Wave reciprocity refers to a principle that the relationship between a source and the resulting response at a receiver is unchanged if one interchanges the source and the receiver. We will report on recent advances in breaking reciprocity by using dynamic-mechanism metamaterials, which are synthetic modulated structures with the time-varying inertial mass, stiffness, and even viscosity. The proposed time-varying mass element is a rotary three-body dynamic system, and we employ this element to construct the lattice metamaterial with inertial mass varying periodically in both space and time. The non-reciprocal wave propagation can be observed when the spatiotemporal modulation constitutes a travelling-wave field pattern, which behaves like a biasing field that breaks the time-reversal symmetry. Dynamic-mechanism metamaterials can be further designed to possess the simultaneous spatiotemporal modulation over mass and stiffness, which allows for selective opening of unidirectional bands in contrast to singly modulated ones. We will also show that in a non-Hermitian mechanical system with an exceptional point, dynamic-mechanism metamaterials can be used to implement the dynamic encircling of the exceptional point by the time-driven elasticity and viscosity. Non-reciprocal mode switching dominated by the encircling direction can be observed. We envision that dynamic-mechanism metamaterials may open a new avenue towards non-reciprocal wave and vibration control.

Metamaterials; Dynamic mechanisms; Non-reciprocity; Elastic wave