Vibroacoustic Simulation. Alexander Peiffer
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Название: Vibroacoustic Simulation

Автор: Alexander Peiffer

Издательство: John Wiley & Sons Limited

Жанр: Отраслевые издания

Серия:

isbn: 9781119849865

isbn:

СКАЧАТЬ asterisk Baseline left-parenthesis bold r right-parenthesis d bold r"/> (2.162)

      and the power radiated by a plane wave through the same area S is given by (2.47)

       normal upper Pi 0 equals one-half upper S rho 0 c 0 mathematical left-angle ModifyingAbove v With caret Subscript z Superscript 2 Baseline mathematical right-angle Subscript upper S (2.163)

      The radiation efficiency is defined as the ratio between the radiated power of a velocity profile vz(r) of a surface S and the standardized power of the plane wave:

       sigma Subscript normal r normal a normal d Baseline equals StartFraction normal upper Pi Over normal upper Pi 0 EndFraction equals StartStartFraction normal upper Pi OverOver StartFraction upper S Over 2 EndFraction rho 0 c 0 mathematical left-angle ModifyingAbove v With caret Subscript z Superscript 2 Baseline mathematical right-angle Subscript upper S Baseline EndEndFraction (2.164)

      The radiation efficiency is used to determine the radiated power of vibrating structures from calculated, estimated, or measured radiation efficiency of specific surfaces

       normal upper Pi equals StartFraction upper S Over 2 EndFraction sigma Subscript normal r normal a normal d Baseline rho 0 c 0 mathematical left-angle ModifyingAbove v With caret Subscript z Superscript 2 Baseline mathematical right-angle Subscript upper S Baseline equals upper S sigma Subscript normal r normal a normal d Baseline rho 0 c 0 mathematical left-angle v Subscript z comma rms Superscript 2 Baseline mathematical right-angle Subscript upper S (2.165)

      2.8 Units, Measures, and levels

      The dynamic range of acoustic quantities can be very high; thus, a logarithmic scale is well established for the quantification of acoustic signals. For convenience a certain time averaged quantity, for example the mean square pressure ⟨p⟩T2=prms2, is compared to a mean square reference value pref2. The pressure level in decibels is defined as follows:

       upper L Subscript p Baseline equals 10 log Subscript 10 Baseline StartFraction p Subscript normal r normal m normal s Superscript 2 Baseline Over p Subscript ref Superscript 2 Baseline EndFraction equals 20 log Subscript 10 Baseline StartFraction p Subscript normal r normal m normal s Baseline Over p Subscript ref Baseline EndFraction with p Subscript ref Baseline equals 20 mu Pa (2.166)

      The factor of 10 is introduced to spread the scale. Linear quantities such as pressure, velocity, or displacement use the mean square values. As level and decibel are used on time signals too, one should not apply the decibel scale to amplitudes. This may lead to confusion, as it is not clear if the mean square values of the amplitude is meant. This makes even more sense when the energy and power levels are defined. The energy must be averaged, as there is no constant value over the period – see Equation (2.46). Energy quantities such as energy, intensity, or power are compared with mean values and not mean square values; hence:

       upper L Subscript w Baseline equals 10 log Subscript 10 Baseline StartFraction normal upper Pi Subscript mean Baseline Over normal upper Pi Subscript ref Baseline EndFraction with normal upper Pi Subscript ref Baseline equals 10 Superscript negative 12 Baseline normal upper W equals 1 pW (2.167)

Source Source strength Impedance Velocity Pressure Radiated power
Mono pole Q,jωV Zrad=k2ρ0c04π p=jkρ0c0Q(ω)4πre−jkr
vr=Q(ω)4πrjk(1+1jkr)e−jkr Qrms2k2ρ0c04π
Breath. sphere Q=4πR2vr zR=jρ0c0kR1+jkR Q4πr[jkρ0c01+jkR]e−jk(r−R)
Q4πr2[1+jkr1+jkR]e−jk(r−R) Qrms2k2ρ0c04π(1+k2R2)
Piston Q=πR2vz zR=ρ0c0(1−J1(2kR)kR+jH1(2kR)kR) jωρ02πrvz[2J1(kRsin⁡ϑ)kRsin⁡ϑ]
ρ0c0(1−J1(2kR)kR+jH1(2kR)kR)Qrms2

      In addition, the decibel scale is used for ratios of similar quantities. A typical example is the transmission loss that is the decibel scale of the transmission factor from Equation (2.118) that relates the transmitted to the radiated power. The definition of the transmission loss (TL) is:

       TL equals 10 log Subscript 10 Baseline StartFraction 1 Over tau EndFraction equals minus 10 log Subscript 10 Baseline tau (2.168)

      The reciprocal definition was chosen in order to get positive values for losses. When linear quantities are compared, for example the pressure at two locations, the mean square values are related. When the squared pressure is compared to the situation with and without a specific equipment or installation, this is called insertion loss (IL)

       IL equals 10 log Subscript 10 Baseline StartFraction p Subscript out Superscript 2 Baseline Over p Subscript in Superscript 2 Baseline EndFraction equals 20 log Subscript 10 Baseline StartFraction p Subscript out Baseline Over normal p Subscript in Baseline EndFraction (2.169)

      The reference quantities for power and pressure are chosen conveniently to simplify the calculations with levels. Taking the equation for the spherical source (2.82) and dividing it by the squared reference value for the pressure yields

       StartFraction p Subscript normal r normal m normal s Superscript 2 Baseline Over p Subscript ref Superscript 2 Baseline EndFraction equals StartFraction rho 0 c 0 Over p Subscript ref Superscript 2 Baseline upper A Subscript ref Baseline EndFraction StartFraction upper A Subscript ref Baseline Over 4 pi r squared EndFraction mathematical left-angle normal upper Pi mathematical right-angle Subscript upper T (2.170)

      and taking the decibel of this

StartLayout 1st Row 1st Column 10 log Subscript 10 Baseline left-brace StartFraction p Subscript normal r normal m normal s Superscript 2 Baseline Over p Subscript ref Superscript 2 Baseline EndFraction right-brace 2nd Column equals 10 log Subscript 10 Baseline <a href=СКАЧАТЬ