GB2370939A - A curved or cylindrical bending wave loudspeaker panel - Google Patents

Abstract

A distributed mode loudspeaker comprises a curved or cylindrical panel 21, 31 having a predetermined radius of curvature and predetermined material properties, wherein the predetermined radius of curvature is such that the ring frequency of a cylinder of the predetermined radius and having the predetermined material properties lies at a predetermined ring frequency, and at least one transducer 22, 32 coupled to the panel at a predetermined location, wherein the acoustic output of a like transducer coupled to a like panel having the predetermined material properties but being flat, not curved, is uneven around a predetermined feature frequency, and the panel is curved such that predetermined ring frequency lies in the range 60% to 110% of the predetermined feature frequency for smoothing the panel response in this frequency range.

Description

TITLE : CURVED PANEL LOUDSPEAKERS

DESCRIPTION FIELD OF INVENTION This invention relates to loudspeakers that radiate sound from bending waves in a plate or panel, and concerns in particular, a form of that type of loudspeaker where the panel is curved.

BACKGROUND TO THE INVENTION A transducer is generally defined as a device that changes one form of energy into some other form. A loudspeaker is a transducer that converts an electrical signal into sound. Loudspeakers achieve this conversion by using the electrical signal to move some form of diaphragm.

This motion is imparted to the air in contact with the diaphragm and sound is thereby produced in the air.

Most loudspeakers utilise a diaphragm (most commonly a

stiff paper cone) which moves as a rigid surface, that is, all points on the diaphragm are moving with the same velocity and in the same direction at any particular instant in time. This sort of motion is referred to as "pistonic", since it resembles the reciprocating motion of a piston. Indeed, much effort has been invested in ensuring that the motion of the cone loudspeaker is truly pistonic and that it does not flex. Any resonant behaviour in the material of the cone, whereby the cone does not move as a rigid body, usually results in variations of the intensity of the resulting sound around the frequency of any such cone resonance. This means that the sound is no longer an accurate reproduction of the electrical signal.

This is an undesirable effect, and the resulting sound is judged by listeners to be"coloured"i. e. not a faithful reproduction. A good loudspeaker will reproduce the same level of sound at all frequencies, for the same electrical input level. A loudspeaker possessing this desirable characteristic is described as having a"flat frequency response".

It is well known that the sound radiated from a piston becomes directional at high frequencies, when the wavelength of the sound is of the same order as the aperture (i. e. the diameter) of the piston. This results in the high frequencies being radiated in a narrow"pencil beam"and as a consequence the frequency response (and hence the degree of"colouration") of the system varies according to whether the listener is located on the axis of

the loudspeaker or off to one side. For this reason (among others) manufacturers often use more than one pistonic drive unit in loudspeaker designs. Often three are used: a large speaker or"bass woofer"for low frequencies; a small speaker or"tweeter"for high frequencies and an intermediate size speaker for the mid-range frequencies. By electrically filtering the signal which drives the system into three separate frequency bands, and applying only the appropriately filtered signals to the three separate units, a uniform angular distribution of sound is obtained over the whole frequency range. This ensures that the problems outlined above are greatly reduced.

Quite recently, a new type of loudspeaker has emerged which uses a different approach. A flat panel is excited by a small"shaker" (a transducer which applies a force and vibrates the panel in sympathy with the applied electrical signal). Moreover, the panel is deliberately designed to move in flexure in this case without the colouration effect that would occur with a pistonic loudspeaker. Because many resonant modes of the panel take part in the radiation, this type of speaker has become known as a"distributed mode"flat panel loudspeaker, to distinguish it from other types which do not rely on resonant bending modes of the panel. The panel can also be large on a wavelength scale and yet not suffer the directionality problem above.

Such a device is shown in Figure 1. It is a loudspeaker consisting of a light, stiff panel 11, which is driven by a small electrodynamic"shaker"12. No details

of the shaker transducer are shown since this item could take many different forms-moving coil or magnet type or piezoelectric devices could be used. The panel responds in flexure, and the resultant bending waves in the panel radiate sound.

Motions in a direction normal to the panel couple more strongly to pressures in the external fluid than motions in the plane of the panel. Thus flexural (or bending) vibrations of the panel, associated with higher normal motions, are much more important to sound radiation than either compressional or shear vibrations. Unlike the sound speed in a fluid, the bending wave speed in a panel varies with frequency. The wave speed increases with frequency, and, for pure bending, is proportional to the square root of frequency. For an isotropic panel, there is a critical frequency known as the coincidence frequency. Here the bending wave speed (or, more precisely, the phase velocity) exactly matches the acoustic wave speed in the surrounding fluid. This situation is slightly more complicated for anisotropic materials, in that the single critical frequency becomes a range of frequencies over which this matching takes place.

