Asymmetric scattering of flexural waves in a parity-time symmetric metamaterial beam.

Non-Hermitian parity-time (PT) symmetric systems that possess real eigenvalues have been intensively investigated in quantum mechanics and rapidly extended to optics and acoustics demonstrating a lot of unconventional wave phenomena. Here, a PT symmetric metamaterial beam is designed based on shunted piezoelectric patches and asymmetric wave scattering in the form of flexural waves is demonstrated through analytical and numerical approaches. The gain and loss components in the PT symmetric beam are realized by the introduction of negative and positive resistances into the external shunting circuits, respectively. Effective medium theory and transfer matrix method are employed to determine the effective material parameters and scattering properties of the PT symmetric metamaterial beam. Unidirectional reflectionlessness has been demonstrated analytically and numerically, together with illustrations of the PT phase transition and exceptional points. The tunability of exceptional points is studied by changing the spacing between piezoelectric patches and shunting circuit parameters. The design explores complex material parameters of the beam structure, and could open unique ways to asymmetric wave control, enhanced sensing, amplification, and localization of flexural waves.