1. 212 Ketter Hall, North Campus, Buffalo, NY 14260 www.civil.buffalo.edu Fax: 716 645 3733 Tel: 716 645 2114 x 2400 Control of Structural Vibrations Lecture #2 Instructor: Andrei M. Reinhorn P.Eng. D.Sc. Professor of Structural Engineering

4. Response of Open Loop

6. Review of SDOF

7. Free Vibrations

11. Efficiency of Damping

13. Equilibrium in Phase Space - Bode Diagram

19. Definition of Spectrum Spectrum is a function of frequency Examples: Spectrum of Light Spectrum in Chromatography / Chemistry Spectrum in Acoustics Spectrum in Mechanics

20. Response Spectrum TnTnTnTn T1T1T1T1 T2T2T2T2 T3T3T3T3dÄ SdSdSdSd T Each pendulum responds differently than the other Each pendulum will have a random response Each Pendulum will have a maximum response at some time The plot of the maximum displacement for each pendulum as a function of its Natural Period, T, is the Displacement Response Spectrum (S d )

21. Response Computations

22. Properties of Response Spectra

23. Pseudo-Spectra

24. Spectrum characteristics

25. Uncertainities in Spectrum

26. Code Spectrum - FEMA / NEHRP 1994

27. Spectral Amplification - Israeli Standard, IS-413, December 1998 R a = 1.25*S/T 2/3 <2.5 S=R a,max *T o 2/3 /1.25 S = { }

28. Spectral Amplification - Israeli Standard, IS-413, December 1998 R a = 1.25*S/T 2/3 <2.5 S=R a,max *T o 2/3 /1.25 S = { }

29. Code Spectrum / NEHRP 1994/ FEMA 303/304 1994 NEHRP SPECTRUM FOR 5% DAMPING (FEMA223A/223B) 1997 SPECTRA FOR HIGHER DAMPING (FEMA303/304)

30. Damping Factors in FEMA 303/304

31. Example - Uncontrolled

32. Example w/ Control

33. Conventional Spectra

34. Composite Elastic ADRS 22

35. Composite DARS(pectra)

37. Composite IDARS

38. Composite IDARS (2)

39. Approximation of Actual IDARS Approximation Methods:

40. Derivation of IDARS form DARS Approximations of factor R d can be obtained form literature

41. IDARS form DARS (3) From NEHRP 1997

42. IDARS form DARS (4) From NEHRP 1997

43. IDARS form DARS (5) From NEHRP 1997 Note: Spectrum for 5% damping

44. Normalized Composite ADRS T=1.00 T o =0.35 T=5.00 For Soil S 1 only. For other soils need to modify corner period T o

47. Modal Spectral Analysis

48. Drift (Displacement) Response