Damped vibration analysis using finite element method with approximated modal damping for automotive double walls with a porous material

This paper provides a description of damped vibration analysis of automotive double walls with a porous material. The double walls are modeled by using finite element calculations and by considering the damping couplings among various materials. Damped sound fields inside of the porous materials are defined by complex effective density and complex bulk modulus. Particle displacements of the internal air in the porous materials are chosen as unknowns. Displacements in the solid materials for the walls are also formulated using finite elements including complex modulus of elasticity. Thus, displacement vectors are common unknown variables for the coupled equations of motion of the damped structures. By applying asymptotic method to complex eigenvalue problem to obtain modal parameters, expressions of modal loss factor are derived approximately for the three-dimensional structures in coupling between elastic components, viscoelastic components, porous components and environmental gas. This approach helps us to obtain fast computation. The proposed approach and our developed code are verified. Damped vibration of the double walls with a porous layer is computed in consideration of coupling in damping between layers. We discuss modal damping between the layers.