Energy-based dual-phase dynamics identification of clearance nonlinearities

Abstract The energy-based dual-phase dynamics identification (EDDI) method is a new data-driven technique for the discovery of equations of motion (EOMs) of strongly nonlinear single-degree-of-freedom (SDOF) oscillators. This research uses the EDDI method to obtain mathematical models for SDOF systems with clearance nonlinearities. The first key aspect of the EDDI method is that it relates the kinetic energy of the system to the dissipated energy and the underlying non-conservative forces acting on the oscillator. The second key aspect is that the EOM is identified with only knowledge of the mass of the oscillator and the transient response. The first phase of the EDDI method constructs the dissipated energy from the kinetic energy, then identifies a mathematical model for the damping based on the dissipated energy. To achieve this, the moments in time when the displacements are zero, where the mechanical and kinetic energies are equal, are used to compute the energy dissipated by the damping of the system. The second phase begins by computing the conservative force acting on the oscillator from either a balance of the other forces in the system or through the Lagrange equation. Finally, the stiffness model is determined by solving a set of linear equations to construct a mathematical model for the conservative (elastic) force. The governing equations are discovered by incorporating both the damping and stiffness terms. The method is demonstrated by employing analytical and real measured responses of nonlinear SDOF systems with different clearances nonlinearities, which shows that the proposed approach is suitable for non-smooth mechanical systems as well as smooth systems.