Numerical analysis on periodic response of nonsmooth dynamic systems

The periodic response analysis of a nonlinear dynamic system, which is of great significant in engineering, is usually carried out by using numerical methods because of high dimension and complicated characters of the system. The current well-known numerical schemes like shooting and incremental harmonic balancing, however, cannot cope with the engineering systems with nonsmooth physical factors, such as elastoplasticity, clearance and dry friction, and also fail to get the strong nonlinear periodic response of smooth dynamic systems sometimes. In the paper the author analyzes the above shortcomings and points out that they result from the explicit or implicit Newton iteration in the schemes. The paper presents eight new schemes based on quasi-Newton iteration or unconstrained function minimization to improve the shooting and the incremental harmonic balancing. The convergence, accuracy and computation efficiency of these new schemes are examined and four of them are suggested for engineering use.