Symmetric elastic wave cloak design for underground protective structures based on multi-center coordinate transformation.

Compared to acoustic cloak, elastic wave cloak is difficult to construct due to inapplicability of form invariance for the control equations. Traditional elastic wave cloak is limited to Willis material or Cosserat material. In this paper, a modified symmetric design method for elastic wave cloak is proposed for underground protective structures based on a multi-center coordinate transformation scheme. First, a symmetry function is established to depict the degenerated symmetric elastic tensor by geometric averaging the elastic tensor components. The shielding performance of the symmetric method proposed in this paper is compared with that of the symmetric method in the literature. The finite element simulation results show that the symmetric cloak proposed in this paper can better reduce the displacement and shield the elastic wave. The proposed method is then used to construct elastic wave cloak for the arch shaped structure which is common in underground protective structures. A multi-center coordinate transformation scheme is applied for this purpose by dividing the arch structure into multiple coordinate transformation regions each with a local coordinate system. The shielding performance of the underground protective cloak against elastic waves with different wave incident directions and frequencies is discussed in details. The simulation results indicates that the symmetrical underground protective cloak can effectively detour the incident elastic waves, and has a good shielding effect at frequencies ranging from 50 to 1000 Hz. [ABSTRACT FROM AUTHOR]