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(a) Sketch a free body diagram for each steel grating that includes the mass's action and reaction forces.

(a) Sketch a free body diagram for each steel grating that includes the mass's action and reaction forces.

Elements Of Electromagnetics
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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y3 F;(1) 13 k3 C3 m2 | C2 V |F:(0) F;(t) k Figure Q1
Transcribed Image Text:y3 F;(1) 13 k3 C3 m2 | C2 V |F:(0) F;(t) k Figure Q1
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 × 4) N/m while damping, c;= (15 × 8) Ns/m, c2= (10 × 8) Ns/m and c3= (5 x 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]y + [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. (d) Analyze the maximum vertical displacement at each floor when the system's Oatural frequency is equal to the external stimulation frequency. Assume non- trivial solution and F1,2,3(t) exhibits harmonic oscillation of sin 0.02t.
Transcribed Image Text: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 × 4) N/m while damping, c;= (15 × 8) Ns/m, c2= (10 × 8) Ns/m and c3= (5 x 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]y + [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. (d) Analyze the maximum vertical displacement at each floor when the system's Oatural frequency is equal to the external stimulation frequency. Assume non- trivial solution and F1,2,3(t) exhibits harmonic oscillation of sin 0.02t.
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