the rolling spring to beam contact be a one way contact and allow bouncing ?

I would propose to start with a fixed contact point and avoid "contact physics" as this is tricky to make to converge, then it should not be too difficult to check that the wheel is not bouncing and lifting off the bridge, if so, then its worth to try to implement a contact model as the vibrations of the beam will change drastically if the Mass gets disconnected.

I see two ways to implement the spring and mass,
1) use a point mass at the end of a small beam you adapt to have the right stiffness Ky, that is constrained to a constant velocity along X
2) add an ODE (or modify the Prescribed Displacement node) to describe the Ky & M combination on the contact point moving at constant Vx velocity via mechanics equations

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Good luck
Ivar