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Unformatted text preview: x = 0 and attached to a spring of sti±ness 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 system’s lowest natural frequencies and mode shapes. 1 4 Problem 4 The mode shapes of a uniform Fxedfree bar are of the form Φ n ( x ) = sin ± (2 n1) πx 2 L ² n = 1 , 2 , 3 , ··· Use the RayleighRitz method with Φ 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 ρ = 7500. 2...
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This note was uploaded on 06/17/2010 for the course AA 242B taught by Professor Charbelfarhat during the Spring '10 term at Stanford.
 Spring '10
 CHARBELFARHAT

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