▎ 摘　　要

The interaction between flexural modes due to nonlinear potentials is critical to heat conductivity and mechanical vibration of two dimensional materials such as graphene. Much effort has been devoted to understanding the underlying mechanism. In this paper, we examine solely the out-of-plane flexural modes and identify their energy flow pathway during the equipartition process. In particular, the modes are grouped into four classes by their distinct symmetries. The couplings are significantly larger within a class than between classes, forming symmetry blockades. As a result, the energy first flows to the modes in the same symmetry class. Breakdown of the symmetry blockade, i.e., inter-class energy flow, starts when the displacement profile becomes complex and the inter-class couplings bear nonneglectable values. The equipartition time follows the stretched exponential law and survives in the thermodynamic limit. These results bring fundamental understandings to the Fermi-Pasta-Ulam problem in two dimensional systems with complex potentials and reveal clearly the physical picture of dynamical interactions between the flexural modes, which will be crucial to the understanding of their contribution in high thermal conductivity and mechanism of energy dissipation that may intrinsically limit the quality factor of the resonator. Published by AIP Publishing.