The noise control of minicar body in white based on acoustic panel participation method

2.1. Weakly coupled structure acoustic method

Passenger compartment cavity and BIW is a typical weakly coupled acoustic-structural system [31]. The control equations for coupling system can be got by integrating the control equations of structure and acoustic, which can be written as [24]:

In which, $x$ and $p$ are the displacement of structural node and pressure of acoustic node, respectively. $M_s$, $M_f$ and $A^T$ are the mass matrix of structure, air cavity and interface matrix of the structure acoustic, respectively. $C_s$ and $C_f$ represent damping matrix of structure and air cavity, respectively. $K_s$ and $K_f$ represent the stiffness matrix of structure and air cavity, respectively. $P_s$ and $P_f$ are the external excitation load imposing on structure and air cavity, respectively.

2.2. The theory of noise transfer function

The definition of NTF is that an external excitation imposes on structure and computes the acoustic frequency response of the point we interested, which is an important reference to evaluate the low frequency noise and acoustic sensitivity. Make the following assumptions before calculating the NTF [9]: The air is a continuous ideal fluid, heat exchange caused by temperature difference is not considered during sound transmission in air, and the vibration of BIW is small which satisfy the linear relationship between the structure vibration and acoustic pressure. A unit sine excitation $P_s=e^{i\omega t}$imposes on structure, where $\omega$ and $i$ is the angular frequency and plural unit, respectively. Set the steady-state responses of Eq. (1) are $x\left(\omega \right)={\rm X}{e}^{i\omega t}$and $p\left(\omega \right)=P{e}^{i\omega t}$. Substituting these relations into Eq. (1), we get the equation in frequency domain as:

According to Eq. (2), the acoustic pressure response of arbitrary point in cavity can be obtained:

The Eq. (3) is the NTF, and expresses it in the form of sound pressure levels ($SPL$) which is shown in Eq. (4), where the reference sound pressure $p_0=$ 2×10^-5 Pa, and the unit of $SPL$ is dB:

2.3. The method of acoustic panel participation

For different panels, the value of APP is different and can be classified into positive, negative and neutral contribution [24]. Assuming that the FE model of structure and air cavity have been established and the vibration displacement of the node $n$ of the panel $m$ is $x_{mn}\left(\omega \right)$, according to the relationship between normal vibration displacement of panel structure and sound pressure response (see Eq. (3)), the acoustic pressure caused by node vibration is calculated:

The acoustic pressure caused by panel $m$ is obtained by summing the sound pressure vectors caused by the vibration of nodes on panel $m$, which can be expressed as:

The total sound pressure $p\left(\omega \right)$ is the sum of sound pressures caused by the vibration of panels surround the cavity and can be written as:

The APP is applied to evaluate the acoustic participation of panel which is illustrated in Eq. (8). The physical meaning of APP is the projection of sound pressure caused by panel vibration. Eq. (9) is the acoustic panel participation factors (APP factors) of panel $m$:

Fig. 1The relationship between total sound pressure and acoustic panel participation

The relationship between total sound pressure and acoustic panel participation is shown in Fig. 1, in which, $\alpha$ is the angle between the sound pressure caused by panel vibration and total sound pressure. If $\left|\alpha \right|<$90°,$\mathrm{}\left|\alpha \right|=$90° or $\left|\alpha \right|>$90°, the vibration of panel $m$ are positive, neutral or negative contribution to total sound pressure, and with increasing the vibration displacement of panel $m$, the total sound pressure increases, keeps unchanged or reduces, respectively.

From the above analysis, it can be concluded that it’s crucial to identify the key acoustic panel before modifying panel structure for noise control. The measures that increase the vibration of positive acoustic contribution panel or decrease the vibration of negative acoustic contribution panel can be used to reduce the noise of target point. However, the traditional control method is to reduce the vibration of panel structures which vibrate strongly, and thus the vibration phase of panel structures are not considered.

3.1. FE model of coupling system

The pre-processing of FE model is realized in Hyperworks software, and the coupled model is computed in MSC.Nastran software.

3.2. Test verification for simulation model

To verify the reliability of simulation mode, the free modal testing of BIW is carried out which can be seen in Fig. 2. For the complexity of BIW structure, the data of many points need to be tested. The measurement method of multi-point excitation and multi-point output is carried out, and the vibration test data of 102 points are got.

