1. 2145-392 Aerospace Engineering Laboratory II Vibration of Beam
by NAV
NAV 2013

2. Vibration of Beam 1. Motivation 2. Introduction/Theory 3. Objectives
4. Apparatus
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3. 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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4. 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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5. 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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6. 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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7. 2. Introduction Vibration 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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8. 2. Theory
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?
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9. 2. Theory Three basic elements in a simplified vibrating system
the element restoring or releasing KE
mass or a mass moment of inertia
the element restoring or releasing PE
an elastic component or a spring
the element dissipating energy
Damper
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10. 2. Theory 
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.
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11. 2. Introduction How important are these quantities?
When the excitation frequency meets the resonance frequency / when the excitation is large
BIG vibration
Structural Failure
See movies
The Chinook resonances
The MD-80 landing
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12. 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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13. Modeling Wing 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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14. 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.
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