We apply isogeometric finite element analysis for computing mechanical vibrations
in the context of large deformation solids with nonlinear visco-hyperelastic
material laws. 
  In the fields of linear vibrational or modal analysis, respectively, and static
large deformation hyperelasticity, the isogeometric approach has already been
shown to possess advantages over classical finite elements and, in particular,
provides higher accuracy of the numerical results. 
  We have introduced a nonlinear framework for isogeometric vibration analysis based
on steady-state frequency response to periodic excitations using the harmonic
balance principle. 
  First results for the new method were demonstrated using a nonlinear
Euler-Bernoulli beam model. 
  Meanwhile, our isogeometric frequency-response analysis has been extended to
3-dimensional large deformation solids with visco-hyperelastic,
frequency-dependent constitutive material models such as rubber. We show the
successful application of the method to several computational examples and study
the properties of the spatial discretization depending on polynomial degree and
global smoothness.
  Furthermore, we aim at large-scale industrial applications where the naive
application of harmonic balance is prohibitive. As remedy, a novel reduction
scheme is introduced that leads to significant savings while maintaining
sufficient accuracy for critical frequencies.

  This work is supported by the European Union within the FP7-project TERRIFIC:
Towards Enhanced Integration of Design and Production in the Factory of the Future
through Isogeometric Technologies (FP7-2011-NMP-ICT-FoF 284981).