Fig. 2Free modal testing of BIW structure

The modal results of simulation and experiment are shown in Table 1. It can be concluded that the modal vibration shapes agree well and relative errors of frequency are less than 5 % mostly, which indicate that the dynamic characteristic of BIW can be predicted well by the FE model.

4.1. Analysis of noise transfer function

A unit sine excitation of $Z$ direction imposes on the passive side of engine mounts respectively, and calculate the acoustic frequency response of driver’s right ear, which is the NTF from $Z$ direction of engine mounts to the driver’s right ear, as shown in Fig. 3. Where nodes 2001, 2002 and 2003 are the left, right and rear mount of engine respectively, node 9001 (0.223 m, 2.095 m, 0.960 m) is the position of driver’s right ear. The load cases are listed in Table 2.

Fig. 3Computational model of noise transfer function

Fig. 4Noise transfer function of each subcase

The NTFs of three paths are shown in Fig. 4. It can be seen from Fig. 4 that the values of $SPL$ (i.e. interior noise) are different for different transfer paths and the value of $SPL$ of path 3 is bigger especially at the low frequency band, the reason for this is that the transfer path from rear mount of engine (node 2003) to driver’s right ear (node 9001) is shorter. The NTFs of path 1 and path 2 are similar, because the BIW and cavity, excitation of subcase 1 and subcase 2 are symmetric about plane $Y$-$O$-$Z$ and the output point of sound pressure response (node 9001) is close to plane $Y$-$O$-$Z$. It is obvious that the NTFs have many peak noises in frequency band 20-200 Hz, and the critical frequencies are 31 Hz, 47 Hz, 59 Hz, 97 Hz and 148 Hz successively. Because the BIW is composed of many sheet metals and connected by welding, which have dense structure modes. If excitation frequency is close to a natural frequency of BIW structure, the vibration of BIW structure increases, which is easy to cause structural resonance and radiate noise seriously.

From the above analysis, it can be found that the interior noises are different for different transfer paths, and short transfer path has big interior noise. There are many critical frequencies in the excitation frequency band.

4.2. Analysis of acoustic panel participation

According to the NTFs analysis above, the values of $SPL$ are larger at frequency point 59 and 97 Hz, and the critical frequency 59 Hz which is a lower frequency is chosen to conduct APP analysis in this part. The $SPL$ values of driver’s right ear are 58.96 dB for subcase 1 and 2, 64.4 dB for subcase 3. The size, position and orientation of structure panels effect the noise in cavity, especially the large panels, such as the roof, floor, front dashboard and front windshield of BIW. The roof and floor are chosen as the research object of APP. The panel dividing methods of roof and floor are shown in Fig. 5. The roof is divided into 20 panels and numbered from P1 to P20, and the floor is divided into 28 panels and numbered from P21 to P48 (see Fig. 5). The position of beams and mounting holes are considered during dividing.

The APP analysis of roof and floor is carried out at frequency point 59 Hz, and the results of APP of roof at subcase 1 are shown in Table 3. It can be found from Table 3 that the values of panel sound pressure $p_m^{panel}$ and acoustic panel participation $p_m^{proj}$are different, the values of $p_m^{proj}$ of P1-P4 are bigger, the reason for this is that these panels are close to the output point of sound pressure response (node 9001). The value of $p_m^{proj}$ can be positive, negative or zero which is determined by the angle $\alpha$, which agrees well with the theory of Eq. (8). The $SPL$ value of driver’s right ear is 58.96 dB (59 Hz) at subcase 1 (see Fig. 4), according to Eq. (4), the effective value of total sound pressure (0.707 $P$) is 1.774×10^-2 Pa. Substituting the total sound pressure $P=$2.51×10^-2 Pa into Eq. (9), the APP factors $D_m$ at 59 Hz are obtained which are given in Table 3. The $p_m^{panel}$ value of P15 is 6.41×10^-4 Pa while the $p_m^{proj}$ value of this panel is small and negative, because $\alpha$ is bigger than and close to 90°. From the above analysis, it can be concluded that the value of acoustic panel participation $p_m^{proj}$ is decided by the value of panel sound pressure $p_m^{panel}$ and the angle $\alpha$.

