Mechanical Vibrations Theory and Applications 1st. Edition by S. Graham Kelly | 9781439062128 | 1439062129 | Holooly

Mechanical Vibrations Theory and Applications [EXP-58302]

235 SOLVED PROBLEMS

Question: 13.5

(a) Determine the autocorrelation function for the process shown in Figure 13.10. (b) Verify that R(0) = E(y^2).

Verified Answer:

(a) The process is periodic of period T thus the a...

Question: 8.17

(a) Determine the natural frequencies for the three degree-of-freedom system shown in Figure 8.13. (b) Calculate and graphically illustrate the normalized mode shape vectors. (c) Demonstrate mode shape orthogonality.

Verified Answer:

The differential equations governing the system ma...

Question: 5.11

(a) Determine the transfer function for a SDOF system of natural frequency 10 rad/s and a damping ratio of 1.5 due to a force input. The mass of the system is 2 kg. (b)Find the response of the system due to a force F(t) = 10e^-3t

Verified Answer:

(a) The differential equation governing the motion...

Question: 13.2

(a) Find the probability distribution for the rectified sine wave p(y) over the half-period 0 ≤ t ≤ T/2. (b) Use p(y) to calculate the mean. (c) Use p(y) to determine y^2.

Verified Answer:

(a) The mathematical form of the rectified sine wa...

Question: 8.12

(a) Write the differential equations satisfied by the principal coordinates for the system of Example 8.2. (b) Find the relation between the principal coordinates and the original generalized coordinates and vice versa. (c) Motion of the system is initiated by moving the third mass a distance δ

Verified Answer:

(a) Recalling from Example 8.2, the natural freque...

Question: 4.20

A 100-kg lathe is mounted at the midspan of a 1.8-m simply supported beam (E = 200×10^9 N/m, I = 4.3× 10^-6 m^4). The lathe has a rotating unbalance of 0.43 kg. m and operates at 2000 rpm. When a free vibrations test is performed on the system it is found that the ratio of amplitudes on successive

Verified Answer:

The beam’s stiffeness is

k=\frac{48EI}{L^{...

Question: 5.17

A 1000-kg machine is subject to a triangular pulse of duration 0.05 s and peak of 20,000 N. What is the range of isolator stiffness for an undamped isolator such that the maximum transmitted force is less than 8000 N and the maximum displacement is less than 2.8 cm?

Verified Answer:

The force spectrum for the triangular pulse shows ...

Question: 4.5

A 150-kg electric motor has a rotating unbalance of 0.5 kg, 0.2 m from the center of rotation. The motor is to be mounted at the end of a steel (E = 210 * 10^9 N/m^2) cantilever beam of length m. The operating range of the motor is from 500 to 1200 rpm. For what values of I, the beam’s cross-sectio

Verified Answer:

The maximum allowable value of

\Lambda[/la...

Question: 2.2

A 200-kg machine is attached to the end of a cantilever beam of length L = 2.5 m, elastic modulus E = 200 × 10^9 N/m^2, and cross-sectional moment of inertia 1.8 × 10^–6 m^4. Assuming the mass of the beam is small compared to the mass of the machine, what is the stiffness of the beam?

Verified Answer:

From Table D.2 the deflection equation for a canti...

Question: 5.9

A 200-kg machine is to be mounted on an elastic surface of equivalent stiffness 2 ×10^5 N/m with no damping. During operation, the machine is subject to a constant force of 2000 N for 3 s. Can vibrations be eliminated without adding damping? If so, what is the maximum deflection of the machine?

Verified Answer:

The differential equation governing motion of the ...

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