Topology Optimization on Periodic Pile Barriers Considering Material Damping Based on Complex Band Diagrams

The frequency bandgaps of pile barriers that are periodically arranged can be used to isolate environmental vibrations. However, the viscosities of piles and soil were usually ignored. Moreover, the attenuation zone for the vibration isolation of traditional pile barriers was limited. To take the viscoelasticity of materials into consideration, the complex band diagram is introduced in this paper, and the effective attenuation zone is evaluated by the minimum imaginary part of the wavenumber. Single objective and multi objective topology optimizations are combined with the calculation of complex band diagram to maximize the width of the effective attenuation zone (EWAZ). The effects of different soil damping ratios and elastic moduli on the optimized pile shapes and EWAZ are analyzed. The optimization results show that the optimized pile shape is changed due to the existence of soil damping, and the EWAZ is larger with a larger soil damping. The excellent isolation effect of the optimized pile barrier is verified by frequency domain analysis in numerical 2D and 3D viscoelastic models. The obtained optimized pile structures show a better isolation effect than traditional structures. Moreover, compared with traditional band diagrams, the complex band diagram can quantitatively evaluate the attenuation performance, which saves computational resources.