Taber vibration isolator for vacuum and cryogenic applications

We present a procedure for the design and construction of a passive, multip ole, mechanical high-stop vibration isolator. The isolator, consisting of a stack of metal disks connected by thin wires, attenuates frequencies in th e kilohertz range, and is suited to both vacuum and cryogenic environments. We derive an approximate analytical model and compare its predictions for the frequencies of the normal modes to those of a finite element analysis. The analytical model is exact for the modes involving only motion along and rotation about the longitudinal axis, and it gives a good approximate desc ription of the transverse modes. These results show that the high-frequency behavior of a multistage isolator is well characterized by the natural fre quencies of a single stage. From the single-stage frequency formulas, we de rive relationships among the various geometrical parameters of the isolator to guarantee equal attenuation in all degrees of freedom. We then derive e xpressions for the attenuation attainable with a given isolator length, and find that the most important limiting factor is the elastic limit of the s pring wire material. For our application, which requires attenuations of 25 0 dB at 1 kHz, our model specifies a six-stage design using brass disks of approximately 2 cm in both radius and thickness, connected by 3 cm steel wi res of diameters ranging from 25 to 75 mu m. We describe the construction o f this isolator in detail, and compare measurements of the natural frequenc ies of a single stage with calculations from the analytical model and the f inite element package. For translations along and rotations about the longi tudinal axes, all three results are in agreement to within 10% accuracy. (C ) 1999 American Institute of Physics. [S0034-6748(99)01806-7].