  The application of immersed boundary methods in static analyses is often
impeded by poorly cut elements (small cut elements problem), leading to
ill-conditioned linear systems of equations and stability problems. While these
concerns may not be paramount in explicit dynamics, a substantial reduction in
the critical time step size based on the smallest volume fraction $\chi$ of a
cut element is observed. This reduction can be so drastic that it renders
explicit time integration schemes impractical. To tackle this challenge, we
propose the use of a dedicated eigenvalue stabilization (EVS) technique.
  The EVS-technique serves a dual purpose. Beyond merely improving the
condition number of system matrices, it plays a pivotal role in extending the
critical time increment, effectively broadening the stability region in
explicit dynamics. As a result, our approach enables robust and efficient
analyses of high-frequency transient problems using immersed boundary methods.
A key advantage of the stabilization method lies in the fact that only
element-level operations are required.
  This is accomplished by computing all eigenvalues of the element matrices and
subsequently introducing a stabilization term that mitigates the adverse
effects of cutting. Notably, the stabilization of the mass matrix
$\mathbf{M}_\mathrm{c}$ of cut elements -- especially for high polynomial
orders $p$ of the shape functions -- leads to a significant raise in the
critical time step size $\Delta t_\mathrm{cr}$.
  To demonstrate the efficacy of our technique, we present two specifically
selected dynamic benchmark examples related to wave propagation analysis, where
an explicit time integration scheme must be employed to leverage the increase
in the critical time step size.
