The demands of space flight can require unique design solutions. Shown below is a testbed demonstration version of a variable frequency TMD designed to damp a large deployable appendage of a spacecraft. While the function of the TMD is to damp the appendage after it is deployed on orbit, the TMD design was driven by the need for the TMD itself to survive the high vibration levels present at launch without requiring launch locks. Since the target modes were in the 3-5 Hz range, it was clearly impossible to harden the TMD against launch vibration by the usual approach: stiffening it to raise its natural frequencies high enough to keep stresses below the allowables.

In addition, the TMD was required to damp modes of the appendage in two directions with nearly equal frequency, and to be designed for minimum weight. More specifically, the moving mass of the TMD was required to account for the largest possible fraction of the total allowable weight, and thus to maximize damping added to the target modes.

The solution to the problems of weight efficiency and omnidirectionality was to use a TMD that itself had two modes at essentially the same frequency. This allowed the full moving mass of the TMD to be effective against both target modes, regardless of their directions. However it also required a magnetic dashpot that would damp in any direction within a plane.  A flat conductor plate is acted on by four "horseshoe" magnet cells.  Together they push flux around a loop, penetrating the plate in two areas per cell. The upper and lower irons serve to increase the flux density and to reduce fringing of stray flux. It was shown both analytically and by test that the arrangement would have negligible directionality of its damping force/velocity ratio. The magnets and back iron of the dashpot assembly are part of the TMD moving mass, and thus their weight need not be minimized.

The conductor plate is fixed rigidly to the base structure to be damped. The TMD mass, or "head", mounts to the base structure on three slender flexure rods as shown. These provide equal transverse stiffness in any direction parallel to the mounting surface.

It was found by analysis that the most difficult problem in qualifying the design against launch vibration was stresses due to local bending modes of the flexures. This was particularly severe if the frequency tuning mechanism required the flexures to be sized for the lower limit of the desired frequency range.

The solution came in two parts. The first was a unique frequency tuning mechanism that allowed the flexures to be sized for the upper end of the range, rather than the lower and thus to be as short and stiff as possible. Frequency tuning is obtained by varying the axial preload on the flexures using a non-contact magnetic preloader.  The entire tuning mechanism, except for the target iron and its support, is part of the TMD moving mass and thus need not be miminum weight.

With the fairly short, stiff flexures made possible by the preloader tuning mechanism, the bending stresses in the flexures under launch vibration could be kept below allowables by using a simple constrained layer viscoelastic treatment on the center 1/4 of the flexure length (not shown on demonstration unit). Since the TMD mode shape produces almost no curvature of the flexure in this region, the VEM treatment has no affect on TMD action after launch.

The frequency adjusting mechanism allows the TMD to be precisely tuned for maximum damping effectiveness. The 15-lb moving mass of the unit is then sufficient to produce 5% of critical damping in the first two cantilever bending modes of a 4000-lb appendage.