212 Ketter Hall, North Campus, Buffalo, NY 14260

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• 212 Ketter Hall, North Campus, Buffalo, NY 14260
  
• www.civil.buffalo.edu
• Fax [phone] Tel [phone] x 2400
• Control of Structural Vibrations
• Lecture 2
• Instructor
• Andrei M. Reinhorn P.Eng. D.Sc.
• Professor of Structural Engineering

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Response of Open Loop
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Review of SDOF
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Free Vibrations
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Efficiency of Damping
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Equilibrium in Phase Space - Bode Diagram
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Definition of Spectrum
Spectrum is a function of frequency Examples
Spectrum of Light Spectrum in Chromatography /
Chemistry Spectrum in Acoustics Spectrum in
Mechanics
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Response Spectrum
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 (Sd)
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Response Computations
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Properties of Response Spectra
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Pseudo-Spectra
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Spectrum characteristics
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Uncertainities in Spectrum
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Code Spectrum - FEMA / NEHRP 1994
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Spectral Amplification - Israeli Standard,
IS-413, December 1998
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Spectral Amplification - Israeli Standard,
IS-413, December 1998
Ra 1.25S/T2/3 lt2.5 SRa,maxTo2/3/1.25 S

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Code Spectrum / NEHRP 1994/FEMA 303/304
1994 NEHRP SPECTRUM FOR 5 DAMPING
(FEMA223A/223B) 1997 SPECTRA FOR HIGHER DAMPING
(FEMA303/304)
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Damping Factors in FEMA 303/304
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Example - Uncontrolled
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Example w/ Control
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Conventional Spectra
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Composite Elastic ADRS
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Composite DARS(pectra)
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Composite IDARS
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Composite IDARS (2)
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Approximation of Actual IDARS
Approximation Methods
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Derivation of IDARS form DARS
Approximations of factor Rd can be obtained
form literature
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IDARS form DARS (3)From NEHRP 1997
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IDARS form DARS (4)From NEHRP 1997
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IDARS form DARS (5)From NEHRP 1997
Note Spectrum for 5 damping
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Normalized Composite ADRS
To0.35
T1.00
T5.00
For Soil S1only. For other soils need to modify
corner period To
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Modal Spectral Analysis
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Drift (Displacement) Response
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