Buckling loads and eigenfrequencies of a braced beam resting on an elastic foundation

The eigenvalue problems of the buckling loads and natural frequencies of a braced beam on an elastic foundation are investigated. The exact solutions for the eigenvalues are pre-sented. The eigenvalues vary with the different parameters and are especially sensitive to the brace location. As the beam of a continuous system has infinite eigenvalues and these eigenvalues are influenced differently by a brace, the eigenvalues show rich variation patterns. Because these eigenvalues physically correspond to the structure buckling loads and natural frequencies, the study on the eigenvalues variation patterns can offer a design guidance of using a lateral brace of translation spring to strengthen the structure.