Q1 A three-level offshore platform located in the Helang Oilfield area has a 1500 kg floorsteel grating supported at each level. The structure sometimes is subjected to a verticalocillation movement during rough sea waves given by function of y(t) = Y sin wt.If the steel grating only moves in the vertical direction and is supported by oneequivalent spring and damper at each steel grating pole level with stiffness, k1 = (300x 4) N/m, k2= (200 × 4) N/m and k3= (100 x 4) N/m while damping, c= (15 × 8)Ns/m, c2 = (10 x 8) Ns/m and c3 = (5 × 8) Ns/m, respectively, as simplified in FigureQ1. Neglect the effect of gravitational force.(a) Sketch a free body diagram for each steel grating that includes the mass's actionand reaction forces.(b) Determine the equation of motion in a matrix form using Newton's second law,[m]ÿ + [c]ý + [k]y = F.(c) By omitting the damping and external force parameter, deduce and express thegeneral solution in the form of ([k] – w?[m]D{Y} = 0. y3 F;(1)13k3C3m2| C2V |F:(0)F;(t)kFigure Q1

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Answered: y3 F;(1) 13 k3 C3 m2 | C2 V |F:(0)…

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y3 F;(1) 13 k3 C3 m2 | C2 V |F:(0) F;(t) k Figure Q1

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

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 wt.
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, k1 = (300
x 4) N/m, k2= (200 × 4) N/m and k3= (100 x 4) N/m while damping, c= (15 × 8)
Ns/m, c2 = (10 x 8) Ns/m and c3 = (5 × 8) Ns/m, respectively, as simplified in Figure
Q1. Neglect the effect of gravitational force.
(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 + [c]ý + [k]y = F.
(c) By omitting the damping and external force parameter, deduce and express the
general solution in the form of ([k] – w?[m]D{Y} = 0.

y3 F;(1)
13
k3
C3
m2
| C2
V |F:(0)
F;(t)
k
Figure Q1

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