Calculate the first three natural frequencies of a cantilever steel beam (E=210 GPa, 7800Kg/m^3) of length...

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Calculate the first three natural frequencies of a cantilever steel beam (E=210 GPa, 7800Kg/m^3) of length L = 0.45 m. Assume that the beam has a rectangular cross-section with, d = 0.003 m, and b = 0.02 m. Recall that I = b bh³. A SDOF oscillates freely once the following IC are provided x(0) = 1, x(0) = 0, The amplitudes of two consecutive peaks of X(t1) = 0.545385m and X(t2) = 0.296315m, where t1=1.0049 sec, and t2=2.0098 sec. (a) Use the logarithmic decrement to calculate the value of the damping ratio . (b) Calculate the natural frequency of the system wn. Calculate the first three natural frequencies of a cantilever steel beam (E=210 GPa, 7800Kg/m^3) of length L = 0.45 m. Assume that the beam has a rectangular cross-section with, d = 0.003 m, and b = 0.02 m. Recall that I = b bh³. A SDOF oscillates freely once the following IC are provided x(0) = 1, x(0) = 0, The amplitudes of two consecutive peaks of X(t1) = 0.545385m and X(t2) = 0.296315m, where t1=1.0049 sec, and t2=2.0098 sec. (a) Use the logarithmic decrement to calculate the value of the damping ratio . (b) Calculate the natural frequency of the system wn.

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Solution a The logarithmic decrement is defined as lnXt2Xt1 t2 t1 Using the given values ... View the full answer