International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

In this paper we study eigenvalue problems for fourth-order ordinary differential equations. These boundary problems usually describe the bending vibrations of a homogeneous beam. Our aim here is to present mixed variational forms depending on a wide class of boundary conditions. In particular, we show when the symmetry in variational formulations is available. This property ensures real spectrum of the corresponding problem. The effect of the theoretical results is illustrated by some realistic examples.