The landing gear of an aircraft can be modelled as a spring-mass-damper system as illustrated in the figure below, where m is the mass of the aircraft, and k and care respectively the total effective stiffness and damping of the landing gear. When taxiing to the runway, the aircraft travels on an uneven surface, where the surface can be described by y(t) = yo sin wt, and with the peaks located a distance I apart. The system is designed so that whilst taxiing the amplitude of vibration of the aircraft is limited to 0.08 m. Tests of the landing gear system show that when the aircraft is stationary and is given an initial displacement and then released, after 2 complete oscillations the amplitude of the peak is 15% that of the initial displacement. We know that the mass of the aircraft is m = 2000kg, yo = 0.2m, l = 6.1m, and w = 7.6rads-¹. Hence determine the following: The damping ratio of the system, $ (non-dimensional): The speed at which the aircraft is moving whilst taxiing, V (m/s): The Transmissibility, TR (non-dimensional): The frequency ratio, ß (non-dimensional): The stiffness of the landing gear, k (N/m): 100 The damping coefficient of the landing gear, c (Ns/m): (HINT: From equation 4.3 in notes, consider how the forces can be rewritten to give an equation for transmissibility in terms of X and Y)
The landing gear of an aircraft can be modelled as a spring-mass-damper system as illustrated in the figure below, where m is the mass of the aircraft, and k and care respectively the total effective stiffness and damping of the landing gear. When taxiing to the runway, the aircraft travels on an uneven surface, where the surface can be described by y(t) = yo sin wt, and with the peaks located a distance I apart. The system is designed so that whilst taxiing the amplitude of vibration of the aircraft is limited to 0.08 m. Tests of the landing gear system show that when the aircraft is stationary and is given an initial displacement and then released, after 2 complete oscillations the amplitude of the peak is 15% that of the initial displacement. We know that the mass of the aircraft is m = 2000kg, yo = 0.2m, l = 6.1m, and w = 7.6rads-¹. Hence determine the following: The damping ratio of the system, $ (non-dimensional): The speed at which the aircraft is moving whilst taxiing, V (m/s): The Transmissibility, TR (non-dimensional): The frequency ratio, ß (non-dimensional): The stiffness of the landing gear, k (N/m): 100 The damping coefficient of the landing gear, c (Ns/m): (HINT: From equation 4.3 in notes, consider how the forces can be rewritten to give an equation for transmissibility in terms of X and Y)
Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)
8th Edition
ISBN:9781305387102
Author:Kreith, Frank; Manglik, Raj M.
Publisher:Kreith, Frank; Manglik, Raj M.
Chapter6: Forced Convection Over Exterior Surfaces
Section: Chapter Questions
Problem 6.32P
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There are a lot of subquestions in this question, but you can only answer a few of them, so I asked the exact same one twice, so please finish this one and move on to the next part, thank you!
Transcribed Image Text:The landing gear of an aircraft can be modelled as a spring-mass-damper system as
illustrated in the figure below, where m is the mass of the aircraft, and k and care
respectively the total effective stiffness and damping of the landing gear. When taxiing to
the runway, the aircraft travels on an uneven surface, where the surface can be described
by y(t) = yo sin wt, and with the peaks located a distance / apart. The system is designed so
that whilst taxiing the amplitude of vibration of the aircraft is limited to 0.08 m. Tests of
the landing gear system show that when the aircraft is stationary and is given an initial
displacement and then released, after 2 complete oscillations the amplitude of the peak is
15% that of the initial displacement. We know that the mass of the aircraft is m = 2000kg,
yo = 0.2m, l = 6.1m, and w=7.6rads-1. Hence determine the following:
The damping ratio of the system, (non-dimensional):
The speed at which the aircraft is moving whilst taxiing, V (m/s):
The Transmissibility, TR (non-dimensional):
The frequency ratio, ß (non-dimensional):
The stiffness of the landing gear, k (N/m):
The damping coefficient of the landing gear, c (Ns/m):
(HINT: From equation 4.3 in notes, consider how the forces can be rewritten to give an
equation for transmissibility in terms of X and Y)
Transcribed Image Text:Wheel
y(t)
Mass of
aircraft, m
Mass of
aircraft, m
k
Housing with
strut and viscous
damping
Tx(1)
the new damping ratio, Cnew
the new transmissibility, TRnew
Runway
1
A different aircraft travels over the same part of the airport whilst taxiing at 22 km/hr. This
aircraft has a mass of 5560 kg, and the stiffness and damping coefficient of the landing
gear of the new aircraft are respectively & = 28.3kN/m and c= 2.75kNs/m. Hence, for the
new aircraft, determine:
the new frequency ratio of the system, new
the vertical displacement of the aircraft whilst taxiing:
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