Using the Irrotational Intensity Field to Study Vibration Energy Paths in Automotive Structures

Although structural intensity was introduced in the 80’s, this concept never found practical applications, neither for numerical nor experimental approaches. Quickly, it has been pointed out that only the irrotational component of the intensity offers an easy interpretation of the dynamic behavior of structures by visualizing the vibration energy flow. This is especially valuable at mid and high frequency where the structure response understanding can be challenging. A new methodology is proposed in order to extract this irrotational intensity field from the Finite Element Model of assembled structures such as Bodies In White. This methodology is hybrid in the sense that it employs two distinct solvers: a dynamic solver to compute the structural dynamic response and a thermal solver to address a diffusion equation analogous to the thermal conduction built from the previous dynamic response. The field separation is based on the Helmholtz-Hodge theorem, which ensures the computation’s full consistency. The methodology is first implemented and validated in the case of a plate assembly, using commercial FE software. This first approach immediately highlights a bias in the current power flow computations, leading to erroneous transmission path understanding. It also shows a remarkable stability of the irrotational intensity patterns regarding frequency. As one would expect, transmission path only makes sense when they stand for a broad enough frequency range. The methodology is then applied to an automotive structure, introducing specific modeling of the mechanical connections between stamped steel parts (spot welds, bolts, bids…). Again the method applies well and shows fully consistent results.