Download Vibration of Cantilever Beam

2145-362 Aerospace Engineering
Experimentation and Laboratory II
Vibration of Beam
by NAV
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Vibration of Beam
1. Motivation
 2. Introduction/Theory
 3. Objectives
 4. Apparatus
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1. Motivation
Aircraft Vibration
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Flaps/Ailerons/Rudders
Aircraft Vibration
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American Airlines flight 587
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November 2001
JFK to Dominican Republic
Crashed in New York
260+5 fatalities
Airbus A300
hit wake turbulence from the JAL
flight just in front of it.
Excessive use of alternating full
rudder inputs
separation of the vertical stabilizer
Aircraft Vibration
Source:
 Engine
 Pump
 Landing gear extension and
retraction
 Extension of speed brakes
Any concern?
 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 Vibration
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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.
2145-392 NAV 2012
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Aircraft Wing Vibration
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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. Vibration 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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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
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the element dissipating energy
 Damper
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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.
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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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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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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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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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