This problem investigates the number of cycles (n) re- quired for a structural oscillation amplitude to decay

Question:

This problem investigates the number of cycles $n$ re-

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quired for a structural oscillation amplitude to decay to $x \%$ of its maximum.

(a) What is the expression for the logarithmic decrement in terms of $n$ and $x$ ?

(b) Solve for $n$ in terms of $\zeta$ and $x$.

(c) Plot $n$ as a function of $\zeta$ for (i) $x=70 \%$, (ii) $x=50 \%$, (iii) $x=20 \%$ using the exact formula, and then using the approximate formula for $\zeta=0.1$ and $\zeta=0.5$.

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Mechanical Vibration Analysis, Uncertainties, And Control

ISBN: 9781498753012

4th Edition

Authors: Haym Benaroya, Mark L Nagurka, Seon Mi Han

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Question Posted: May 06, 2024 04:01 AM

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This problem investigates the number of cycles (n) re- quired for a structural oscillation amplitude to decay

Question:

Table 3.1: Cases for tmax in Problem 9. Case (0) (in) (0) (in/s) w (rad/s) 1 2 0 5 0.1 2 5 0 0.1 2 3 5 5 0.1 2 4 5 5 0.5 2 5 5 5 1.1 2 6 5 7 5 5 0.1 4 5 0.1 10

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Mechanical Vibration Analysis, Uncertainties, And Control

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