In the recent letter, Sui et al.1 claim that they created and tested sandwich material with a transmission loss (TL) of 35–55 dB (Figure 3) and 55 dB in (Figure 4) at a frequency of f = 200 Hz. Both sandwich constructions are tested in an impedance tube test bench as described by Song and Bolton.2 This test method provides the sound transmission loss of small, flat probes fixed in an impedance tube and excited by plane sound wave normal to the surface.
Simulated field transmission loss (TLfield) for an impedance tube specimen and a large size panel. Due to the stiffness effect and the high first resonance, the low frequency TL is heavily overestimated compared to real size panels.
Simulated field transmission loss (TLfield) for an impedance tube specimen and a large size panel. Due to the stiffness effect and the high first resonance, the low frequency TL is heavily overestimated compared to real size panels.
As mentioned by Bies and Hansen,3 e.g., the normal transmission loss (TLtube) measured in an impedance tube cannot be directly compared to the field transmission loss (TLfield) of specimen of realistic size measured in a two room configuration excited by a diffuse sound field. This is because of two reasons: first, the dynamics of the specimen with clamped boundary conditions is not representative for panels or sidewalls of realistic size, and second, the exciting wave field is a plane normal wave and not a diffuse sound field. In Figure 1 according to Ref. 2, the TLfield of a clamped panel is shown over the frequency range. Below the first resonance, the TL shows a negative slope resulting from the stiffness controlled dynamics. After the first resonance, the TL curve enters the mass controlled regime and later the coincidence controlled regime. The latter is very critical for noise and vibration control.
Typical TL as a function of frequency according to Ref. 3. In order to get a first resonance, the panel must be clamped at the boundaries. In twin room tests, this is hardly to achieve. Thus, the stiffness controlled slope can usually not be found in test results, but in simulations and for small specimen as used in impedance tubes.
Typical TL as a function of frequency according to Ref. 3. In order to get a first resonance, the panel must be clamped at the boundaries. In twin room tests, this is hardly to achieve. Thus, the stiffness controlled slope can usually not be found in test results, but in simulations and for small specimen as used in impedance tubes.
In order to illuminate the difference between TLtube and TLfield, we created finite element (FE) models of sandwich specimen similar to “sandwich panel w/o membrane” layup as shown in Figure 4 of the letter. The sandwich core of thickness t = 25 mm is assumed to be out of typical aerospace honeycomb with = 48 kg/m3, The skin plates are each 1 mm thick and out of quasi isotropic carbon fiber composite plastic (CFRP). Such sandwich plates are representative for flat panels in aerospace applications, except that the chosen skin thickness is much higher than for typical aircraft lining. The diameter of the cylindrical probe in the tube is D = 10 cm. Assuming simply supported boundary conditions (translations fixed and rotations free), we get one single mode at f1 = 1716 Hz below 2000 Hz (Figure 2).
Mode shapes of simulated sandwich specimen. Two CFRP skin with a honeycomb core. (a) First mode of impedance tube specimen at 1716 Hz, (b) first mode of 1 × 1 m2 panel at 90 Hz, and (c) mode 271 at 1999H.
Mode shapes of simulated sandwich specimen. Two CFRP skin with a honeycomb core. (a) First mode of impedance tube specimen at 1716 Hz, (b) first mode of 1 × 1 m2 panel at 90 Hz, and (c) mode 271 at 1999H.
A specimen of size 1 × 1 m2 was selected as a representative example for a realistic panel and an FE model of this structure created. Here, we get with the same boundary conditions 271 modes below 2000 Hz with the first mode at f1 = 90 Hz. Using those FE models, we calculated the field transmission loss of both using the hybrid method from Ref. 4 and also described by Peiffer et al.5 for TL configuration.
The results for the field transmission losses of both are shown in Figure 3. The very high TL in the low frequency area of the small size sandwich drops down tremendously for the large panel made out of the same sandwich material. The reason for this is that the dynamics of the small specimen cannot be compared to the large size panel. The small specimen is mainly operating in stiffness mode. Thus, such tests cannot be used to conclude on the low frequency performance, and all statements in the article related to the high TL at 200 Hz are not applicable for sidewalls or lining panels. Collings and Stewart6 have tested plasterboard panels in both test benches showing the same strong discrepancy between TLtube and TLfield. They provide the same explanation as given before.
The coincidence of structure- and fluid wavenumbers, which is considered as the most critical effect for the transmission loss in text books of engineering acoustics,3,6 is not discussed at all in this letter. Thus, a mandatory subject of noise control is not addressed.
The first specimen described in the letter is a honeycomb core covered with one latex rubber membrane on one side. The first membrane resonance of each hexagonal unit cell corresponds to the first resonance in Figure 1, here called “STL dip frequency.” As can be seen from the impedance tube test and the simulation in Figure 2(a) in this letter, the probe works in stiffness mode below 1100 Hz. Thus, the claimed performance is not relevant for noise control of real panels.
The mentioned “zero density effect” is caused by the resonance drop, but it is not related to any wavelength in the specimen at all because a membrane is considered as a limb element in an acoustic network like this. There is no decaying wave involved in the latex membrane; it works as a spring with given surface mass. The spring behavior is confirmed by the authors themselves in the next paragraph and in Equation (2) using the impedance formulation of for the stiffness of the membrane. If this expression is compared to the acoustic network presentation of a mass layer of mass per area : this would lead to the so called “negative mass” in the low frequency as mentioned in the letter.
In Equation (2), the mass of the membrane is missing. Thus, the expression will not be correct at the resonance dip. The correct expression for a membrane must include the mass of the membrane. If the mass is introduced in the membrane model, the lowest value of will occur at the resonance frequency, leading to “zero density” if damping is neglected.
In Figure 3 of the letter, the TLtube of the first specimen and a sandwich with both skins as latex membrane are shown. The higher TL in the low frequencies comes from the double stiffness caused by the doubled static stiffness of two membranes, so this assumption is correct. The authors argue that the different shape at resonance comes from the interaction of the two membranes and a “natural mode” of air between the membranes. In the estimation of this mode the authors consider only the normal mode of the air in the unit cell and neglect the mass of the membranes. This is the reason why the estimated frequency is too high. In text books like in Ref. 7, this mass-spring-mass resonance is called the double wall resonance at and is given by
This frequency will be significantly lower than 6.8 kHz and should explain the TL of the double latex skin sandwich.
The article finishes with a modification of the sandwich specimen with 2 CFRP skin. Here, a layer of latex rubber is introduced in middle of the core. No simulation results were shown, but experimental results from the impedance tube. The centered rubber layer is a typical measure for noise control and denoted as “constrained layer” damping. It is not aimed at the low frequency performances, which is mass law dominated. But this layer reduces the resonances, the coincidence effect, or structure borne noise; see Ref. 7 for details. The low frequency TLtube depends strongly on the boundary conditions of the specimen in the tube. The boundary conditions determine the stiffness of the probe, and therefore, the TLtube in the stiffness dominated frequencies. Thus, we assume that the improvement of TL results from the stronger clamping of the specimen with membrane and does not correspond to any improved TLfield.
In conclusion, we consider the presented results tested and simulated in an impedance tube context as irrelevant for noise transmission of real enclosures or airplanes. The authors did not seem to be aware of the theoretical framework of engineering noise control. Some of the derivations are not precise or not complete like Equation (2) and the estimation of the double wall resonance on page 4. The assumption that the transmission loss tested in an impedance tube below the first resonance frequency is similar to the diffuse field transmission loss of large size panels is not correct.
