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24 terms

Complex Vibrations and Waveform Analysis

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Complex vibration
the sum of two or more simple vibrations
Frequency components or partials
the simple vibrations that make up a complex vibration
Fourier Theorem
states that any complex vibration is the sum of various sinusoidal motions of varying amplitude, frequency, and phase.
Aperiodic vibration
A vibrations without a repeating pattern in time
Periodic motion
a motion that repeats itself in regular intervals until it is stopped by external action
Period
the time it takes to complete a certain nubmber of cycles
measured in seconds
T = t/cycles
Frequency
the number of cycles per second
measured in Hz
F = cycles/t
Waveform Synthesis
The process of combining several individual sinusoidal motions into a complex waveform
Harmonics
Frequency components of a complex waveform that are whole-number multiples of its fundamental frequency
Greatest Common Factor
The fundamental frequency of a complex waveform; how we calculate fundamental frequency
Missing fundamental
A complex periodic wave in which no component is equal to the fundamental frequency; there is no energy at the fundamental frequency
Waveform Analysis
the process of breaking down a complex waveform and determine its components

shows amplitude and frequency
Spectrum
a graphical representation of a complex waveform showing the waveform energy (amplitudes) of the individual components (y axis) arranged in order of frequency (x axis)
Spectrum components
Individual components arranged in order of frequency
Continuous spectrum
When thousands of spectral components are in a spectrum they do not appear as individual lines, but because they are so close together, they cannot be differentiated from each other
Octave
The doubling of frequency
Impedance
The opposition to the flow of energy through a system

For a given force (F) applied to a mechanic system, the complex mechanic characteristics of the system affect its velocity (v)
F = Z x v

Measured in ohms
relates the velocity of a system to the force acting on the system
Compliance (C)
The inverse of stiffness (K)

C = 1/K
2 forms of Complex Vibration
1. Periodic
2. Aperiodic
Aperiodic
- Sloppy, cannot make out one period from the next
- Random
- Noise
Periodic
Repeating pattern
Frequency domain
the domain for analysis signals with respect to frequency, rather than time.
Periodic Motion
motion that repeates iteself in regular intervals until it is stopped by external action
Simple Sinusoidal Motions are graphed
as a function of time
the x axis indicates time
the y axis is the magnitude of a quantity