560
15 Random Vibrations
Prob. 15.7
the mean square response and the probability of the tower exceeding a
vibration amplitude of 0.01 m. Assume = ζ0.02.
15.8 Following the steps given in Art. 15.10, determine the random response of
a shear beam due to a distributed random load.
15.9 For a random process having a constant spectral density diagram of magnitude S 0 over a band of frequency between ω 1 and ω 2 and zero outside the
band, determine the autocorrelation function.
15.10 Consider a random process
y(x, t) = A sin(kx − ωt)
in which k and ω are deterministic, but the amplitude A is random. The
probability density of A is shown in the figure. Determine E [Y ], E [Y
2
] and
R y (τ ).
Prob. 15.10
Prob. 15.11
15.11 For the frame shown in the figure, determine the mean square E [Z
2
] and
the autocorrelation function R z (τ ) of the relative displacement z, when the
ground acceleration ¨
x g (t) is idealised as white noise, with autocorrelation
R ¨
x ¨
x (τ ) = 2π S 0 δ(τ ) where δ(τ ) is the Dirac-delta function.