Vibo-acoustic metamaterial model in energy based finite element method applied to automotive structures

Classical numerical methods such as the finite element method (FEM) or the boundary element method (BEM) are limited in the frequency domain due to its need of frequency dependent discretization. In contrast to this, energy based methods use a formulation that is independent from kinematic degrees of freedom. Instead, energy density and energy flow are used as primary variables. This allows solving large acoustic problems in the high frequency domain up to 20 kHz or higher. Vibro-acoustic metamaterials allow optimizing properties like group speed and structural damping coefficient at specific frequency bands. To improve the assessment of the impact on more complex structures numerical simulation is helpful. Combining energy based methods with a metamaterial model provides the possibility to analyze the impact of metamaterials on larger structures such as full car models. This includes effects such as reflections on the interface between isotropic material and metamaterial and the influence of secondary paths on the target variable. Coupling fluid and structure via transmission coefficients provides the possibility to predict noise levels inside and outside of the car cabin. In this contribution a method of taking into account metamaterials in energy based finite element simulations is presented. This method is based on analytical descriptions of the energetic properties like wave number and structural damping coefficient of the metamaterial. The results are compared to results of FEM for academic structures and more advanced application-related structures.

Subjects

energy finite element method

metamaterials

DDC Class

620.3: Vibrations

620.2: Acoustics and Noise

510: Mathematics

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Vibo-acoustic metamaterial model in energy based finite element method applied to automotive structures