Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
M3 C3 k2 C2 Figure Q1

M3 C3 k2 C2 Figure Q1

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
See similar textbooks
icon
Related questions
Question
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 oscillation 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, k; = (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 × 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] – w²[m]){Y} = 0. (d) Analyze the maximum vertical displacement at each floor when the system's natural 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 form as an illustration for wi, w2 > wi and w3 > w2 > wi.
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 oscillation 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, k; = (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 × 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] – w²[m]){Y} = 0. (d) Analyze the maximum vertical displacement at each floor when the system's natural 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 form as an illustration for wi, w2 > wi and w3 > w2 > wi.
Expert Solution
steps

Step by step

Solved in 3 steps with 4 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Dimensional Analysis
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.
Similar questions
Recommended textbooks for you
Elements Of Electromagnetics
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
Mechanics of Materials (10th Edition)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
Thermodynamics: An Engineering Approach
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
Control Systems Engineering
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
Mechanics of Materials (MindTap Course List)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
Engineering Mechanics: Statics
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY
SEE MORE TEXTBOOKS