Shape- and topology optimization often require regularization, and implicit PDE based approaches are commonly used for this purpose. There is usually a large number of design variables, so gradient based optimization based on adjoint sensitivity analysis is also needed. The regularization is formulated as a stationary problem, and therefore maximization of eigenfrequencies require a one-way coupled between stationary-then-eigenvalue computation. The sensitivity analysis requires a coupled approach in the opposite order. We will show results for structural mechanics focusing on shells and solids for the shape optimization, while the results for topology optimization is limited to solids. Mode switching is handled by always solving for the first 6 modes and considering all of the associated eigenfrequencies in every optimization iteration. In practice a maximin problem is formulated and solved with the MMA optimization algorithm. Variations of these results might also be presented as no coding is required for changing the physics, objective or the amount of design freedom. All of the presented results will be available for download.