A nonintrusive reduced order method for the NVH assessment and automotive structural dynamics

The goal of this work is to develop a computational method able to optimize the design process of a car structure and provide a tool which can support designers during the decision-making phase. The design of a car body-in-white (BIW) structure is the process which goes from the initial idea to the final approved model. During this phase, which represents the most time-consuming part of the whole development process, designers have to deal with very complex parametric problems where material and geometric characteristics of the car components are the unknown. Any change in these parameters might significantly affect the global behaviour of the car. A target which is very sensitive to small variations of the parameters is the noise and vibration response of the vehicle (NVH test), which strictly depends on the global static and dynamic stiffness. In order to find the optimal solution, a lot of configurations exploring all the possible parametric combinations need to be tested. Standard numerical methods are computationally very expensive when applied to this kind of multidimensional problems. An alternative is represented by reduced order models (ROM), which are based on the idea that the essential behaviour of complex systems can be accurately described by simplified low-order models. In this work, the encapsulated proper generalized decomposition (Encapsulated-PGD) toolbox, based on the PGD Least-Squares approximation [3] is proposed. As a main advantage, this ROM technique requires only one offline computation. The latter provides a separable solution which depends explicitly on an a-priori unknown number of parametric and mechanic modes or snapshots. Then, during an online stage, the solution can be particularized in realtime for any set of the parameters. In a previous work [4], a coupling of the PGD method with the Inertia Relief technique was implemented in order to perform the parametric static analysis of an unconstrained structures. A novel algebraic approach allowed to incorporate both material and complex geometric parameters and to perform shape optimization. Here, the method is extended to the case of a parametric generalized eigenvalue problem, in order to identify how a variation of user-defined parameters affects the dynamic response of the structure in terms of dominant eigenmodes and related natural frequencies. Moreover, thanks to the nonintrusive format of the toolbox, an interaction with commercial software is possible, which makes it particularly interesting for real industrial applications.