Transient Response of Beams

The response of beams to transient excitation applied through the supports is considered. A general method of analysis, based on the integral equation of motion, is developed, applicable to single-and multi-span beams; for non-uniform beams the conventional approximation of replacing the distributed mass by a number of discrete masses is made, and an equivalent matrix analysis is given. For all beams the response is obtained in terms of normal modes. Response spectra, dependent upon bending moment or stress, are given for various pulse shapes for simple beams, and it is shown that for single pulse excitation the maximum response depends primarily on the rise-time of the pulse and only marginally upon the shape of the pulse. The accuracy of approximate methods of determining response spectra is discussed. The effects on transient response of flexibility in the supports and of the support positions are considered. Application of the theory to an engineering system is discussed briefly.