Power equipment is prone to vibrations. Removing eigenfrequencies of a structure from the interval of working frequencies reduces the probability of resonance during operation. In this contribution, a structural optimization problem is formulated whose objective at a minimum removes all eigenfrequencies from a given frequency interval. We consider systems without damping whose mass and stiffness matrices depend continuously on real parameters. The approach relies on the identity proposed by Futamura for eigenvalue count on intervals. The identity uses a contour integral in a complex plane of a trace of a specially constructed matrix. The contour integral is evaluated numerically using the trapezoidal rule over a circular path. The latter expression is differentiable. Present contribution extends the identity by adding a concave weighting function strictly positive in the interval. Furthermore, an explicit expression for the gradient of the objective and a simple optimization strategy are presented. Finally, a multi-degree of freedom example illustrates the performance of the approach.