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RESEARCH PAPERS

# Passive, Nonlinear, Mechanical Structures for Seismic Attenuation

[+] Author and Article Information
Riccardo DeSalvo

LIGO Laboratory,  California Institute of Technology, Pasadena, CA 91125desalvo@ligo.caltech.edu

J. Comput. Nonlinear Dynam 2(4), 290-298 (Jan 10, 2007) (9 pages) doi:10.1115/1.2754305 History: Received October 18, 2005; Revised January 10, 2007

## Abstract

Gravitational wave detectors aim to detect strain perturbations of space-time on the order of $10−21–10−22$ at frequencies between $1Hz$ and a few kHz. This space-time strain, integrated over kilometer scale interferometers, will induce movements of suspended mirrors on the order of $10−18–10−19m$. Seismic motion in this frequency band varies between $10−6m$ and $10−12m$. Required seismic attenuation factors, as large as $10−12$, by far exceed the performance of motion sensors, and are only obtained by means of a chain of passive attenuators. High quality springs in configurations yielding nonlinear response are used to generate attenuation at low frequency. Similarly, nonlinear mechanisms are used in the horizontal direction. A description of some of these systems and some of the technical challenges that they involve is presented.

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## Figures

Figure 1

Sketch of the GAS mechanism. At the working point (top sketch) the vertical spring S supports the weight of the payload. The two opposite springs A are compressed, and their forces cancel. Moving out of the working point (bottom sketch) the opposing forces of the A springs do not cancel completely, generating a vertical component proportional to the displacement from the working point, the anti-spring force. The opposing springs may be mechanical or magnetic.

Figure 2

Sketch illustrating the GAS mechanism: side and top view. Two (or more) flat blades (1) are prestressed (bent cylindrically) and mounted face to face against a keystone (2) which suspends the payload. The blades are held in 45deg clamps (3) that can slide into coulisses (4). The radial compression of the blades, governing the geometric anti-spring mechanism, is obtained by micrometrically pushing on the blade clamps with tuning screws (5). The blades are cut with a characteristic ogival profile (visible in the top view) so that in working conditions they bend in a perfectly circular arc (side view) and the material is subject to uniform stress.

Figure 3

A typical frequency versus load curve at fixed radial compression is shown. The a.u. are used because they scale with the blade’s size. The a.u. correspond to mm for ∼200‐mm-long blades.

Figure 4

Quality factor measurements for similar blades made of copper–beryllium (full squares and solid line fit) and Maraging 250 (empty squares and dashed line fit) (42)

Figure 5

The wandering of a GAS spring equilibrium point caused by the magnified effects of hysteresis is shown; see text for description of the measurement procedure.

Figure 6

Mechanical transfer function of two different GAS blades. Note that the peak at higher frequency “shows” the lower Q factor only because of measurement instrument settings. This is therefore not in contradiction with the behavior later illustrated.

Figure 7

Mechanical transfer functions of the same GAS filter with different EM gain levels

Figure 8

The transfer function slope is less steep than 1∕f2 for very low-frequency tunes of the GAS filter

Figure 9

Attenuation slope behavior of a GAS filter for low-frequency tuning

Figure 10

Cutout sketch of an IP table. A typical IP table has three or four legs. An IP leg is composed (following the assembly from the bottom up) of a stand, the main cylindrical flex joint providing the return torque, a counterweight bell to center the leg’s percussion point on the flex joint, the main leg tube, and the small flex joint connecting to the table structure.

Figure 11

Typical frequency tuning for an IP table. In this case, to reach a resonant frequency of 30mHz a load tuning of half a kg (∼0.1%) was necessary. Resonant frequency of 13mHz has been achieved in quiet air, lower may be achievable in vacuum.

Figure 12

Typical IP transfer function (before frequency tuning). The smooth curve is a simulation; the other curve is measurement data. The structure above 20Hz is due to the stack of ballast weights used in the test.

Figure 13

One of the four GAS springs forming the last vertical attenuation stage for the TAMA mirror test masses. The beginning of a second spring is visible on the right.

Figure 14

Design of a prototype, in-vacuum, passive seismic attenuation system for the advanced LIGO HAM optical tables. Visible inside the vacuum chamber (1), between the support beams (2) and the optical bench (3) is the SAS attenuation structure. The IP legs (4) provide the horizontal isolation. They are formed by a thin aluminum tube connected to the base structure through a stiff flex joint (4b), which provides the angular rigidity, and to the vertical stage through a soft flexure (4a). The vertical stage is formed by four GAS filters (5). Each GAS filter is provided with a LVDT position sensor and a voice coil actuator (6) mounted coaxially on the same support tube. These four sensor-actuator pairs provide the means for vertical positioning and control. Similarly four pairs of sensor actuators (7) allow horizontal controls. The insert shows a side view of a pair of sensor actuators The LVDT primary coil (7b) and the actuator magnetic yoke (7c) are mounted on the moveable part, while the LVDT primary coil (7a) and actuator coil (7d) are connected to ground. The static horizontal positioning of the optical bench is provided by stepper motors (8), driving micrometric sleds, acting on parasitic springs. Similarly, in the vertical direction (9), the columns (10) are safety structures providing earthquake stops.

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