final_soln

final_soln - y t ( ) = y sin ! t x R k no slip c m O...

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Unformatted text preview: y t ( ) = y sin ! t x R k no slip c m O Problem No. 1 vibration isolation Consider the base-excited, single-DOF system shown below. Assume the disk to be homogeneous with its center of mass at O and with its centroidal mass moment of inertia being I O = 1 2 mR 2 . The spring is unstretched when x = y = . Determine the range of values for the stiffness k for which the amplitude of steady- state response, x P t ( ) , is less than y . Express your answer in terms of, at most, the parameters m, c, k and . SOLUTION T = 1 2 I C 2 = 1 2 3 mR 2 2 x R 2 = 3 4 m x 2 U = 1 2 k x y ( ) 2 R = 1 2 c x y ( ) 2 EOM: 3 2 m x + c x + kx = c y + ky = c y cos t + k y sin t or, x + 2 n x + n 2 x = 2 n y cos t + n 2 y sin t where n 2 = 2 k 3 m . From lecture: x p t ( ) = 1 + 2 / n ( ) 2 1 / n ( ) 2 2 + 2 / n 2 y sin t ( ) = T ( ) y sin t ( ) From lecture we know that T ( ) < 1 for > 2 n , or: 2 n 2 = 4 k 3 m < 2 k < 3 4 m 2 ! Problem No. 2 vibration absorption An undamped three-DOF system has the following EOMs in terms of an unknown stiffness variable K: M x + K x = f sin t where M = 20 10 30 kg K = 300 200 200 200 + K K K 100 + K N m f = 100 N Determine the value for K for which the coordinate x 1 experiences complete vibration absorption when = 10 rad / sec . SOLUTION X ( ) = 2 M + K 1 f = 20 2 + 300 200 200 10 2 + 200 + K K K 30 2 + 100 + K...
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final_soln - y t ( ) = y sin ! t x R k no slip c m O...

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