Definition of decibel scaling used

The magnitude of a level in decibels is ten times the logarithm to the base 10 of the ratio of power-like quantities, i.e.

where: L = level of power-like quantity

X = quantity under consideration

XO = reference quantity of the same kind

A difference in the levels of two like quantities X1 and X2 is described by the same formula because, by the rules of logarithms, the reference quantity is automatically divided out as follows:

 

Where Transmissibility (insertion loss or gain) is defined as the non-dimensional ratio of the response amplitude of a system to the excitation amplitude. The ratio may be one of forces, displacements, velocities or accelerations. A doubling of level causes a 6dB increase, and a tenfold change is equivalent to 20dB. A positive insertion loss indicates a disbenefit, and conversely a negative insertion loss indicates a benefit.

The word 'disbenefit' is not currently in the English dictionary, although is used to convey the obvious interpretation.

Abbreviations used in Figures

SDOF single degree of freedom

FE finite element

Trans transmissibility

crit critical damping ratio

ch channel

psd power spectral density (auto spectrum)

col column

TR test room

V vertical

L longitudinal

T tangential

 

List of Symbols

Chapter 2

h depth of source

VP P wave velocity

VR Rayleigh wave velocity

VS S wave velocity

Chapter 3

aw frequency weighted acceleration

t time

VDV Vibration Dose Value

Chapter 5

(t) function of time

fS spring force

fD damping force

fI inertial force

k spring constant

c damping coefficient

cc critical damping coefficient

m mass

p, po applied force

u displacement

ù du/dt (velocity)

ü d2u/dt2 (acceleration)

ur relative displacement

U absolute displacement

ug ugo ground displacement

peff effective load

Z arbitrary complex constant

s constant

w n undamped natural angular frequency

w D damped natural angular frequency

x damping ratio

Z1, Z2 constants

A constant

B constant

C vector amplitude

q phase angle

G1 G2 constants

  • phase angle

    • y 1, y 2 phase angles

    M Dynamic magnification factor

    W work over cycle

    t time

    T transmissibility

    h , h o loss factor

    fn natural cyclic frequency

    j mode number

    w j angular frequency of mode j

    L length of column

    m integer

    E Young's modulus

    x j modal critical damping ratio

    w j angular frequency of mode j

    D w j frequency interval for mode j

    d m logarithmic decrement determined from waveform m cycles apart

    w a frequency point above resonance

    w b frequency point below resonance

    w r resonance frequency

    q a angle to point (a) above resonance

    q b angle to point (b) below resonance

    K constant

    i -1

    Re real

    Im imaginary

    Chapter 6

    Gxx auto spectra of stationary random process x(t)

    Gyy auto spectra of stationary random process y(t)

    Gxy cross spectra between two stationary random processes

    x(t) & y(t)

    Ttotal Total transmissibility

    Tdirect Direct transmissibility

    x(t) function of time (t)

    y(t) function of time (t)

    h(t ) unit impulse response function

    H(f) Fourier transform of impulse response function

    Y(f) finite Fourier transform of y(t)

    X(f) finite Fourier transform of x(t)

    g xy2(f) coherence function

    m mean value of a random variable

    Be effective bandwidth of spectral window

    T record length

    n number of adjacent spectral lines to the side of central value

    e b bias error

    Br half power point bandwidth at resonance

    x critical damping ratio

    fr resonance frequency

    e r random error

    To optimum averaging time

    Bo optimum bandwidth

    CT time resolution bias error coefficient

    Chapter 7

    Transmissibilities

    D1 test block to un-loaded raft

    D2 test block to raft loaded with un-isolated mass on 'rigid' blocks

    D3 test block to un-isolated mass

    D4 test block to isolated mass

    D5 test block to raft loaded with isolated mass

    D6 raft loaded with isolated mass to isolated mass

    Si = Component area

    a i = Component sound absorption coefficient

    W = sound power (watts)

    r c = characteristics impedance of air (407 mks rayls)

    Sx = area of radiating surface (m2)

    V = r.m.s velocity of vibration of surface (m/s)?

    SWL = Sound Power Level (dB) ?

    Wref = 10-12 watts

    SPL =Sound Pressure Level (dB re20m Pa)?

    S = total surface area of room (m2)

    Lp = SPL dB re 20Pa

    La = rms vibration acceleration of floor (re: 10-6g)

    f = frequency, either octave or 1/3rd octave

    Lv = Vibration re 10-5m/s2

    LAmaxf = A-weighted maximum SPL using fast time weighting

    Lvmax = vibration velocity re 10-9 m/sec

    Chapter 10

    Appendix 3.1

    aw frequency weighted acceleration

    VDV Vibration Dose Value

    eVDV estimated Vibration Dose Value

    aw(rms) r.m.s frequency weighted acceleration

    t event duration

    n event number

    N total number of events

    r.m.s root mean square

    r.m.q root mean quad

    Appendix 8.1

    F = force

    mr = mass x radius of gyration

    w = angular frequency

    Chapter 1