2145-362 Aerospace Engineering Experimentation and Laboratory II Vibration of Beam by NAV

Vibration of Beam 1. Motivation 2. Introduction/Theory 3. Objectives 4. Apparatus 2145-362 NAV 2016

1. Motivation Aircraft Vibration Flaps/Ailerons/Rudders

Aircraft Vibration American Airlines flight 587 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 2145-362 NAV 2016

Aircraft 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. 2145-392 NAV 2012

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 2145-362 NAV 2016

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? 2145-362 NAV 2016

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 2145-362 NAV 2016

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. 2145-362 NAV 2016

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 2145-362 NAV 2016

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 2145-362 NAV 2016

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 2145-362 NAV 2016

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. 2145-362 NAV 2016