Chapter 4: Complex Vibration and Waveform Analysis Flashcards
components
frequency components
(partials in music)
an individual element of a complex system ( e.g., a sinusoidal component of a complex waveform or a component of an electric circuit)
the sinusoidal vibrations that make up a complex vibration.
Fourier Theorem
any complex vibration is the sum of various sinusoidal motions of varying amplitude, frequency, and phase.
a theorem stating that any complex oscillatory (vibratory) motion is the sum of various sinusoidal motions of varying amplitude, frequency, and phase.
fundamental period
(To) the duration of one cycle.
the amount of time it takes to complete one cycle of complex periodic vibration
fundamental frequency
the lowest frequency of a vibrating system; the reciprocal of the fundamental period of a complex periodic wave.
(fo or f1) fo = 1/To
complex vibration
the sum of two or more simple vibrations.
aperiodic vibration
a vibration without a repeating pattern in time.
periodic vibration
vibratory motion in which an object returns to the same point in space periodically (at equal periods of time) during the motion.
waveform synthesis
the process of combining several individual sinusoidal motions into a complex waveform.
adding sine waves to form complex waveforms.
harmonics
frequency components of a complex waveform that are whole-number multiples of its fundamental frequency.
(f2 is the first harmonic for this class)
missing fundamental
when the greatest common factor of a group of harmonically related frequency components of a waveform is not present in the waveform, this waveform has a missing fundamental.
periodicity
the concept that a periodic wave keeps repeating itself for an infinite amount of time.
noise
a stochastic (random) sequence of events resulting from the combination of a very large (infinite) number of unrelated components.
transient
a brief single event that ceases to exist after a very short time (door slam)
complex inharmonic vibration
the sum of a finite number of components that does not repeat its pattern within a time period of observation.
waveform analysis
(spectrum analysis)?
taking a complex waveform and breaking it down into individual components
time domain
representation of a phenomenon as a function of time
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, displayed as lines perpendicular to the x axis, are called spectrum components (spectrum components, frequency components) Thus, the spectrum provides a graphical representation of the Fourier series of a complex vibratory motion.
frequency domain
representation of a phenomenon as a function of frequency.
line spectrum (discrete spectrum)
a spectrum that consists of one or more separate vertical lines.
continuous spectrum
a spectrum in which the energy is spread across a rang of frequencies rather that at discrete sinusoidal components.
white noise
a noise that consists of an infinite number of sinusoidal components having the same amplitude, but random phase, that spread evenly across a wide frequency range; a noise that has a spectrum density that is independent of frequency.
amplitude spectrum
the distribution of the amplitudes of the sinusoidal components of a vector quantity as a function of frequency.
power spectrum
a distribution of energy (power) as a function of frequency.
phase spectrum
(did he say to skip this?)
a spectrum display that indicate the initial ( t=0) phase angle of all the spectral components as a function of frequency
nodes
a point or line in space or along a vibrating element at which the magnitude displacement is zero for the mode of vibration.
where the string is attach to guitar.
antinodes
the place on vibrating system or in a sound field where the changes in a specific quality greatest
mode
the specific vibration pattern of a vibrating system associated with each resonance frequency of the system
octave
a relative unit of frequency in which one octave represents a doubling in frequency.
rod
a rigid, one dimensional structure made of a material such as metal or wood, which has a small cross section in comparison to its length and is round.
bar
a rigid, one dimensional structure made of a material such as metal or wood, which has a small cross section in comparison to its length and is square or rectangular.
transverse vibrations
when vibration is along a rod or bars length
torsional vibrations
when vibration is along a rod or bars axis.
plate
a two-dimensional physical object in which the thickness of the object is much smaller than the length and width and it can vibrate without any structured support.
radical mode
mode of vibration that runs across a plate or membrane.
circular mode of vibration
mode of vibration that runs in a circular manner in a plate or membrane.
chladni figures (patterns)
figures that illustrate the distribution of the various nodes of vibration of a plate.
impedance
the opposition to the flow of energy through a system
mechanical impedance
impedance of a mechanical system; depends on the mass, stiffness, and friction coefficient of the system.
resistance(R)
the opposition of a system to movement; resistance is the result of internal and external friction.
reactance (X)
the opposition of a system to change in its state by the system’s ability to store energy and prevent its transfer to or from another system
mass reactance (Xm)
the ability of a mass to store energy and prevent its transmission through a system.
stiffness reactance (Xs)
the ability of the stiffness of a system to store energy and oppose its passage through a system.
compliance (C)
the inverse of stiffness (K) that is C=1/K
admittance (Y)
the ease with which a system can vibrate due to an applied force; the inverse of impedance
conductance (G)
the ease with which energy travels through a frictional element in a system; the inverse of resistance.
susceptance (B)
the ease with which energy travels through a mass or spring (stiffness) element in a system; the inverse (reciprocal) of reactance (X)
mass susceptance (Bm)
the ease with which energy flows through a mass.
stiffness susceptance (Bs)
the ease at which energy travels through a spring element.
source and load (pg87)
to transfer the greatest possible amount of energy from one system to another, the impedance of both objects -the source and the load (receiver of energy)- should be equal.
impedance matching
the practice of making the impedance of a load equal the impedance of a source of power in order to transfer as much energy as possible from the source to the load.
membrane
a thin sheet-like material that is stretched and fixed along its edges to create stiffness. (ear drum)
overtone
a harmonic other than the fundamental frequency
cycle
one full repetition of a periodic motion
elasticity
the property of matter that allows matter to recover its form (size and shape) after it has been distorted (expanded or compressed).
