# How to Model Aircraft Landing Gear Vibrations?

• pige
In summary, the conversation discusses a project for a vibrations course where the task is to analyze mechanical vibrations in an aircraft landing gear system. The speaker plans to model the system as a non-homogenous second order differential equation and is seeking help with deriving parameters such as damping ratio and equivalent spring constants. They also mention using MATLAB for quantitative analysis and generating data and plots for maximum passenger acceleration and gear displacement. The conversation also raises questions about reducing the system to a single second order system and specifying which part of the aircraft motion will be modeled.
pige

## Homework Statement

Working on a project for a vibrations course, task is to quantitatively analyse a system in which mechanical vibrations occur. I chose to model aircraft landing gear, for a variety of different airplanes, namely one large transport (747), a simple tricycle gear GA plane with cantilever suspension (Cessna 172), and either a taildragger or else another trike with an oleo type shock absorber.

## Homework Equations

I was planning on modelling the system as a non-homogenous second order differential equation, with the forcing function being some sort of impulse or sum of impulses (possibly using the Dirac Delta function or a convolution integral, but I still need to work that out). However, I was wondering if anyone would be able to help me to figure out or derive parameters such as damping ratio, equivalent spring constants, and also how factors like Weight and Balance, would affect the system response. I plan to do some quantitative analysis in MATLAB for this project, and what I would ultimately like to be able to do is to generate data and plots for maximum passenger acceleration and also gear displacement as a function of time.

Just a few questions for you to think about.

1. Before touchdown, the aircraft in the air has 6 rigid body DOF, in addition to all the many vibratory DOF. This is true for all of your three air craft types. Even on the ground, moving, it still has 6 DOF if we allow for the fact that the tires and shocks offer significant vertical motion, and all other motions are almost as free as they were in the air. How then do you propose to reduce this to a single second order (1DOF) system?

2. Might it be a good idea to specify in advance what part of the aircraft motion you are going to attempt to model, say perhaps the heave and pitch following touch down? Or will you be more ambitious and try to model things like the yaw motion? or the possible flutter of the nose wheel? Just how far are you going to attempt to go in your model? It would seem wise to spell out your goals in advance, otherwise you will never know where you have met them or not.

## 1. What factors affect the modelling of an airplane landing?

Several factors can affect the modelling of an airplane landing, including the aircraft's weight, speed, wind conditions, runway length and surface, and pilot input.

## 2. How do you determine the ideal approach and landing speed for an airplane?

The ideal approach and landing speed for an airplane is determined by considering the aircraft's weight, wind conditions, and runway length. This can be calculated using performance charts provided by the aircraft manufacturer or through advanced computer simulations.

## 3. What are some common techniques used in modelling an airplane landing?

Some common techniques used in modelling an airplane landing include mathematical equations, computer simulations, and physical scale models. Each method has its own advantages and limitations, and the choice of technique depends on the specific goals and resources of the study.

## 4. How do you account for human factors in the modelling of an airplane landing?

Human factors, such as pilot experience and decision-making, can greatly influence the outcome of an airplane landing. To account for these factors, researchers may conduct simulations with experienced pilots or use data from real-world flights to inform their models.

## 5. How accurate are the results from a model of an airplane landing?

The accuracy of the results from a model of an airplane landing depends on several factors, including the quality of the data and assumptions used in the model, the complexity of the scenario being simulated, and the chosen modelling technique. It is important to validate the model's results against real-world data and continuously refine the model to improve its accuracy.

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