A review of dynamic vibrations of shear-type immersed beam (CDM method)

A modeling method for bending vibration analysis of immersed Timoshenko beam is introduced. The stuctures is discretized into rigid bars and the Lagrangian coordinates are selected to be the vertical displacements of the rigid bars; Cell Discretization Method (CDM). The advantage of this simplification and that it reports the study of the beam within the rigid systems. Usually, approximate free vibration frequencies can be obtained by standard Rayleigh-Ritz (R-R) method [11], whereas in this note lagrangian approach is adopted. The proposed analysis seems to be rather interesting; at least if compared with more usual R-R methods, since a lower-upper bound can be obtained. The paper ends with some numerical examples and comparison with results.