WARose
Structural
- Mar 17, 2011
- 5,594
I've been pondering this issue a lot lately.....and hoping for some tips/ideas here. With SDOF [Single Degree Of Freedom] models of vibrating foundations, the rotational (i.e. rocking) and translational modes of vibration are easy to separate and check for coupling where required. However, for MDOF [Multiple Degree Of Freedom] models (via FEA),.....many do not include the rotational springs (see 'Design of Structures and Foundations for Vibrating Machines', by: Arya, et al for such a example). Instead, just the translational springs representing the foundations.
But that presents a few problems: even if you included the rotational springs, you'd (then) be misestimating the foundation's rotational stiffness because the vertical springs by themselves provide rocking restraint......speaking of that.....if you've ever checked the resulting rotational restraint provided by the vertical springs, it's typically way off (in terms of magnitude) from what the rotational spring constant is (if you were doing a SDOF model).
So in other words: you don't have a accurate representation of the base stiffness. Which can be dangerous for a dynamic analysis.
What to do? I've typically taken one of several different approaches:
1. Have my model sit on a infinitely stiff block and control the DOF that way. That does present some issues if the foundation is big (and flexible) enough. Even for MDOF models, a lot of people try to have the mat/foundation thick enough to where localized displacements don't impact results. But that's not always practical.
2. Have separate models.....one "tuned" to the translational modes, and another tuned to the rocking modes. Possibly combine the results by some sort of superposition. Hopefully one (typically the translational mode) will be far enough away from any natural frequency that it won't be a issue. (The previously mentioned text [by Arya, et al] has a formula for checking coupling.)
But my bottom line question is: Are you aware of a better approach? Thanks.
But that presents a few problems: even if you included the rotational springs, you'd (then) be misestimating the foundation's rotational stiffness because the vertical springs by themselves provide rocking restraint......speaking of that.....if you've ever checked the resulting rotational restraint provided by the vertical springs, it's typically way off (in terms of magnitude) from what the rotational spring constant is (if you were doing a SDOF model).
So in other words: you don't have a accurate representation of the base stiffness. Which can be dangerous for a dynamic analysis.
What to do? I've typically taken one of several different approaches:
1. Have my model sit on a infinitely stiff block and control the DOF that way. That does present some issues if the foundation is big (and flexible) enough. Even for MDOF models, a lot of people try to have the mat/foundation thick enough to where localized displacements don't impact results. But that's not always practical.
2. Have separate models.....one "tuned" to the translational modes, and another tuned to the rocking modes. Possibly combine the results by some sort of superposition. Hopefully one (typically the translational mode) will be far enough away from any natural frequency that it won't be a issue. (The previously mentioned text [by Arya, et al] has a formula for checking coupling.)
But my bottom line question is: Are you aware of a better approach? Thanks.