The mechanisms for sound radiation are different above and below coincidence, so these regimes will be discussed separately in the next two subsections.

At frequencies above the coincidence frequency, the phase velocity of bending waves is supersonic: i. e. exceeds the speed of sound in the surrounding fluid. Thus the

bending wavelength AB is greater than the acoustic wavelength Ao. Because it is possible to match the bending wavelength on the panel to the acoustic wavelength at some radiation angle e (see Figure 2), these two sets of waves couple in a phase-coherent way, producing strong radiation in that preferred direction. The angle e is frequency

dependent and given by the equation : sin () =.

B In this supersonic regime the radiation efficiency is high.

The entire area of the panel effectively drives the radiated sound, and the radiated power is proportional to this area-so this phenomenon is referred to as area radiation (as opposed to edge radiation, see later).

Below coincidence the bending wavelength is less than the acoustic wavelength. The pressure at any notional receiver position can be regarded as the sum of contributions from all points on the panel. Unlike the above-coincidence case, these do not add in a phasecoherent way-that is, the contributions from different parts of the plate interfere destructively. Note that for an infinite panel this would mean zero power radiated. For a finite panel however, the coherent cancellation is not perfect and radiation occurs, usually from regions associated with the edges. The result is a radiated field which is statistically more uniform (omnidirectional) than that above coincidence.

The radiation efficiency of a flat panel in this subsonic regime is lower than it is above coincidence, and depends on the size and shape of the panel.

For most panel materials, one might expect that there would be a increase in radiated power at coincidence.

However, the original idea incorporated in W092/03024 is to provide a coincidence frequency as low as possible, coupled with low internal damping. Under these conditions the total damping of the panel is dominated by radiation damping down to a frequency some way below the coincidence frequency. This means that virtually all the energy injected is radiated at those frequencies. The average drive impedance of a flat plate is more or less constant, due to the constant modal density. Neglecting mode shape effects, each mode accepts the same power from a point force, so the resulting frequency response for bending waves is also flat. This fact, combined the radiation property mentioned above, means that the radiated sound frequency response is also flat, with no large peak occurring at coincidence.

The disadvantages of that approach are that the stiffness requirement implies low modal density; the damping requirement implies low modal overlap (i. e. a peaky response); and operating above coincidence implies a directional sound field.

A distributed mode speaker operates quite differently, since it does not rely on coincidence.

The density and bending stiffness of the panel is

chosen so that flexural (bending) waves are excited in the panel when the shaker applies a force. The transverse motion associated with these waves can radiate sound, and even though the panel may have many resonances, it has proved possible to produce such a speaker with a reasonably flat (though not perfect) frequency response. Because the motion is not pistonic (i. e. different parts of the panel are moving differently, and even in opposite directions), the sound is less prone to becoming directional at high frequencies, and quite large panels can be utilised without severe directionality problems arising.

However, peaks in the power response can occur through coincidence; the radiation just above coincidence can be higher than just below.

SUMMARY OF THE INVENTION According to a first aspect of the invention'there is provided an acoustic device comprising a curved panel having a predetermined radius of curvature and predetermined material properties, wherein the predetermined radius of curvature is such that the ring frequency of a cylinder of the predetermined radius and having the predetermined material properties lies at a predetermined ring frequency, and at least one transducer coupled to the panel at a predetermined location, wherein the acoustic output of a like transducer coupled to a like panel having the predetermined material properties but

being flat, not curved, is uneven around a predetermined feature frequency, and the panel is curved such that predetermined ring frequency lies in the range 60% to 110% of the predetermined feature frequency for smoothing the panel response in this frequency range.

The feature frequency is preferably the coincidence frequency, below which the power output may be reduced.

Alternatively the feature frequency may be a low (bass) frequency below which coupling to the panel is poor.

The exact value of the ring frequency will depend on the frequency and form of the feature to be smoothed. The ring frequency is preferably from 75% to 98% of the feature frequency, depending on the form and size of feature to be smoothed. Most commonly, the ring frequency chosen will be 90% 1 5% of the feature frequency.

According to a second aspect of the invention there is provided an acoustic device comprising a curved panel having a predetermined radius of curvature and predetermined material properties, and a transducer coupled to the panel, wherein the predetermined radius of curvature is such that the ring frequency of a cylinder of radius equal to the predetermined radius and having the same predetermined properties as the curved panel lies between 60% and 110% of a coincidence frequency of the curved panel.

