Total Decoupling of 2D Lattice Vibration

Lattice structures find broad application in aerospace, automotive, biomedical, and energy systems owing to their exceptional structural stability. These systems typically exhibit complex internal couplings that facilitate vibration propagation across the entire network. The primary objective of this study is to achieve total decoupling of 2D lattice vibration system, which involves eliminating all inter-subsystem interactions while preserving spectrum. Building upon prior research, we develop structure-preserving isospectral transformation flow (SPITF) framework to address this challenge. Two principle results are established: first, the equations of motion are systematically derived for lattice vibration systems; second, total decoupling is successfully realized for such systems. Numerical experiments validate the decoupling capability of lattice vibration systems.