# Vehicle Interior Noise Prediction Based on Elman Neural Network
## 2 Establish a Finite Element Model
### Modal Analysis  
In the automotive NVH performance design and optimization, the first-order global modal data must be fully considered because of the low first-order modal frequency value, which is easily excited by external excitations such as those in the engine and on the road surface, thereby leading to vehicle body resonance. Given that the first-order global modal acts as the overall modal of the vehicle body, the accessory parts of the vehicle body will vibrate at the occurrence of resonance  
as the fourth-order modal in this article. [PERSON] et al. [38] improved the first-order torsion modal frequency and the first-order bending modal frequency of the body-in-white through structural optimization, and the initial modal frequencies were 38.4 Hz and 51.5 Hz, respectively. The frequency of the first-order torsional modal is highly close to the frequency of the first-order torsional modal in this article. [PERSON] et al. [39] experimentally measured the modal frequency of the vehicle, the first-order modal is the roof local modal, and the modal frequency is 31.31 Hz. The frequency of the first-order torsional modal is close to that of the first-order bending modal, and the frequencies are 36.67 Hz and 38.41 Hz. The fourth-order modal is the lateral local modal of the front water tank bracket, which is consistent with the third-order modal in this article and the modal frequency is very close. [PERSON] et al. [40] tested the first four modals of the body-in-white, and the numerical values are in good agreement with the modal values calculated by the simulation. The frequency of the first-order modal is 28.82 Hz, and the fourth-order modal is the first-order torsional modal, and the frequency is 42.54 Hz. [PERSON] et al. [20] conducted modal experiments, The obtained body-in-white first-order modal frequencies, roof local modal frequencies and first-order torsional modal frequencies are 18.97 Hz, 29.04 Hz, and 39.42 Hz, respectively. [PERSON] et al. [28] calculated that the first-order modal frequency of the body-in-white and the local modal frequency of the roof were 19.62 Hz and 40.1 Hz, respectively. [PERSON] et al. [41] obtained the first-order bending modal frequency of the body-in-white and the local modal frequency of the front door are 49.67 Hz and 55.34 Hz, respectively. The maximum vibration displacement of the front door is at the junction of the door and the glass, and the modal frequency differs from the local modal frequency of the front door glass in this article by only 0.89 Hz. Figure 4: The first-order bending modal shape of the body-in-white. Figure 3: The first-order torsional modal shape of the body-in-white. Analyze the modal shapes and modal frequencies of the body-in-white in the above article. For the same vibration shape, although the modal frequencies of different models are different, the frequencies are not much different and fluctuate in a small range. The frequency range of the first-order modal of the body-in-white is 18.97-31.31 Hz. The frequency range of the first-order torsion modal and the first-order bending modal of the body-in-white are relatively small, and the frequency ranges are 33-42.54 Hz and 38.41-58.9 Hz, respectively. Due to the larger area of the roof panel, more modal vibration shapes, and a larger range of modal frequency changes, the frequency range is 27.2-48.9 Hz. In this article, the modal analysis mainly considers the first eight modals of the body-in-white whose low modal frequency can reflect the low-frequency vibration characteristics of the vehicle body. In the finite element calculation results, the frequencies of the first-order modal, the first-order torsional modal, and the first-order bending modal are all