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SolSec 6.7

# SolSec 6.7 - 6 52 Problems and Solutions Section 6.7(6.53...

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6- 52 Problems and Solutions Section 6.7 (6.53 through 6.63) 6.53 Calculate the response of Example 6.7.1 for l = 1 m, E = 2.6 × 10 10 N/m 2 and ρ = 8.5 × 10 3 kg/m 3 . Plot the response using the first three modes at x = l /2, l /4, and 3 l /4. How many modes are needed to represent accurately the response at the point x = l /2? Solution: w x t l e t x n n t n n n n ( , ) . ( ) cos sin . = + = 0 02 1 2 2 1 0 01 2 1 σ ω σ ω Where σ π ω σ ρ ω ω n n n dn n n l E = = = ( ) . 2 1 2 0 9999 For l = 1 m E = × = × 2 6 10 8 5 10 10 3 . . N/m kg/m 2 3 ρ Response using first three modes at x l l l = 2 4 3 4 , , plotted below. Three modes accurately represents the response at x l = 2 . The error between a three and higher mode approximation is less than 0.2%.

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