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

Abstract

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