Dynamic analyzing of thin damping circular plate under eccentric impact load by generalized multi-symplectic method

Symmetry breaking is one of important properties of the complex dynamic system that affect the nonlinear characteristics of the dynamic systems. Focusing on the two typical symmetry case, including the asymmetry of the load as well as the dissipation effect, the vibration problem on the thin damping circular plate under the eccentric impact load is investigated by the generalized multi-symplectic method. Firstly, the control equation of the plate is established and the generalized multi-symplectic form is deduced for the control equation. And then, the errors of the conservation laws are given in the formwork of the generalized multi-symplectic theory. Finally, a generalized multi-symplectic scheme is constructed to simulate the vibration of the plate and the effects from the symmetry breaking are analyzed from the simulation results. The results obtained in this paper lay the foundation of the investigation on the relationship between the symmetry and the dissipation effect.