Embedding negative structures to model holes and cut-outs
Ilanko, S. (2009). Embedding negative structures to model holes and cut-outs. In Proceedings of 7th International Symposium on Vibrations of Continuous Systems, Zakopane, Poland, July 19-24, 2009 (pp. 30-32).
Permanent Research Commons link: https://hdl.handle.net/10289/5779
It has now been established that geometric boundary conditions and continuity conditions can be modelled by using either positive or negative stiffness or inertia type penalty term [1-5]. The experience of working with negative stiffness and inertial parameters has led to the question: what if both stiffness and mass were to be taken as negative? Changing the sign of all stiffness and inertial terms of a structure is simply equivalent to multiplying both sides of an eigenvalue equation by minus one, which does not change its frequencies or modes. Basically, a negative structure in such a sense has the same vibratory properties as that of its positive counterpart, although the structure itself may not have a physical meaning.
This article has been published in the Proceedings of 7th International Symposium on Vibrations of Continuous Systems, Zakopane, Poland, July 19-24, 2009. Used with permission.