SolSec7.6

# SolSec7.6 - Problems and Solutions Section 7.6 (7.25-7.31)...

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Problems and Solutions Section 7.6 (7.25-7.31) 7.25 Referring to Section 5.4 and Window 5.3, calculate the receptance matrix of equation (7.25) for the following two-degree-of-freedom system, without using the system’s mode shapes. 2 0 0 1  ξ 1 2 + 3 -1 1 1 2 + 6 -2 2 1 2 = φ 0 0 σιν ϖτ Solution: 2 0 0 1 ξ + 3 -1 -1 1 ξ + 6 2 ξ = 1 0 0 σιν( 29 α ( w ) = ( K - w 2 M + jw C ) - 1 ( w ) = 1 D 2 - w 2 + jw 2 + jw 2 + jw 6 - 2 w 2 + j 3 w é ë ê ù û ú ∆ = 2 w 4 - 12 w 2 + 8 + j (- 5 w 3 + 8 w )

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7.26 Repeat Problem 7.25 using the undamped mode shapes. Note that the system has proportional damping since C = α M + β K , where α = 0, α = 1/2. Use this result and the result of Problem 7.25 to verify equation (7.33). Solution: For the system 2 0 0 1  ξ + 3 -1 -1 1 ξ + 6 -2 2
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## This note was uploaded on 11/28/2010 for the course ME 4440 taught by Professor Hill during the Winter '09 term at Detroit Mercy.

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SolSec7.6 - Problems and Solutions Section 7.6 (7.25-7.31)...

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