Sound radiation and transmission. Professor Phil Joseph. Departamento de Engenharia Mecânica

Sound radiation and transmission Professor Phil Joseph Departamento de Engenharia Mecânica

SOUND RADIATION BY A PISTON The piston generates plane waves in the tube with particle velocity equal to its own.

SOUND RADIATION BY A VIBRATING PISTON The sound wave generated by the piston has pressure amplitude p = 0 c 0 v where 0 c 0 is the acoustic impedance of air and v is the piston velocity amplitude. The sound radiated by the piston can be quantified using sound power. This is given by W rad 1 p. u S c S v 2 0 0 2 where S is the surface area of the piston, 2 v is the mean-square velocity. We can assess the sound radiation of other sources by comparison with this simple result.

SOUND RADIATION BY A MONOPOLE SOURCE A monopole represents a pulsating source

SOUND RADIATION BY A MONOPOLE SOURCE A dipole is typical of an oscillating source it is less efficient than a monopole

SOUND RADIATION BY A QUADRUPOLE SOURCE Quadrupoles are less efficient than monopoles or dipoles.

SOUND RADIATION BY A QUADRUPOLE SOURCE Quadrupoles are less efficient than monopoles or dipoles.

RADIATION OF SOUND BY A VIBRATING STRUCTURE Vibrations of most mechanical systems exhibit complex frequencydependent spatial distributions of amplitude and phase. But the sound power can be written simply as W rad c 2 0 0S v 2 v is the surface-averaged mean square normal velocity (over space) (over time) (perpendicular to surface) where S is the total surface area, 0 c 0 is the acoustic impedance of air, is called the radiation ratio or radiation efficiency L = 10 log 10 is called the radiation index (db re 1)

RADIATION OF SOUND BY A VIBRATING STRUCTURE W rad c 2 0 0S v When = 1 a structure radiates as efficiently as the 1-D piston. At low frequencies, << 1 (structure is small compared with acoustic wavelength) At high frequencies, 1 (structure is large compared with acoustic wavelength) NB > 1 is possible ( is not a true efficiency).

Radiation ratio EXAMPLE OF RADIATION RATIOS OF SIMPLE SOURCES Analytical solutions exist for a pulsating sphere or an oscillating sphere. These correspond to a monopole and a dipole source at low frequencies. 10 0 10-1 10-2 10-3 Monopole: Pulsating sphere f 2 Sphere radius 0.1 m Dipole: Oscillating sphere f 4 Real structures can be represented by these 10-4 Structure small simple models when they are small compared with compared with the 10-5 wavelength. 100 1000 Frequency [Hz] Transition frequency a=/3 f = 1.1 khz Structure large compared with

Radiation ratio EXAMPLE OF RADIATION RATIOS OF SIMPLE SOURCES e.g. An engine 0.60.350.2 m, surface area S rad = 0.8 m 2. Radius of equivalent sphere (S=4a 2 ) is 0.25 m. 10 0 10-1 10-2 10-3 Sphere radius 0.25 m Dipole: Oscillating sphere f 4 Transition frequency a=/3 f = 450 Hz 3a= f = c/ = c/3a = 450 Hz 10-4 Structure small compared with Structure large compared with 10-5 100 1000 Frequency [Hz]

Radiation index, db MEASURED RADIATION EFFICIENCY OF 24 DIESEL ENGINES 20 10 0-10 -20 dipole a = 0.25 m (+8 db) +/- standard deviation mean of 14 engines 100 1k 10k Frequency, Hz Radiation efficiency obtained from measurements of engine block vibration and 1 m L p. Similar to a dipole with roll-off around 400 Hz. Constant level of +8 db: noise from sump and valve cover, effects of the test cell and near field effects.

SOUND RADIATION FROM AN OPEN PIPE At low frequencies (ka < 1) most sound is reflected back by an open end and only a small amount of sound is radiated.

