# SolSec3.5 - 3 36 Problems and Solutions Section 3.5(3.33...

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3- 36 Problems and Solutions Section 3.5 (3.33 through 3.36) 3.33 Calculate the mean-square response of a system to an input force of constant PSD, S 0 , and frequency response function () ω j H 2 3 10 + = Solution: Given: j H S S ff 2 3 10 and 0 + = = The mean square of the response can be found from Eqs (3.66) and (3.68): xE x H S d xS j d ff 22 2 2 0 2 10 32 = [] = () () = + −∞ −∞ ωω Using Eq. (3.67) yields 3 50 0 2 S x π =

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3- 37 3.34 Consider the base excitation problem of Section 2.3 as applied to an automobile model of Example 2.3.1 and illustrated in Figure 2.10. In this problem let the road have a random stationary cross section producing a PSD of S 0 . Calculate the PSD of the response and the mean-square value of the response. Solution: Given: 0 S S ff = From example 2.3.1: N/m 000 , 400 kg/s, 000 , 20 kg, 1007 = = = k c m ed) (underdamp 498 . 0 2 = = km c ζ So, H k m jc j H j H ω ωω () = −+ = ×− + () + ×+ × 11 4 10 1007 20 000 1 4 10 1007 20 000 1 1 01 10 4 06 10 1 6 10 25 2 2 52 2 2 2 2 64 82 1 1 , , ... The PSD is found from Eq. (3.62): SH S S xx ff xx () = () () × 2 1 1 1 1 01 10 4 06 10 1 6 10 The mean square value is found from Eq. (3.68): xE x H S d xS j d ff 22 2 2 0 2 1 4 10 1007 20 000 = [] = () () = + −∞ −∞ , Using Eq. (3.70) yields x S 2 0 9 81 0 = × π
3- 38 3.35 To obtain a feel for the correlation functions, compute autocorrelation
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SolSec3.5 - 3 36 Problems and Solutions Section 3.5(3.33...

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