Random Vibrations Analysis of Structural and Mechanical Systems 1st. Edition by Lutes, Loren D.; Sarkani, Shahram | 9780750677653 | 750677651

Random Vibrations Analysis of Structural and Mechanical Systems [EXP-50496]

182 SOLVED PROBLEMS

Question: 11.8

A particular mechanical bracket has been subjected to constant-amplitude fatigue tests at the single level of Sr = 150 MPa, and the observed fatigue life was Nf = 10^6 cycles. Based on experience with similar devices, it is estimated that the parameter m of the S/N curve is in the range of

Verified Answer:

Beginning with

m=3

we find the va...

Question: 5.8

Analyze the response covariance for the SDF of Eq. 5.45 with c = 0 and k = 0.

Verified Answer:

Rather than looking for limits of the general expr...

Question: 5.9

Choose Go for a delta-correlated approximation of a stochastic process with autocovariance function GDD(τ)=Ae^-c|τ|

Verified Answer:

From Eqs. 5.65

G_{0}=\int_{-\infty }^{\inft...

Question: 11.7

Compare the Rayleigh and rainflow predictions of the fatigue life for the special case of a stationary, mean-zero, Gaussian stress process and an S/N curve given by Eq. 11.43 with m = l.

Verified Answer:

From Eqs. 11.50

E(\Delta D)=K^{-1}(2)^{3m/2...

Question: 11.4

Compare the ηX(U) values from Eqs. 11.17, 11.23, 11.25, and 11.26 for a stationary, mean-zero, Gaussian, narrowband process with α1= 0.995. (One particular process with this value of α1 is the response to white noise of an SDF oscillator with approximately 0.8% of critical damping.)

Verified Answer:

The basic upcrossing rate

\nu ^{+}_{X}(u) ...

Question: 11.5

Compare the ηX(u) values from Eqs. 11.28-11.30 with those obtained by other methods in Example 11.4 for a stationary, mean-zero, Gaussian, narrowband process with α1 = 0.995.

Verified Answer:

Using the Gaussian relationships and the Cramer an...

Question: 4.24

Consider a covariant stationary stochastic process {X (t)} for which the joint probability density function of X (t) and the derivative X (t) at the same instant of time is given by pX(t)X(t) (u , v) = 1/ π 2^1/2 u exp( -u^2 – v^2 / 2 u^2 ) Find the marginal probability density function pX(t) (u)

Verified Answer:

To find the marginal probability density function ...

Question: 6.3

Consider a linear system governed by the differential equation c x(t) + kx(t)=f(t) , for which the impulse response function was found in Example 5.1 as hx(t) = c^-1 e^-kt/c U(t) . Find the harmonic transfer function from the Fourier transform of hx(t) , as in Eq. 6.30, and compare with

Verified Answer:

From Eq. 6.30

H_{x}(\omega )=2\pi h_{x}(\om...

Question: 5.3

Consider a linear system governed by the differential equation m x(t) + c x(t) + k x(t)= f (t) The accompanying sketch shows one physical system that is governed by this differential equation, with m being a mass, k being a spring stiffness, and c being a dashpot value. This system is called the

Verified Answer:

Provided that

m\neq 0

, we can di...

Question: 5.2

Consider a linear system governed by the differential equation m x(t) + c x(t) = f (t) The accompanying sketch shows one physical system that is governed by this differential equation, with c being a dashpot value and f(t) the force applied to the mass m. Find the impulse function hx(t) such that

Verified Answer:

This time we obtain

m\frac{d^{2}h_{x}(t)}{...