How Should Damping Characteristics Be Designed for a Plane Landing System?

In summary, the conversation discusses the design of a damping system for an aeroplane's landing which needs to absorb ground energy within 5 seconds. The suggested approach is to use MATLAB to vary the spring stiffness and damping ratio until a smooth curve is obtained with an oscillation that dies after 5 seconds. The values of k (spring stiffness), C (damping coefficient), Cc (critical damping) and the use of unforced method are mentioned. The concern about the damping ratio being greater than 1, which indicates an over-damped system, is also noted. The possibility of using a forced method is also mentioned, but the calculation of the required force is not clear.
  • #1
Asim Riaz
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0

Homework Statement



If an aeroplane of a mass of = 5000 with a velocity of ̇ = 500/ℎ has to land on a daily
basis what would be your design characteristic of a damping system to absorb the ground energy
contact within 5 seconds.
Hint: Your answers may include:

i. The values of k (the spring stiffness), C (the damping coefficient), Cc (the critical damping) etc.

ii. Matlab code, graphs and comments to illustrate your solution.

Homework Equations

The Attempt at a Solution



as spring stiffness and damping ratio is not given in the question and I was told to keep changing the spring stiffness and damping ratio in MATLAB until you get a smooth curve, an oscillation which dies after 5 seconds. that is why i started with MATLAB, graph and coding is attached below.
i am using unforced method, not sure if it is right or not, my only concern is damping ratio. which is 4.5 in this case. normally if damping ratio < 1 ... it is under damped. if equal to 1 than critical damped. bigger then 1 over damped..
in my case it is bigger that 1 so must be over damped but graph looks like critical damped.

i tried this question with forced method as well. but i don't know how to calculate the force required
aircraft function.JPG
aircraft graph.JPG
few friends said F=kx, but i don't know how to calculate x in order to find F,
 
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What is a mass spring damper system?

A mass spring damper system is a mechanical system that consists of a mass, a spring, and a damper connected together. It is commonly used to model the behavior of objects that oscillate or vibrate, such as a pendulum or a car suspension system.

How does a mass spring damper system work?

The mass spring damper system works by utilizing the principles of Newton's laws of motion. The mass provides inertia, while the spring stores and releases energy as the mass moves. The damper dissipates the energy, reducing the amplitude of the oscillations.

What are the applications of a mass spring damper system?

A mass spring damper system has a wide range of applications in engineering, physics, and other fields. It is commonly used to model the behavior of mechanical systems such as car suspensions, buildings, and bridges. It is also used in control systems and in the design of musical instruments.

How do you analyze a mass spring damper system?

To analyze a mass spring damper system, you need to use mathematical equations that describe the behavior of the system. These equations take into account the mass, stiffness of the spring, and damping coefficient of the damper. By solving these equations, you can determine the motion of the mass over time.

What factors affect the behavior of a mass spring damper system?

The behavior of a mass spring damper system is affected by the mass, stiffness of the spring, damping coefficient of the damper, and the initial conditions, such as the displacement and velocity of the mass. Changes in any of these factors can affect the amplitude, frequency, and stability of the system.

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