# Structural and Vibro-Acoustics Optimization of a Car Body Rear Part
## 1 Introduction  
The development of additive technology is attracting more and more interest from companies considering the wide variety of materials that can be used. The rising cost of steel is leading companies to turn to different materials, processed by technologies, such as 3D printing, far removed from traditional ones. These technologies offer the possibility of cost-efficient production of artefacts with complex geometries and are, nowadays, widely spread in the automotive sector [1]. The automotive industry faces new challenges every day, new design trends and technological deployments from research push companies to develop new models in the short term, requiring new tools or tool reshaping. The automotive industry is one of the most competitive business areas where time-to-market decrease plays an important role. Additive manufacturing is the solution that enables the flexible production of customizedproducts without significant impact on costs and lead time. Automotive companies develop new models, pushed by new design trends and technological evolution, where aesthetics, aerodynamics, safety, and weight reduction in the vehicle are key issues [2]. The vibro-acoustic analysis of structural components, used in aircraft, spacecraft, and land vehicles, plays a vital role in the design of these systems with regard to human health and living comfort. The perceived vibro-acoustic comfort inside the passenger compartment under driving conditions is strictly related to the car body torsional behavior. In this work, the focus of the implemented optimization was on the first torsional mode frequency because the first modes, torsional and flexural, can be considered the most important in relation to comfort. As a matter of fact, a similar target was pursued in [3], where the first flexural frequency of a train chassis was increased to achieve vibro-acoustic benefits. In [4], vibro-acoustic improvements were obtained for a car roof, made with an innovative composite material: a structural optimization allowed to recover for the new configuration the original static and dynamic stiffness properties, decreasing the weight and the noise inside the cabin. The same approach adopted for this work was implemented in [5], but with reference to crashworthiness rather than vibro-acoustics; in particular, the objective was to apply additive manufacturing to obtain a plastic automotive component with reduced weight and costs, preserving, at the same time, its crash performance. Deterministic methods, e.g., based on multibody simulation [6], combined FEM (Finite Element Method)-BEM (Boundary Element Method) [7], hybrid BEM/empirical approaches [8], and fast multipole method (FMM) [9], are widely adopted to tackle vibration and acoustic assessments of complex structures. For this work, FEM was adopted for solving both the vibrational and acoustic problems. A multi-objective optimization was proposed to improve the vibro-acoustic performance of the considered car model. The related constraints came from the need to reduce the weight, by focusing on the car rear part, without compromising its crash performance. In order to reduce the crash and durability testing times, a possible choice might be to perform the topology optimization (aimed at car weight reduction) just on those parts that do not affect the impact resistance [10]. On the contrary, in this work, the optimization was carried out considering some components that can heavily affect the impact performance. Therefore, a countercheck of the new design against crash performance was necessary, but this part was not implemented in this work. For the acoustic modeling, it was important to identify the entry points of the vibrational forces (suspension attachment points and engine mounts) responsible for generating structural noise inside the passenger compartment. There are several works in the literature aiming at car body lightening, under the constraint of preserving original structural or acoustic performance.