Homework Help is Here – Start Your Trial Now!
Engineering
Mechanical Engineering
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 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):

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

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!

https://www.bartleby.com/questions-and-answers/mechanical-engineering-question/4e2f464c-1131-4f1e-8638-7c84799e5239

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: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)
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:
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:
Expert Solution
steps

Step by step

Solved in 4 steps with 3 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Knowledge Booster
Convection
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