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Consider a simple model of an airplane which models the main body attached to the two wings as a cantilevered beam. The mass of the main body is 4 times the mass of each of the wings. The equations of motion for the transverse motion of the airplane are given as m₁₁ =k(x2x1) - - m2x2 = − k(x2 − x1) - k(x2 − x3) m33 =k(x2 - x3) where the transverse bending stiffness k = 3EI/1³, m1 = 3EI/1³, m1 = m3 = m and m2 = 4m. The parameter values are as follows: mass m = 1000 kg, Young's modulus E = 6.9 × 109 N/m², length of each wing = 2 m, and moment of inertial I = 5.2 × 10-4 m². Find and describe the mode shapes Confirm your description by plotting the position of the main body and wings in response to appropriate initial conditions for 1 second. (HINT: you may find the MATLAB command initial useful.)

Consider a simple model of an airplane which models the main body attached to the two wings as a cantilevered beam. The mass of the main body is 4 times the mass of each of the wings. The equations of motion for the transverse motion of the airplane are given as m₁₁ =k(x2x1) - - m2x2 = − k(x2 − x1) - k(x2 − x3) m33 =k(x2 - x3) where the transverse bending stiffness k = 3EI/1³, m1 = 3EI/1³, m1 = m3 = m and m2 = 4m. The parameter values are as follows: mass m = 1000 kg, Young's modulus E = 6.9 × 109 N/m², length of each wing = 2 m, and moment of inertial I = 5.2 × 10-4 m². Find and describe the mode shapes Confirm your description by plotting the position of the main body and wings in response to appropriate initial conditions for 1 second. (HINT: you may find the MATLAB command initial useful.)

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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Consider a simple model of an airplane which models the main body attached to the two wings as a cantilevered beam. The mass of the main body is 4 times the mass of each of the wings. The equations of motion for the transverse motion of the airplane are given as m₁₁ =k(x2x1) - - m2x2 = − k(x2 − x1) - k(x2 − x3) m33 =k(x2 - x3) where the transverse bending stiffness k = 3EI/1³, m1 = 3EI/1³, m1 = m3 = m and m2 = 4m. The parameter values are as follows: mass m = 1000 kg, Young's modulus E = 6.9 × 109 N/m², length of each wing = 2 m, and moment of inertial I = 5.2 × 10-4 m². Find and describe the mode shapes Confirm your description by plotting the position of the main body and wings in response to appropriate initial conditions for 1 second. (HINT: you may find the MATLAB command initial useful.)
Transcribed Image Text:Consider a simple model of an airplane which models the main body attached to the two wings as a cantilevered beam. The mass of the main body is 4 times the mass of each of the wings. The equations of motion for the transverse motion of the airplane are given as m₁₁ =k(x2x1) - - m2x2 = − k(x2 − x1) - k(x2 − x3) m33 =k(x2 - x3) where the transverse bending stiffness k = 3EI/1³, m1 = 3EI/1³, m1 = m3 = m and m2 = 4m. The parameter values are as follows: mass m = 1000 kg, Young's modulus E = 6.9 × 109 N/m², length of each wing = 2 m, and moment of inertial I = 5.2 × 10-4 m². Find and describe the mode shapes Confirm your description by plotting the position of the main body and wings in response to appropriate initial conditions for 1 second. (HINT: you may find the MATLAB command initial useful.)
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