  A key advantage of isogeometric discretizations is their accurate and
well-behaved eigenfrequencies and eigenmodes. For degree two and higher,
however, optical branches of spurious outlier frequencies and modes may appear
due to boundaries or reduced continuity at patch interfaces. In this paper, we
introduce a variational approach based on perturbed eigenvalue analysis that
eliminates outlier frequencies without negatively affecting the accuracy in the
remainder of the spectrum and modes. We then propose a pragmatic iterative
procedure that estimates the perturbation parameters in such a way that the
outlier frequencies are effectively reduced. We demonstrate that our approach
allows for a much larger critical time-step size in explicit dynamics
calculations. In addition, we show that the critical time-step size obtained
with the proposed approach does not depend on the polynomial degree of spline
basis functions.
