y3 F;(1)13k3C3m2| C2V |F:(0)F;(t)kFigure Q1 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 verticaloscillation 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, k; = (300x 4) N/m, k2= (200 × 4) N/m and k3= (100 × 4) N/m while damping, c= (15 × 8)Ns/m, c2 = (10 × 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] – w²[m]){Y} = 0.(d) Analyze the maximum vertical displacement at each floor when the system'snatural frequency is equal to the external stimulation frequency. Assume non-trivial solution and F1,2,3(t) exhibits harmonic oscillation of sin 0.02t.(e)Describe an eigenvector using a three-degree-of-freedom system's mode formas an illustration for wi, w2 > wi and w3 > w2 > wi.

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Answered: M3 C3 k2 C2 Figure Q1

Engineering

Mechanical Engineering

M3 C3 k2 C2 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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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.
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