LSC Meeting Baton Rouge, LA, V.Boschi for the HAM-SAS team Ben Abbott, Valerio Boschi, Dennis Coyne, Michael Forte, Jay Heefner, Yu-mei Huang, David Ottaway, Riccardo de Salvo, & Virginio Sannibale HAM-SAS Mechanics Status of modeling DCC G R

LSC Meeting Baton Rouge, LA, Introduction HAM-SAS Attenuation Stages HAM-SAS is a seismic attenuation system expressly designed to fit in the tight space of the LIGO HAM vacuum chamber. Rigid Bodies - 4 Inverted Pendula Legs (IPs) - 4 MGAS Springs: Spring Box (SB) - Optical Table (OT) - Payload (mode cleaner suspensions, etc.)

LSC Meeting Baton Rouge, LA, Introduction Modeling Approach A state-space model of HAM-SAS mechanical structure have been developed using an Analytical approach. Let’s summarize the approximations used in the model: Lumped system, i.e. rigid body approximation Elastic elements are approximated using quadratic potentials, i.e. small oscillation regime Dissipation mechanisms are accounted using viscous damping which approximate structural/hysteretic damping in the small oscillation regime The system is considered symmetric enough to separate horizontal displacements x, y, and yaw from pitch, roll and vertical displacement z Internal modes of the mechanical structures are not accounted

LSC Meeting Baton Rouge, LA, Introduction Modeling Approach GAS - Blade stiffness modeled with simple Springs - Hysteretic/structural damping approximated with viscous damping. - Transmissibility saturation modeled using the "magic wand" Inverted Pendulum - Flexural Joint with Ideal pivot point about the attachment point. -Leg, a rigid body - Hysteretic/structural damping approximated with viscous damping.

LSC Meeting Baton Rouge, LA, IP Table Asymmetric leg length: Horizontal Transm. 30 mHz IP frequency 1.2 Hz Horizontal GAS frequency 105 mHz Little pendulum D.o.f. Contamination

LSC Meeting Baton Rouge, LA, IP Table Asymmetric leg length: Angular Transm.

LSC Meeting Baton Rouge, LA, IP Table Courtesy of I.Taurasi (Univ. of Benevento, Italy) ANSYS modeling of Rigid Leg Resonances Resonance frequency with counterweight Resonance frequency without counterweight ~110.6 Hz ~122 Hz Diameter of small flex joint: 1.5 mm Mass of counter weight: Kg Ansys shows that counter weight doesn’t reduce significantly the resonances. They can be damped

LSC Meeting Baton Rouge, LA, Eddy current dampers Before installation t = 4.3 s After installation t = 35 ms Measured and succesfully damped in a prototype without counterweight IP Table Damping of Rigid Leg Resonances Courtesy of I.Taurasi (Univ. of Benevento, Italy)

LSC Meeting Baton Rouge, LA, IP Table Leg Counterweight tuning

LSC Meeting Baton Rouge, LA, MGAS Table Asymmetric spring elastic constant k D.o.f. contamination

LSC Meeting Baton Rouge, LA, MGAS Table Asymmetric spring elastic constant k (expected Quality Factors) Very small effect

LSC Meeting Baton Rouge, LA, Triple Pendulum Model

LSC Meeting Baton Rouge, LA, Comparison Triple Pendulum Model We can compare our results with a previous (2003) Mathematica model made by M. Burton Test massIntermediate massUpper mass

LSC Meeting Baton Rouge, LA, Triple Pendulum + Horizontal Stage Model 30 mHz IP frequency Suspension Resonances Hz Little Pendula

LSC Meeting Baton Rouge, LA, Final considerations We are confident that we can meet the HAM optical table seismic attenuation requirements.