VIBRATION OF STRUCTURES ELASTICALLY CONSTRAINED AT DISCRETE POINTS

The forced vibration of a structure with an added spring constraint acting at a point is discussed. A set of constrained vibration modes is obtained in terms of the assumed known modes of the unconstrained structure, and it is shown that these constrained modes are orthogonal. It is shown in the Appendix that the unconstrained modes form a complete set for the constrained beam. The forced vibration response can be described in terms of either set of modes. The two descriptions are shown to be equivalent only if the damping is independent of the mode number. The damping may, however, be an arbitrary function of the forcing frequency. A finite element model of a heat exchanger tube is used to investigate the importance of the restriction on the damping and the relative numbers of modes needed to provide an accurate estimate of the response over a wide range of frequencies. © 1979.