Topology optimization of two-dimensional wave barriers for the reduction of ground vibration transmission

Abstract. This paper studies topology optimization as a tool for designing barriers for ground vibration transmission. A two-dimensional problem is considered where material is stiffened in the design domain, located in the transmission path between the wource and the receiver. The two-dimensional homogeneous halfspace is excited at the surface. The response at the receiver is minimized for a harmonic load by distributing a stiffened material in the design domain using topology optimization. The performance is compared to a wall barrier which has the same volume of material and has a depth equal to the depth of the design domain. At low frequencies, where the wavelengths are large compared to the height of the domain, the optimized wave barrier reflects and guides waves away from the surface. At high frequencies, destructive interference is obtained that leads to high values of the insertion loss. The presence of small features in the designs makes the performance sensitive to deviations in the geometry. In order to obtain a design which is robust with respect to geometric imperfections, a worst case approach is followed. The resulting design not only outperforms the wall barrier, but is also robust with respect to deviations in the geometry. This paper also shows that the robust design can be used to develop simplified design solutions.