(a) Sketch a free body diagram for each steel grating that includes the mass's action and reaction forces.
Design Against Fluctuating Loads
Machine elements are subjected to varieties of loads, some components are subjected to static loads, while some machine components are subjected to fluctuating loads, whose load magnitude tends to fluctuate. The components of a machine, when rotating at a high speed, are subjected to a high degree of load, which fluctuates from a high value to a low value. For the machine elements under the action of static loads, static failure theories are applied to know the safe and hazardous working conditions and regions. However, most of the machine elements are subjected to variable or fluctuating stresses, due to the nature of load that fluctuates from high magnitude to low magnitude. Also, the nature of the loads is repetitive. For instance, shafts, bearings, cams and followers, and so on.
Design Against Fluctuating Load
Stress is defined as force per unit area. When there is localization of huge stresses in mechanical components, due to irregularities present in components and sudden changes in cross-section is known as stress concentration. For example, groves, keyways, screw threads, oil holes, splines etc. are irregularities.
![Q1 A three-level offshore platform located in the Helang Oilfield area has a 1500 kg floor
steel grating supported at each level. The structure sometimes is subjected to a vertical
ocillation movement during rough sea waves given by function of y(t) = Y sin ot
If the steel grating only moves in the vertical direction and is supported by one
equivalent spring and damper at each steel grating pole level with stiffness, k, = (300
xT) Nim, k= (200 x T) Nm and k = (100 × T) Ním while damping, c: = (15 x U)
Nsm, c: = (10 x U) Ns'm and c; = (5 x U) Nsim, respectively, as simplified in Figure
Q1. Neglect the effect of gravitational force.
Use
T=4 and U = 6
Table 1
5th digit of
matric number
6th digit of
matrix number
T
4
1
4
1
4
2
3
3
6
4
4
6.
5
3
6.
6.
2
6
7
2
7
1
6.
1
(a) Sketch a free body diagram for each steel grating that includes the mass's action
and reaction forces.
(b) Determine the equation of motion in a matrix form using Newton's second law,
[m]ÿ + [clý + [k]y = F.
(c) By omitting the damping and extermal force parameter, deduce and express the
general solution in the form of ([k] – w*[mHY) = 0.
(d) Analyze the maximum vertical displacement at each floor when the system's
natural frequency is equal to the extermal stimulation frequency. Assume non-
trivial solution and Fas() exhibits harmonic oscillation of sin 0.02t.
(e) Describe an eigenvector using a three-degree-of-freedom system's mode form
as an illustration for wi, w2 > Wi and w3 > w2 > Wi.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fb50f0e73-a2fd-43f4-92c6-9b4b486f1ff4%2F73427a99-1eb0-4062-a7a3-afc5261e57e3%2Fp8bscjj_processed.png&w=3840&q=75)
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