On the bipenalty method: why is it advantageous to add stiffness and mass

Abstract

In a recent paper, Askes et al [1] 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.