Monolithic geometric anti-spring blades

Here we address the theoretical description of the mechanical device, focusing on the most important quantities for the low-frequency regime, on the distribution of internal stresses, and on the thermal stability. In order to obtain physical insight of the attenuator peculiarities, we devise some simplified models, rather than use the brute force of finite element analysis. Those models have been used to optimize the design of a seismic attenuation system prototype for LIGO advanced configurations and for the next generation of the TAMA interferometer.