Curvature couples motion of a panel perpendicular to the surface with in-surface motions. Quasi-bending

vibrations replace pure bending vibrations which have some in-surface distortion associated with them. These vibrations have a significant fraction of their strain energy in in-surface compression and shear. Effectively there is an increased stiffness associated with the vibrations, particularly for waves which transmit primarily along the cylinder, as opposed to around the cylinder.

This is the same effect that gives a corrugated shell its stiffness in the direction of the corrugation. Wave speed, hence also wavelength, increases with stiffness, so the wavelength of these quasi-bending vibrations is greater than that of their counterparts on the flat panel. Again the effect is most pronounced for waves transmitting primarily along the cylinder.

The above description applies, to a degree, at all frequencies. However the effect of curvature is most significant at a low frequency. In this context the ring frequency may be defined for the cylinder. In fact, two (or more) definitions of ring frequency can be found in the literature, and both are relevant in somewhat different ways to cylinder dynamics. However, numerically they are almost equal, differing only by a factor, which depends on Poisson's ratio. The simpler version of the two, used in

this patent application, is : = fR-CP 2) za where Cp is the compressional wave speed in a thin rod composed of the material of the cylinder, a is the radius

of curvature d f, is frequency in Hz.

The acoustic device may be a loudspeaker. In such cases, the extra sound output below the ring frequency may be used to alleviate any reduction in the power output of the loudspeaker just below coincidence.

The curved panel may be curved in two directions with the same or different radii of curvature. The panel may be isotropic, or anisotropic; such anisotropic panels may have different bending stiffnesses and hence different coincidence frequencies associated with different axes.

In such cases, one of the ring frequencies may be arranged to be between 60% and 110% of the coincidence frequency, and the other may be arranged to have a frequency 5%-30% lower than the aforementioned ring frequency.

The ring frequency may have different values at different locations on the panel. For example the panel may be curled at the edges. The predetermined ring frequency may be, for example, the ring frequency in the curled edge region, or indeed the ring frequency at other locations. Curvature near the panel edges may be used to increase radiation from the panel modes below coincidence.

A range of ring frequencies may be used to provide power uplift over the frequency range.

Damping may be provided to further improve the acoustic properties of the panel.

In order to alleviate the fall-off of response at low frequency and obtain an even power response, a high

impedance drive may be used. A piezoelectric drive of the type known as a piezoelectric shear drive may be particularly useful in this respect.

Further improvement may be obtained with anisotropic materials. In particular, the increased stiffness caused by the curved surface of the cylinder might be offset by reducing the stiffness in one direction. In particular, the stiffness of the panel material may be intrinsically higher for bending along the axis than for bending along the direction tangential to the circumference.

An elliptic cylinder may be driven on its minor axis to obtain a lower impedance drive.

BRIEF DESCRIPTION OF THE DRAWINGS The invention will now be described, though by way of example only, with reference to the accompanying diagrammatic drawings in which: Figure 1 is a schematic drawing of a known flat panel distributed mode loudspeaker; Figure 2 illustrates sound emission above coincidence; Figure 3 is a schematic drawing of a distributed mode loudspeaker in which the panel has been given curvature in both directions; Figure 4 is a schematic drawing of a distributed mode loudspeaker in the form of a cylinder; Figure 5 illustrates cylinder motion of a single angular order at a variety of frequencies; Figure 6 illustrates the axial dispersion

characteristic of a cylinder ; Figure 7 illustrates radiation losses as a function of angular order and frequency for a cylinder; Figure 8 illustrates power radiated for 1W input power for a cylinder; Figure 9 illustrates power radiated for IN point force applied to a cylinder; Figure 10 illustrates the power radiated for 1W input power by a 1m by 0.4 m plate for various radii of curvature; and Figure 11 illustrates the power radiated for IN point force applied to the same plates as for Figure 10.

BEST MODES FOR CARRYING OUT THE INVENTION Figure 3 shows an embodiment of the invention which uses a panel which is curved in just one direction, in the form of a cylinder 31, excited by a vibration transducer 32. One embodiment of this form of the invention could simply be a single-curved panel, but the radiation properties of a complete cylinder are more easily calculated.

In accordance with the invention, the ring frequency of the cylinder is arranged to be 5% below the coincidence frequency to enhance the power output just below coincidence.

