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Normal Modes

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Joanna Barzycki

on 9 January 2015

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Transcript of Normal Modes

Normal Modes
What is a Normal Mode?
pattern in the motion of an oscillating system
sinusoidal movement
same frequency
boundary conditions - no oscillation
constructive interference
string instrument harmonics
Millennium Bridge
Aim of the Experiment
Study the transverse vibration modes of a continuous system

- bare wire
identify the normal modes
determine the properties of the wire
Study the transverse vibration modes of a non-continuous system

- weighted wire
identify the normal modes
extract the frequencies of an impulse response using a Fourier Transform
Continuous Results
Continuous - Bare Wire
wire held under tension
alternating current passed through the wire
electromagnetic fields interact
Lorentz Force acts on the wire
wire oscillates with same frequency as alternating current
sinusoidal pattern achieved when frequency of forced oscillations matches one of the normal modes
Non-Continuous - Weighted Wire
Non-Continuous - Weighted Wire
identical wire weighted with 6 equal weights
wire held under tension
vibration generator used to oscillate the wire
wire oscillates with same frequency as vibrator
sinusoidal pattern achieved when frequency of forced oscillations matched one of the normal modes, as before
vibration sensor psu connected to PC
PC used a Fourier Transform to find the frequencies of oscillation
Jo Barzycki
2nd Year Lab Conference 2015
Experimental Set-Up
Experimental Set-Up
validated theory of continuous and non-continuous normal modes
no dispersion relation for the continuous system
sinusoidal dispersion relation for the non-continuous system
lower frequencies for the weighted wire compared to the bare wire due to a lower phase velocity
group velocity also lower for the weighted wire
only 6 normal modes for weighted wire due to 6 degrees of freedom
phase velocity is not equal to group velocity
sinusoidal dispersion relation
only 6 degrees of freedom
frequency response of the weighted wire was found for each harmonic
6 normal modes
odd modes only
6 nomal modes
very high response from second mode
Full transcript