Matrix method application to vibrations in beam type periodic structures

The transfer matrix method is applied to the study of combined logitudinal and flexural vibrations in planar periodic structures which consist of Timoshenko beam models. The transfer matrices for longitudinal, flexural, and torsional vibration in an elastic rod are reviewed and modified. The mathematical properties of the transfer matrices for a single beam undergoing one or more of the various types of vibrations are explored. The use of these properties in the application of the matrix method to structural vibration is developed. Detailed analysis is carried out for the case of longitudinal vibration in an elastic bar. The traditional technique used in the application of the transfer matrix method to vibrations in planar and three dimensional structures is reviewed and given the name, Free-Body technique. A new technique, called as the Superposition technique, is introduced. The Superposition technique is planned such that it could be very efficient in the computer application of the transfer matrix method to vibrations in planar or three dimenstional structures.