Figure 4 shows a similar loudspeaker to that of the prior art Figure 1, but using a panel 21 which is curved in two directions, and a transducer 22 which applies a dynamic

force. The curvature of the panel has an effect on the velocity of bending waves in the panel. Effectively, the curvature makes the panel stiffer from the point of view of flexure, and this is responsible for the higher wave speed.

Taken to the extreme, a spheroid would represent an embodiment of this form of invention.

Theoretical results will now be presented. Basically, the symmetry of a cylinder allows its motion to be described as a set of one-dimensional problems, each corresponding to a particular waveguide mode having the form cos (noce) cos (kz-rot) in cylindrical polar coordinates, with the cylinder axis in the z-direction. Each integer "angular order"nc has a"cut-on"frequency, below which no modes of axial propagation exist. Figure 5 illustrates the motion on the cylinder excited at one end, for a high angular order (a) below cut-on, (b) at cut-on and (c) and (d) above cut-on. Below cut-on, no modes propagate to the end of the cylinder.

Figure 6 below illustrates the effect of the increased stiffness, due to curvature, on the dispersion characteristic. Frequency is plotted against axial wavenumber for the first 21 values of angular order nc (i. e. 0 to 20). The interesting thing is that below the ring frequency the lower angular orders fold over and are in reverse frequency order to what happens at higher frequencies. Increasing frequency actually favours lower angular orders (i. e. lower circumferential wavenumbers). At

these low frequencies and angular orders the phase velocity of these quasi-bending waves is higher than the corresponding waves on a flat panel, in some case much higher, even approaching the compressional wave speed of the material of the panel. Over a significant proportion of the possible wave transmission directions, the phase velocity can exceed the sound speed in the surrounding fluid. These components of the panel vibration are supersonic, and consequently have associated with them much higher radiation efficiency, in excess of 1.0, in a similar way to modes above coincidence on a flat panel shown in Figure 2.

Figure 7 shows the result of calculations of the radiation losses from a cylinder having a flat-plate coincidence frequency well above the ring frequency. The dotted line represents the cut on frequencies for each angular order (i. e. axial bending waves can only exist above that line).

The value of the radiation loss factor is represented as a variable length horizontal stripe. It is clear that there is radiation above the flat-plate coincidence frequency, but there is also radiation at much lower frequencies due to the lower angular orders. If we average across angular orders in Figure 7 we can produce an overall radiation efficiency.

Below coincidence there would be no radiation from the equivalent infinite flat plate. However, for a finite length cylinder the radiation efficiency is much higher

than the equivalent flat plate value. The radiated sound power is also proportional to the area of the plate rather than its perimeter.

However, because the effect depends upon frequency and the direction of bending wave propagation, and because the panel itself is curved, the resulting radiation will not have the undesirable directional characteristics of the above-coincidence equivalent on the flat panel.

With this graph, the idea of the invention can be explained. If the ring frequency can be arranged at the correct level, the modes just below the ring frequency can complement the power response to produce a combined response which may be smoother or otherwise improved.

Note that so far we have been discussing cylinders of infinite length. There are of course end effects in the finite cylinder and in finite curved shells which will now be discussed.

Figure 8 shows the power radiated from a flat plate and several different cylinders of the same surface area, made of the same material. For reasonable"speaker-size" cylinders made of very light, stiff materials, the ring frequency is generally already higher than the coincidence frequency, and accordingly of little practical benefit.

Consequently, for illustration of the principle, we have chosen a fairly large cylinder (1m radius x 5m length) made from a less stiff material (aluminium). The ring frequency for this realisation is about 1kHz and we have looked at differing thicknesses of shell in order to vary the

coincidence frequency. Figure 8 shows the calculated power for four different cylinders driven with 1 Watt input mechanical power, compared with equivalent size flat panels. The coincidence frequency varies between about 10 kHz (a) and 1kHz (d).

It is clear from figure 8 (a, b and c) where the coincidence frequency is well above the ring frequency that there is a region between the ring frequency and the coincidence frequency where there is a much-reduced efficiency of radiation.

As the coincidence frequency is reduced to arrive at a loudspeaker according to the invention (by thickening the shell) this region disappears when the ring and coincidence frequencies are close (Figure 8d) and the cylinder radiates more sound than the flat plate below coincidence. Indeed, there is an order of magnitude difference in the radiated powers of the cylinder and flat plate.

Note that we have assumed a 1% damping factor in these calculations. The power radiated may be slightly affected and adjusted by higher internal damping, if that were appropriate. The response of the cylinder in Figure 8 (d) is also much smoother around coincidence than that of the flat plate.