Fig. 5Structure dividing methods of roof and floor

a) Dividing method of vehicle roof

b) Dividing method of vehicle floor

Fig. 6Results of acoustic panel participation of roof and floor (three subcases, frequency 59 Hz)

a) Acoustic panel participation of roof

b) Acoustic panel participation of floor

Fig. 6 shows the results of APP of roof and floor (three subcases, frequency 59 Hz). It can be seen from Fig. 6 that, the values of APP are different for different panels at the same subcase, and the values of APP are also different for same panel at the different subcases. The values of APP at subcase 1 and 2 are similar, because the BIW and cavity, panel dividing, excitation of subcase 1 and subcase2 are almost symmetric about plane $Y$-$O$-$Z$ and output point of sound pressure response (node 9001) is close to plane $Y$-$O$-$Z$. In terms of vehicle roof (see Fig. 6(a)), the APP values of P1-P4 and P17-P20 (i.e. the front and rear of roof) are big and positive, and according to the theory above the measure of reducing vibration of these panels will be effective to decrease the noise at 59 Hz. The APP values of P5, P6, P10, P11, P12, P15 and P16 are big and negative, and increasing the vibration of these panels will be feasible to control noise. For vehicle floor (see Fig. 6(b)), the APP values of floor are almost all positive and the results of P21-P26, P32, P34, P35, P41, P45-P47 are big, thus the measure of reducing vibration of these panels will decrease the noise at 59 Hz remarkably.

Using the APP analysis method, the acoustic participation property of panels are classified, the values are ranked as well as the key acoustic panels are identified from the complex structure of BIW. According to the above analysis, it can be found that the values of APP are different for different panels and the property of APP is determined by the angle $\alpha$. If $\left|\alpha \right|$ is smaller, bigger than or close to 90°, the APP values of corresponding panels will be positive, negative or zero.

4.3. Improvement of panel structure

There are three methods to control noise [33]: (1) Reduce the vibration or noise of excitation source; (2) Cut or attenuate the vibration transfer path between excitation source and noise receptor; (3) Protect the noise receptor. The second method, attenuating the vibration transfer path, is chosen to control the noise in cavity in this paper.

Fig. 7Structure improvement method of Opt_1

Fig. 8The 14th mode of BIW

The way to reduce the vibration of the main positive acoustic participation panels is adopted to control noise at 59 Hz. Because increasing the vibration of negative acoustic participation panels need to reduce the thickness of corresponding panels, and thus the thickness of roof and floor are not unified which is bad for once stamping forming of sheet metal. The damping layer (Young modulus $E=$5000 MPa, mass density $\rho =$1.4×10³ kg/m³, Poisson ratio $\mu =$0.45 and damping ratio 0.3) is pasted on P1-P4, P17-P20, P21-P26, P34, P41, P45-P47 and the thickness of it is 5 mm. A “U” section beam (length 420 mm, width 45 mm, high 35 mm and thickness 1.2 mm) is welded on the floor to reduce the vibration of P32, P35 and P41 (see Fig. 7), and the structure improvement based on APP method is denoted by Opt_1. The 14th structure mode of BIW (mode frequency 59.9 Hz) is nearest to critical frequency 59 Hz (see Fig. 8), and the large panels (roof, floor and left side wall of BIW) vibrate strongly which is easy to cause a big sound pressure in cavity. Thus, compared with other structure modes closing to 59 Hz, the way of pasting damping layer according to the 14th structure mode of BIW will control the sound pressure more effectively. The vibration of P50 and P51 (i.e. panels P5-P12 in Fig. 7) is larger while these panels are negative acoustic participation (see Table 3 and Fig. 6(a)), hence, the positions of strong vibration in mode are not always large acoustic participation which agrees with the above panel acoustic theory perfectly. The same damping layer is pasted on P50, P51, P52, P53, P54, and the beam of Opt_1 is welded on P55 to reduce the panel vibration. The structure improvement based on modal method is denoted by Opt_2 (see Fig. 8).

