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

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