There is however a down side to this improved efficiency of radiation achieved by the stiffening effect of curvature. The increased stiffness increases the driving point mechanical impedance, requiring more force than the flat plate to obtain the 1 Watt input that Figure

8 refers to.

Figure 9 shows the power radiated for a 1N point force applied to the plate and cylinders, for the same set of parameters used in Figure 8. The response falls off below the ring frequency. This effect might be less with a large area of excitation. Indeed, curvature of the panel in the same direction that a shear transducer applies its force may well benefit the coupling to bending waves. We now consider a more"useable"configuration of a plate with a large radius of curvature rather than a closed cylinder.

Here edge radiation will play a much more significant rle than was the case with the large cylinder above.

Figure 10 shows a set of results along similar lines to those of Figure 8, but for three radii of curvature and a flat version. Each panel measures 1m x. 4m, with the curvature along the longer side. Again we can see that curvature can have what at first sight appears to be an advantage. Coincidence is just off the frequency scale.

Its presence is indicated by the rise in the flat plate radiated power at the highest frequencies plotted. Again, curvature appears to give a decided advantage.

If we examine the effect on the driving point impedance however, we see the same increased impedance as for the larger panel. Figure 11 shows the power radiated from the same set of panels driven with a 1N point force.

In fact, it now looks as though the edge radiation in the flat plate is more effective at the lowest frequencies than the stiffening effect in the cylinder, since the flat panel

radiated power exceeds that of all the curved plates. The fall-off of the response of the curved plates below the ring frequency is due to the fact that less energy is injected, so the corresponding edge modes cannot radiate as much as those in the flat plate Note that there is still the possibility of placing the peak around the actual ring frequency (where the radiated power is still much higher than the flat plate edge radiation) at a feature frequency where the practical speaker response fails due to not being able to achieve sufficient force. It is, in effect, possible to use the ring frequency to give the same sort of boost to the response as a"bass-reflex"design does in traditional pistonic speaker technology.

Other features, especially dips in acoustic response, may also be smoothed in accordance with the invention by placing the ring frequency around the frequency of the feature.

Claims (13)

1. An acoustic device comprising a curved panel having a predetermined radius of curvature and predetermined material properties, wherein the predetermined radius of curvature is such that the ring frequency of a cylinder of the predetermined radius and having the predetermined material properties lies at a predetermined ring frequency, and at least one transducer coupled to the panel at a predetermined location, wherein the acoustic output of a like transducer coupled to a like panel having the predetermined material properties but being flat, not curved, is uneven around a predetermined feature frequency, and the panel is curved such that predetermined ring frequency lies in the range 60% to 110% of the predetermined feature frequency for smoothing the panel response in this frequency range.

2. An acoustic device according to claim 1, wherein the feature frequency is the coincidence frequency.

3. An acoustic device according to claim 1 or claim 2, wherein the ring frequency is in the range from 75% to 98% of the feature frequency.

4. An acoustic device according to claim 3, wherein the ring frequency is 90% t 5% of the feature frequency.

5. An acoustic device comprising a curved panel having a predetermined radius of curvature and predetermined material properties, and a transducer coupled to the panel, wherein the predetermined radius of curvature is such that

the ring frequency of a cylinder of radius equal to the predetermined radius and having the same predetermined properties as the curved panel lies between 60% and 110% of a coincidence frequency of the curved panel.

6. An acoustic device according to any preceding claim, wherein the acoustic device is a loudspeaker, and wherein the transducer is arranged to apply bending wave energy to cause the panel to radiate an acoustic output.

7. An acoustic device according to any preceding claim, wherein the curved panel is curved in two directions with the same or different radii of curvature.

8. An acoustic device according to any preceding claim, wherein the panel is anisotropic and has different bending stiffnesses and hence different coincidence frequencies associated with different axes.

9. An acoustic device according to claim 8, wherein one of the ring frequencies is arranged to be between 60% and 110% of the coincidence frequency, and the other is arranged to have a frequency 5%-30% lower than the aforementioned ring frequency.

10. An acoustic device according to any preceding claim, wherein the ring frequency has different values at different locations on the panel.

11. An acoustic device according to claim 10, wherein the panel is curled at the edges and the predetermined ring frequency is the ring frequency in the curled edge region.

12. An acoustic device according to any preceding claim, wherein the transducer is of high impedance.

13. An acoustic device according to claim 12, wherein the transducer is a piezoelectric device of the type known as a piezoelectric shear driver.