A receptance-based method for predicting latent roots and critical points in friction-induced vibration problems of asymmetric systems

This paper studies the latent roots and critical points of friction-induced vibration problems in which the stiffness matrix is asymmetric. The asymmetric terms are represented by a parameter or parameters related to the friction coefficient. As the parameter value increases, some latent roots of the asymmetric system change, and even become complex with positive real parts at a critical point, indicating flutter instability. A method is put forward for computing the latent roots and predicting the critical value of this parameter at the flutter instability boundary of the asymmetric system based on the receptance of the symmetric system. When measured receptances of the symmetric system (at those locations where friction forces would be acting in the corresponding asymmetric system) are available, the simulated numerical example shows that this method is efficient.