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Unformatted text preview: x = 0 and attached to a spring of stiness k at x = L . 1. Determine a set of w i ( x ), i = 1 , , 4 2. Use the RayleighRitz method with the functions obtained above and kL 3 /EI = . 5 to approximate the systems lowest natural frequencies and mode shapes. 1 4 Problem 4 The mode shapes of a uniform Fxedfree bar are of the form n ( x ) = sin (2 n1) x 2 L n = 1 , 2 , 3 , Use the RayleighRitz method with i ( x ), i = 1 , 2 , 3 to approximate the lowest natural frequencies and mode shapes of a Fxedfree tapered bar of length L = 3, circular cross section of radius r ( x ) = 0 . 05 (1. 01 x ) 2 , and with E = 2 10 11 and = 7500. 2...
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 Spring '10
 CHARBELFARHAT

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