Ilanko, S. & Monterrubio, L.E. (2011). On the bipenalty method: why is it advantageous to add stiffness and mass. In Proceedings of the 8th International Symposium on Vibrations of Continuous Systems Whistler, British Columbia, Canada, 17-23 July 2011 (pp. 25-27).
Permanent Research Commons link: https://hdl.handle.net/10289/5780
In a recent paper, Askes et al  proposed the simultaneous use of stiffness and inertia of large magnitude to model constraints in time domain analysis. From a frequency domain perspective, as stiffness and inertia have opposite effects on the natural frequencies, this seems counter-intuitive. With increasing stiffness, the natural frequencies either increase or remain unchanged, whereas the opposite is true for inertia. However, it can be shown, through very simple illustrative examples, that the natural frequencies and modes of continuous systems can be found in this way, and that there are advantages in using both stiffness and mass simultaneously.
This article has been published in the Proceedings of the 8th International Symposium on Vibrations of Continuous Systems Whistler, British Columbia, Canada, 17-23 July 2011. Used with permission.