Vibrations of elastically restrained frames

This paper deals with the determination of eigenfrequencies of a frame which consists of a beam supported by a column and is submitted to intermediate elastic constraints. The ends of the frame are elastically restrained against rotation and translation. The individual members of the frame are assumed to be governed by the transverse and axial vibration theory of an Euler–Bernoulli beam. undary and eigenvalue problem which governs the dynamical behavior of the frame structure is derived using the techniques of calculus of variations. Exact values of eigenfrequencies are determined by the application of the separation of variables method. Also, results are obtained by the use of the finite element method. The natural frequencies and mode shapes are presented for a wide range of values of the restraint parameters. Several particular cases are presented and some of these have been compared with those available in the literature.