Assignment 2 - Comparison of Natural Frequencies Remarks...

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Unformatted text preview: Comparison of Natural Frequencies Remarks Natural Frequency × 10 3 / rad sec Mode 1 Mode 2 Mode 3 Undamped . 0 6982 . 3 3166 . 4 5291 Dampe d ( ) Case i .- . 0 6983 0 0070i .- . 3 3168 0 0332i .- . 4 5293 0 0453i Case ( ) ii .- . 0 6982 0 0007i .- . 3 3166 0 0033i .- . 4 5291 0 0045i Case ( ) iii . + 0 7265 . 0 1995i .- . 3 3168 0 0332i .- . 4 5297 0 0784i Case ( ) iv . + 0 6985 . 0 0207i .- . 3 3166 0 0033i .- . 4 5291 0 0078i Plots for Eigen Vectors Undamped Vibrations 2 4 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 M o d e 1 2 4 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 0 . 8 M o d e 2 2 4 0 . 1 0 . 2 0 . 3 0 . 4 0 . 5 0 . 6 0 . 7 M o d e 3 ( ): α = . Case i Damped Vibration with 0 02 1 2 3 4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Real part of Mode 1 1 2 3 4-1-0.5 0.5 1 Real part of Mode 2 1 2 3 4-0.8-0.6-0.4-0.2 0.2 0.4 0.6 Real part of Mode 3 1 2 3 4-5 5 10 15 x 10-18 Imaginary part of Mode 1 1 2 3 4-0.05 0.05 Imaginary part of Mode 2 1 2 3 4-0.04-0.02 0.02 0.04 Imaginary part of Mode 3 ( ): α = . & [ ]. Case ii Damped Vibration with 0 02 Modified D 1 2 3 4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Real part of Mode 1 1 2 3 4-0.1-0.05 0.05 0.1 Real part of Mode 2 1 2 3 4-0.06-0.04-0.02 0.02 0.04 0.06 Real part of Mode 3 1 2 3 4-0.012-0.01-0.008-0.006-0.004-0.002 Imaginary part of Mode 1 1 2 3 4-1-0.5 0.5 1 Imaginary part of Mode 2 1 2 3 4-0.8-0.6-0.4-0.2 0.2 0.4 0.6 Imaginary part of Mode 3 ( ): α = . Case iii Damped Vibration with 0 002 1 2 3 4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Real part of Mode 1 1 2 3 4-1-0.5 0.5 1 Real part of Mode 2 1 2 3 4-0.8-0.6-0.4-0.2 0.2 0.4 0.6 Real part of Mode 3 1 2 3 4-2.5-2-1.5-1-0.5 0.5 1 x 10-19 Imaginary part of Mode 1 1 2 3 4-2-1 1 2 x 10-4 Imaginary part of Mode 2 1 2 3 4-1.5-1-0.5 0.5 1 1.5 x 10-4 Imaginary part of Mode 3 ( ): α = . & [ ] Case iv Damped Vibration with 0 002 Modified D 1 2 3 4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 Real part of Mode 1 1 2 3 4-0.01-0.005 0.005 0.01 Real part of Mode 2 1 2 3 4-6-4-2 2 4 6 x 10-3 Real part of Mode 3 1 2 3 4-1.2-1-0.8-0.6-0.4-0.2 x 10-3 Imaginary part of Mode 1 1 2 3 4-1-0.5 0.5 1 Imaginary part of Mode 2 1 2 3 4-0.8-0.6-0.4-0.2 0.2 0.4 0.6 Imaginary part of Mode 3 , M K and D matrices [ ] =...
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This note was uploaded on 10/20/2011 for the course STRUCTURAL MEL840 taught by Professor Svmodak during the Spring '11 term at IIT Kanpur.

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Assignment 2 - Comparison of Natural Frequencies Remarks...

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