SOUND RADIATION FROM AN OPEN PIPE At high frequencies (ka > 1) much more sound is radiated by the open end.

DISPERSIVE AND NON-DISPERSIVE WAVES Dispersive waves have a wavespeed that depends on frequency.

Wavelength m EFFECT OF BLADE BLENDING For thin structures we need to consider the effect of bending modes in plates or beams. Acoustic waves in air have a wavelength air = c 0 /f where c 0 is the constant wavespeed (343 m/s). But bending vibrations in plates and beams have wavelengths B 1/f. There is therefore a frequency at which their wavelengths are equal, B = air. This is called the critical frequency. 10 1 0.1 0.01 air critical frequency 100 1k 10k Frequency Hz steel 10 mm 5 mm 2 mm 1 mm

Material f Young's modulus E, N/m 2 CRITICAL FREQUENCY c 1/ 2 0 2 2 12 m(1 ) c 2h Poisson's ratio, c0 1.8hc Density m, kg/m 3 hf c, m/s at 20C in air Steel 2.0 x 10 11 0.28 7800 12.4 Aluminium 7.4 x 10 10 0.33 2770 11.9 Magnesium 4.5 x 10 10 0.30 1800 13.5 Plastic 1.5 x 10 10 0.35 1410 19.1 Glass 6.0 x 10 10 0.24 2400 12.7 E The critical frequency is important for the radiation of sound from panels and the transmission of sound through partitions. e.g. Steel plate 1 mm thick: h = 0.001, f c = (12.4/0.001) Hz = 12.4 khz Note that hf c is similar for steel, aluminium or glass (because c L is similar). 2 L

RADIATION FROM PLATES IN BENDING At low frequencies f << f c : << 1 For an infinite plate with a free bending wave, the sound radiation is zero. This is because of acoustic short-circuiting between the radiation from maxima and minima of the vibration pattern. For a finite plate, the edges and corners result in a net radiation of sound: + + + + + + + + baffle cancellation residual

SOUND RADIATION BY A VIBRATING PLATE Below the critical frequency an evanescent field is created.

RADIATION FROM PLATES IN BENDING At high frequencies f > f c : 1 air radiated sound B Sound is radiated in a direction at an angle to the plate normal: air = B sin At the critical frequency, sin = 1, i.e. sound is radiated parallel to the plate.

SOUND RADIATION BY A VIBRATING PLATE Above the critical frequency sound is radiated to the far-field.

10 log, db re 1 EXAMPLE OF RADIATION RATIOS OF THIN PLATES 10 0-10 -20 plate 2.5 mm x 1 m x 0.3 m plate 5 mm x 1 m x 0.3 m plate 10 mm x 1 m x 0.3 m infinite plate 2.5 mm -30-40 31.5 63 125 250 500 1k 2k 4k 8k Frequency [Hz] critical frequency decreases as h increases. below the critical frequency acoustic short-circuiting reduces. thick (or stiff) plates radiate more noise than thin ones for a given vibration level.

Sound transmission

SOUND TRANSMISSION We often use walls, barriers or partitions to block out sound. Consider a sound field incident on a panel. Most of the sound is reflected, but due to motion of the panel, a small part is transmitted to the other side. The Sound Reduction Index, R (or transmission loss TL) is defined as R = 10 log 10 ( I i / I t ) [db] Reflected Incident Transmitted V where I i is the incident intensity and I t is the transmitted intensity. NB a large sound reduction index implies a good acoustic performance. Usually the sound reduction index is used for a diffuse incident sound field (equal intensity from all directions).

TYPICAL SOUND REDUCTION INDEX CURVE f c NB Mass law region applies over much of the frequency range of interest for automotive structures.

