Q2 The vibration in the vertical direction of an airplane and its wings can be modelled as a three-degree-of-freedom system with one mass corresponding to the right wing, one mass for the left wing, and one mass for the fuselage. The stiffness connecting the three masses corresponds to the wing and is a function of the modulus E of the wing. The equation of motion is: [100x₁ EI m0N 0₂ + -3 0 0 1 m where N=2.5 (i.e. the fuselage mass is N=2.5 times the wing mass). The model is shown in Fig. 2. Calculate the natural frequencies and mode shapes. Interpret the mode shapes in terms of the airplane's deflections in each mode. Use the following data: E=(7.1.10¹) Pa, l=3.5 m, m=3000 kg, and I= (1.05.10-5) m¹. k= 3 -3 6 0 -3 3EI 7³ Nxm m x₁(t) x₂ (1) Figure 2 EI 0 313-8 -3 x₂ k= 3EI x₂ (1) Nxm m x₂ (1) EI m x₂ (1)

Q2 The vibration in the vertical direction of an airplane and its wings can be modelled as a three-degree-of-freedom system with one mass corresponding to the right wing, one mass for the left wing, and one mass for the fuselage. The stiffness connecting the three masses corresponds to the wing and is a function of the modulus E of the wing. The equation of motion is: [100x₁ EI m0N 0₂ + -3 0 0 1 m where N=2.5 (i.e. the fuselage mass is N=2.5 times the wing mass). The model is shown in Fig. 2. Calculate the natural frequencies and mode shapes. Interpret the mode shapes in terms of the airplane's deflections in each mode. Use the following data: E=(7.1.10¹) Pa, l=3.5 m, m=3000 kg, and I= (1.05.10-5) m¹. k= 3 -3 6 0 -3 3EI 7³ Nxm m x₁(t) x₂ (1) Figure 2 EI 0 313-8 -3 x₂ k= 3EI x₂ (1) Nxm m x₂ (1) EI m x₂ (1)

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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Concept explainers

Properties of Fluids

The term fluid represents a type of substance that can easily change its shape under any external pressure/force and can flow. Fluids can acquire any shape in which it is stored and can resist normal stresses but cannot resist shear stress in rest condition. Whenever external shear stress is applied to fluids, it starts to flow. The fluids may be liquid or gas. Example- water, air, etc.

Question

Q2
The vibration in the vertical direction of an airplane and its wings can
be modelled as a three-degree-of-freedom system with one mass corresponding to
the right wing, one mass for the left wing, and one mass for the fuselage. The
stiffness connecting the three masses corresponds to the wing and is a function of the
modulus E of the wing. The equation of motion is:
[1 0 0x₁
m 0 N 0₂ +
0 0 1₂
m
xy (1)
EI
where N=2.5 (i.e. the fuselage mass is N=2.5 times the wing mass). The
model is shown in Fig. 2. Calculate the natural frequencies and mode shapes.
Interpret the mode shapes in terms of the airplane's deflections in each mode. Use
the following data: E=(7.1.10¹0) Pa, l=3.5 m, m=3000 kg, and
I= (1.05.10-5) m¹.
3EI
k=
3 -3 0
-3 6 -3
0 -3 3
Nxm
منه
Figure
x₁(t)
x₂
19
ΕΙ
3EI
k= 7³
x₂ (1)
Nxm
m
x₂ (1)
m
x3 (1)

Solve for the free response of the system in Problem 2 above,
following a gust of wind that causes the initial displacements of masses 1, 2, and 3 to
be x10=0 m, x20=0 m, x30=0 m respectively, and initial velocities to be be
m
m
V10=0.5
m
V20=0
V30=0
8
8
S
. Discuss your solution.

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