Page 470 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Chap. 13 Problems 457

small and the variation of is gradual, the last equation becomes
________ d{f/L)
' ' f [ i - ( / / / „ ) ' ] uaf/Df
+
S ( f \L l JL
^xKJn) 1^2 4 ¿'
which is Eq. (13.8-11). Derive a similar equation for the mean square value of the
relative motion z of a single-DOF system excited by the base motion, in terms of the
spectral density of the base acceleration. (See Sec. 3.5.) If the spectral density
of the base acceleration is constant over a given frequency range, what must be the
expression for z^?
13-34 Referring to Sec. 3.5, we can write the equation for the absolute acceleration of the
mass undergoing base excitation as
k io)c
X = -------- ^------- • y
k —mo) + i(i)C

Determine the equation for the mean square acceleration x^. Establish a numerical
integration technique for the computer evaluation of
13-35 A radar dish with a mass of 60 kg is subject to wind loads with the spectral density
shown in Fig. P13-35. The dish-support system has a natural frequency of 4 Hz.
Determine the mean square response and the probability of the dish exceeding a
vibration amplitude of 0.132 m. Assume ^ = 0.05.

S(»v) =

100x10^

Figure P13-35.

13-36 A jet engine with a mass of 272 kg is tested on a stand, which results in a natural
frequency of 26 Hz. The spectral density of the jet force under test is shown in Fig.
P13-36. Determine the probability of the vibration amplitude in the axial direction of
the jet thrust exceeding 0.012 m. Assume C= OlO-