Stability analysis of an aeroelastic system with friction

In this paper, harmonic balance method, exact formulation and numerical simulation method are adopted to study the effects of different friction stiffness on the stability of 1.5 degrees of freedom aeroelastic system. On this basis, the expressions of input energy and dissipated energy are deduced, and the energy method is used to reveal the mechanisms of the stable boundary and unstable boundary existing in the system and the effects of different friction stiffness on the stability of the system. Studies have shown that the stability region and the critical aerodynamic damping ratio of the system rise with the increase of the friction stiffness, while the friction stiffness has little effect on the stability boundary. In the analysis of the stability of system, the results of harmonic balance method, exact formulation and Newmark of numerical simulation method are in good agreement. Compared with exact formulation and numerical simulation method, the concept and conclusion of harmonic balance method are simple in the system stability analysis.

Performance of DDA time integration

Discontinuous deformation analysis(DDA) is a numerical method for analyzing the deformation of block system. It employs unified dynamic formulation for both static and dynamic analysis, in which the so-called kinetic damping is adopted for absorbing dynamic energy. The DDA dynamic equations are integrated directly by the constant acceleration algorithm of Newmark family integrators. In order to have an insight into the DDA time integration scheme, the performance of Newmark time integration scheme for dynamic equations with kinetic damping is systematically investigated, formulae of stability, bifurcation, spectral radius, critical kinetic damping and algorithmic damping are presented. Combining with numerical examples, recognition and suggestions of Newmark integration scheme application in the DDA static and dynamic analysis are proposed.