Have you calculated the natural frequency of the beam/weight combination? The question may fall in to the category of "am I exciting a mode of the weight/beam"? Do you know the frequency of vibration of the block? And, what stress are you concerned about...stress in the beam? the block?
There are other questions related to the modeling: What boundary conditions do you plan on using? How will you apply the load (centrifugal, moment, force, etc.).
I know I keep coming up with more questions than answers, but I'm really trying to grasp what it is you are trying to do...
If you are trying to determine the stress in the block due to the vibration of the block and the inertia of the beam/weight combination, you need to check the vibration absorption due to the elasticity of the beam (AE/L is the spring constant) and see if it will even move the weight. If it does, the weight could be positioned at a node if that is important (a vibratory node...not an FEA node) then it would't move despite the vibration.
If your dimensions are set and weights determined so that there is no additional design involved, you still need to know the flexibility of the beam to see how much elastic energy will be "whipping" your weight. It's not unlike a fishing pole...a rigid rod won't "whip" your bait over the pond, but a flexible one will.