  We develop quadrature rules for the isogeometric analysis of wave propagation
and structural vibrations that minimize the discrete dispersion error of the
approximation. The rules are optimal in the sense that they only require two
quadrature points per element to minimize the dispersion error [1], and they
are equivalent to the optimized blending rules we recently described. Our
approach further simplifies the numerical integration: instead of blending two
three-point standard quadrature rules, we construct directly a single two-point
quadrature rule that reduces the dispersion error to the same order for uniform
meshes with periodic boundary conditions. Also, we present a 2.5-point rule for
both uniform and non-uniform meshes with arbitrary boundary conditions.
Consequently, we reduce the computational cost by using the proposed quadrature
rules. Various numerical examples demonstrate the performance of these
quadrature rules.
