example_III_2_02 - j Guess " j L (2*j-1) #$ /2 1 $ /2...

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Example 3 - free response of a cantilevered bending beam Find the general form of the free vibration solution of a cantilevered homogeneous bending beam having a flexural rigidity EI, cross-sectional area A and mass/volume ! . x = 0 x=L u(x,t) EI, ! , A From last example, we know that: u x , t ( ) = " x ( ) T t ( ) where T t ( ) = c cos t + s sin t x ( ) = a cosh # x + b sinh x + c cos x + d sin x
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! L/ " -1.5 -1 -0.5 0 0.5 1 1.5 0 1 2 3 4 5 cos ! L - 1/cosh ! L Numerical Results (the first three roots are also presented in Section 9.5 of text):
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Unformatted text preview: j Guess " j L (2*j-1) #$ /2 1 $ /2 1.8751 1.5708 2 3 $ /2 4.6941 4.7124 3 5 $ /2 7.8548 7.8540 4 7 $ /2 10.9955 10.9956 5 9 $ /2 14.1372 14.1372 6 11 $ /2 17.2788 17.2788 7 13 $ /2 20.4204 20.4204 8 15 $ /2 23.5619 23.5619 9 17 $ /2 26.7035 26.7035 10 18 $ /2 29.8451 29.8451...
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example_III_2_02 - j Guess " j L (2*j-1) #$ /2 1 $ /2...

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