The dynamics of monolithic suspensions for advanced detectors: a 3-segment model

In order to reduce the suspension thermal noise, the second generation GW interferometric detectors will employ monolithic suspensions in fused silica to hold the mirrors. The fibres are produced by melting and pulling apart a fused silica rod, obtaining a long thin wire with two thicker heads. The dynamics of such a fibre is in principle different from that of a cylindrical, regular fibre, because most of the deformation energy is stored in the neck region where the diameter is variable. This is an advantage, since adjusting the neck tapering, a thermoelastic noise cancellation effect can be obtained. Therefore, a careful study of the suspensions behavior is necessary to estimate the overall noise and to optimize the control strategy. To simplify the control design, a simple three segment model for the silica fibres has been developed, fully equivalent to the beam equation at low frequencies. The model, analytically proved for a regular cylindrical fibre, can be extended to a fibre with tapered necks, provided that the equivalent bending length is suitably measured. We developed a tool to measure the position of the bending point for each fibre, thus allowing to experimentally check the validity of the model. A numerical code has been written to solve the beam equation for wires with varying diameter. This code confirms the validity of the three segment model. Moreover, it is possible to extend the solution to higher frequencies thus computing the transfer function and the energy distribution of the suspension system and estimating the thermal noise contribution.