Frequency-Domain Bridging Multiscale Method for Wave Propagation Simulations in Damaged Structures

Efficient numerical models are essential for the simulation of the interaction of propagating waves with localized defects. Classical finite elements may be computationally time consuming, especially when detailed discretizations are needed around damage regions. A multi-scale approach is here propose to bridge a fine-scale mesh defined on a limited region around the defect and a coarse-scale discretization of the entire domain. This "bridging" method is formulated in the frequency domain in order to further reduce the computational cost and provide a general framework valid for different types of structures. Numerical results presented for propagating elastic waves in 1D and 2D damaged waveguides illustrate the proposed technique and its advantages.