I am not sure what you mean by vibration as an expected result instead of displacement..as long as it is a steady state static load on one end and the fixed nodes on the other end. I would normally model solids with tet10 elements,,could do it with tet4's as well,,but tet4 are stiffer than 10. I guess for a uniform cross sectioned cantilever beam hex elements should be ok. I would have rather modeled it with 1D beam elements since it is just a simple cantilever.

 As far as plastic deformation is concerned..are u using a non linear analysis?? Plastic deformations from linear static solutions does not mean anything