1. Support Tube Dynamic Analysis KEK’s ANSYS simulation –model details –Single Point Response Spectrum analysis SUGGESTED improvements –beam model –Harmonic Response Analysis –Random Analysis –Transient Dynamic Analysis (time domain) E. Doyle 12/6/99

3. KEK model constraints horiz rotations free, all other d.o.f. fixed

7. Four freq/displacement points used in KEK SPRS analysis - analysis of max response to transient event - damping accounted for in response curve

8. Beam Model - simply supported more efficient than shell model

9. Beam Model vs. Shell Model Natural frequencies in Hz

10. Beam Model - cantilever

11. Responses of Concern Differential motion between Q1 magnets Resulting from –non-uniform ground motion at two ends –structure asymmetry ANSYS can be used to explore these – tube support dynamics –benefit from joining two cantilevers (creation of common modes)

12. Excitation Modes of Concern Harmonic - cultural sources –Harmonic Response Analysis Random - natural and cultural sources –Random PSD (power spectral density) –Transient Analysis (time domain)

13. Harmonic Analysis Sinusoidal excitation at specified ampl & freq Response at magnet mount points Combine responses at all frequencies of interest

14. Harmonic analysis - vert base motion, unit amplitude Different damping for the two beams

15. Random Vibration Analysis Input PSD of base motion Result is PSD response at each magnet how to interpret?

17. Absolute PSD Response ( 1m 2 /hz flat input) --------- FREQUENCY

18. PSD Response relative to base motion --------- FREQUENCY

19. Transient Dynamic Analysis Input sampled ground motion (time domain) Response is motion in time domain Combine in time domain (outside ANSYS) Generate cross correlation function (outside ANSYS)