Prediction and assignment of latent roots of damped asymmetric systems by structural modifications

This paper studies the latent roots of damped asymmetric systems in which the stiffness matrix is asymmetrical. The asymmetric terms are due to ‘external’ loads and are represented by a parameter or parameters. The latent roots of such asymmetric systems are complex and the real parts become positive at some critical values of the parameter(s) (critical points). The work reported in this paper consists of two parts. The first part presents a method for predicting the latent roots of the damped asymmetric system from the receptance of the damped symmetric system. The second part presents an inverse method for assigning latent roots by means of mass, stiffness and damping modifications to the damped asymmetric system again based on the receptance of the unmodified damped symmetric system. The simulated numerical examples of a friction-induced vibration problem show the complexity in assigning stable latent roots for damped asymmetric systems. It is found that it is quite difficult to assign the real parts of latent roots to stabilise the originally unstable asymmetric system and sometimes there is no solution to the modification that is intended to assign certain latent roots.