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2145-392 Aerospace Engineering Laboratory II

Vibration of Beam

by NAV2145-392 NAV 2013

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Vibration of Beam

1. Motivation 2. Introduction/Theory 3. Objectives 4. Apparatus

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1. Motivation

Aircraft Vibration Engine Pump Landing gear extension and retraction Extension of speed brakes Wing

Normal? Low Vibration, background noise, turbulence Abnormal? Engine rotor imbalance, malfunction of

mechanical equipment, and airflow disturbances acting over doors

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Aircraft Wing Vibration Wing Fluttering

• Flutter is an unstable condition in which unsteady aerodynamics excite near or at the natural frequencies of the structure over which the air flows.

• The resulting vibrations can grow to a magnitude that causes the structure to fail.

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Aircraft Wing Vibration If the aircraft’s structure is low damped, it means that the

various natural frequencies of different parts of the aircraft’s structure do not dampen out and thus can ‘flutter’.

In worst case scenarios flutter is a potentially dangerous condition in which the vibrations of various parts of the structure become divergent – leading to structural failure

Flutter testing is important as it evaluates the aircraft’s stability and dampening modes at limit speeds and high altitude

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2. Introduction/Theory

Vibration is the branch of engineering that deals with repetitive motion of mechanical systems.

Examples: engineering structure to earthquakes

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2. IntroductionVibration Related Examples: unbalanced rotating machine -> shut-down, failure plucked string of a musical instrument -> sound ride quality of an automobile or motorcycle -> stiff,

smooth

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Only the most important features are considered in the analysis to predict the behavior of the system under specified input conditions.

The analysis of a vibrating system usually involves Step 1: Physical modeling Step 2: Mathematical modeling = derivation of the

governing equations Step 3: Solving the equations Step 4: Interpreting of the results (numerical, graphical,

etc).

Can we go backwards? Graphical results equation?

2. Theory

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Three basic elements in a simplified vibrating system the element restoring or releasing KE Þ mass or a mass moment of inertia

the element restoring or releasing PE Þ an elastic component or a spring

the element dissipating energy Þ Damper

2. Theory

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These elements are related to the behaviors of the

system subjected to various kinds of excitation To analyze the vibration problem, the quantities of

these elements must be determined via some measurements.

The natural/resonance frequencies are then calculated.

2. Theory

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How important are these quantities?

When the excitation frequency meets the resonance frequency / when the excitation is largeÞ BIG vibration Þ Structural Failure

See movies The Chinook resonances The MD-80 landing

2. Introduction

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3. Objectives To determine values of the basic quantities of a

simplified beam system i.e. the stiffness of the spring and the damping coefficient of a damper through experiments by observing the time response [displacement vs time graphs].

To study the vibration behavior of the system when the conditions/parameters vary.

Ultimate goal: To understand the vibration characteristics of a simplified aircraft wing and apply the understanding to (partially) design of wing structure

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ModelingWing flutters due to excitation e.g. from wind

Simplify the model of the wing as a beam

Continuous system with structural stiffness and damping

Physical model turns into a math model with a governing partial differential equation

Simplify more and make the mass “lumped” together

Simplify even more to get one rigid beam pivoted at the end with a spring and a damper

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4. Apparatus

The vibration testing apparatus “Universal Vibration”

It represents physical plants including rigid and flexible beams subjected to an unbalance force available free and damped vibration.