MASS LAW (between first panel resonance and critical frequency) For a plane wave normally incident on a panel of mass per unit area in air: R(0) 20log 10 2 c 0 0 where 0 c 0 is the characteristic specific impedance of air (= 415 rayls). R increases at 20 db/decade (6 db/octave). For air, the above expression reduces to: R(0) 20 log 10 (f) 42 e.g. for 1 mm steel at 1 khz, R(0) = 36 db.

MASS LAW (between first panel resonance and critical frequency) For a plane wave normally incident on a panel of mass per unit area in air: R(0) 20log 10 20c0 where 0 c 0 is the characteristic specific impedance of air (= 415 rayls). R increases at 20 db/decade (6 db/octave). For air, the above expression reduces to: R(0) 20 log 10 (f) 42 e.g. for 1 mm steel at 1 khz, R(0) = 36 db. For a diffuse field (plane waves assumed to propagate in all directions with equal probability), many measurements of real partitions suggest the following empirical formula applies in much of the frequency range: R d = R(0) 5 This approximation is sometimes called the field incidence sound reduction index. NB R d cannot be less than 0. The above formula is only valid for R(0) >> 0.

SUMMARY: SOUND REDUCTION THROUGH PARITIONS For practical automotive structures at most frequencies mass law applies. So Adding stiffening has no effect over much of the frequency range (it can make matters worse by lowering the critical frequency). Adding damping to the structure is only effective at high frequencies. Doubling the mass gives only a 6 db increase in transmission loss. Reducing vehicle mass will tend to worsen airborne noise transmission. Attention should be paid to weak points, close up gaps, etc.

DOUBLE SKIN PARTITIONS Double panels can give much increased transmission loss at high frequencies without significant increase in mass: R = R 1 + R 2. But only effective above: f 0 1 2 2 0 1.80c ( 1 2) d where d is the gap width and i is mass per unit area of panel i. 1 2 e.g. two 1 mm steel panels 1 cm apart are more effective than a single 2 mm panel above about f 0 =400 Hz. Below this, they behave like a single 2 mm partition. Also double windows. Vehicle trim materials often have a heavy barrier layer as well as foam layers to introduce this effect.

EFFECTS OF PLATE THICKNESS negative effect of increased thickness radiation efficiency is increased in the acoustic short-circuiting region. positive effect of increased thickness sound reduction index increased (mass law) 10 log 10 10 1m x 1m steel plate 0 R db 50 40 5 mm 2 mm -10 5 mm 30 1 mm -20 2 mm 20-30 1 mm 10-40 31.5 63 125250500 1k 2k 4k 8k Frequency [Hz] overall effect also depends on vibration level. 0 31.5 63 125250500 1k 2k 4k 8k Frequency [Hz] But not at all frequencies!

EFFECTS OF STIFFERNING RIBS Adding stiffeners to a plate increases its impedance. This is beneficial if the stiffeners are added where a force excitation acts (e.g. where a resilient mount is attached). Adding stiffeners to a plate reduces the acoustic shortcircuiting effect (lengthening the perimeter), hence increasing the radiation efficiency. 10 0 1m x 1m x 1mm steel plate -10-20 -30 4x4 ribs 4 ribs no ribs -40 31.5 63 125 250 500 1k 2k 4k 8k Frequency [Hz]

INSERTION LOSS When a sound reducing measure of any kind (e.g. an enclosure, a barrier, a resilient mount) is introduced, its effectiveness can be measured by its insertion loss. This is defined as the difference in sound pressure levels with and without the measure: IL = L p,without L p,with [db] If a sound source is surrounded by an enclosure, two opposite effects occur: The enclosure introduces attenuation, measured by TL. A reverberant field builds up inside the enclosure, increasing the level of the incident sound field by some amount L. Moreover for close fitting enclosures the sound power radiated by the source can be increased, also contributing to L. Then the insertion loss is given by: IL = TL L < TL To maximize the effect of an enclosure, absorption should be added to reduce the reverberant field and hence L. If no absorption or damping is present, IL 0.

EXAMPLE OF ENGINE ENCLOSURE