The NTFs of subcase 2 and subcase 3 are shown in Fig. 9 and Fig. 10, in which the original BIW is denoted by base mode (BM). The value of $SPL$ at 59 Hz decreases after panel structure improved, and the phenomenon is more obviously in subcase 2. It can be seen from Fig. 9 that, comparing the results of Opt_1 and BM, the peak value of $SPL$ around 59 Hz decreases from 58.91 dB to 52.14 dB (58 Hz), 6.77 dB reduced totally, however, the $SPL$ value of 47 Hz small increases. Comparing with the results of BM, the $SPL$ value of Opt_2 around 59 Hz decreases from 58.91 dB to 53.55 dB (59 Hz), 5.36 dB reduced totally. It can be found from Fig. 10 that, comparing with the results of BM, the $SPL$ value of Opt_1 around 59 Hz reduces from 64.61 dB to 60.48 dB (57 Hz), 4.13 dB reduced totally, while for Opt_2, the $SPL$ value of 59 Hz decreases from 64.61 dB to 61.07 dB (57 Hz), 3.54 dB reduced totally. The noise value at critic frequency reduces obviously after panel structures improvement, while the noise increases slightly at some frequency points. Compared with the results of Opt_2, the noise value of Opt_1 reduces more effectively which means that the panel structures improvement based on APP method control noise better. The mass of damping material used in Opt_1 is 10.5 kg and 11.2 kg in Opt_2, thus the structures improvement of Opt_1 control noise better with less damping material used. According to the above analysis, it can be found that the key acoustic panels are identified by using the panel acoustic analysis which makes the improving of panel structural more targeted, and this structural improvement method not only controls the interior noise better but also uses less damping material.

Fig. 9The noise transfer function of subcase 2

Fig. 10The noise transfer function of subcase 3

Fig. 11The VTF of node 10000 at subcase 3

Fig. 12Acoustic panel participation of P2 (Subcase 3)

Fig. 11 is the velocity transfer function (VTF) of node 10000 where the panel around is positive acoustic participation. The definition of VTF is that unit sine excitation imposes on structure and solve the velocity response of target point. It can be seen from Fig. 11 that, compared with the results of BM, the VTF of Opt_2 around 59 Hz decreases from 1.09×10^-4 m/s to 9.93×10^-5 m/s (57 Hz), 8.9 % reduce totally. The reason for this is that the stiffness of BIW increases slightly after pasting damping material and welding beam, and thus the vibration of node 10000 reduces. The VTF value of Opt_1 around 59 Hz decreases from 1.09×10^-4 m/s to 8.51×10^-5 m/s (57 Hz), 21.9 % reduced totally. Because the damping layer is pasted on panels P1-P4 specially, leading to the vibration of panels P1-P4 reduced as well as the vibration of node 10000 reduced. The APP of panel 2 at subcase 3 is shown in Fig. 12, where the node 10000 is on this panel. It can be found from Fig. 12 that the property of APP of each case keeps unchanged, while the value of it changes, and the APP value of Opt_1 decreases more. Because the APP value of P2 is positive (see Fig. 6(a) and Fig. 12), and the damping layer pasted on P2 of Opt_1 (see Fig. 7) which reduces the vibration of panel2 targeted decreases the acoustic participation of panel2. It can be known from Fig.11 and 12 that pasting damping material on positive acoustic panels reduces the vibration of these panels, which lead to the APP value decreased, the property of APP unchanged and the noise at critic frequency decreased at last. This agrees well with the theory of Section 2.3.

Fig. 13 shows the VTF of node 10001 where the panel around is negative acoustic participation. Focusing on the results in Fig. 13, the VTF value of Opt_2 around 59 Hz decreases from 2.92×10^-4 m/s to 1.09×10^-4 m/s (57 Hz), 62.7 % reduce totally, because the damping layer pasted on P50 (see Fig. 8) lead to the vibration of node 10001 reduced seriously. Compared with the results of BM, the VTF value of Opt_1 around 59 Hz decreases from 2.92×10^-4 m/s to 2.11×10^-4 m/s (57 Hz), 27.7 % reduce totally. The reason for this is that the stiffness of BIW increases after pasting damping material and welding beam. The APP of panel 6 at subcase 3 is shown in Fig. 14, where the node 10001 is on this panel. It can be found from Fig. 14 that the property of APP of each case keeps negative, while the value of it changes and the APP value of Opt_2 decreases more. The reason for this is that pasting damping material on P6 of Opt_2 (see Fig. 5(a) and 8) which reduces the vibration of P6 targeted decreases the value of the negative acoustic participation. It can be known from Fig. 10, 13 and 14 that, comparing the results of Opt_1 and Opt_2, pasting damping material on negative participation panels reduces the vibration of these panels, which lead to the APP value decreased, the property of APP unchanged and the noise at critic frequency increased at last. This also agrees well with the theory of Section 2.3.

Fig. 13The VTF of node 10001 at subcase 3

Fig. 14Acoustic panel participation of P6 (Subcase 3)