Vibration of Structure with Interior Hinges

The object of this note is to demonstrate the use of the internal displacement excitation concept in analysis of the free and forced vibration of a structure modified by the addition of interior hinges. The insertion of a hinge in a beam is equivalent to making a cut in the slope at the coordinate. When a harmonic displacement is imposed between the terminals of the cut, the ensuing response may be expressed in a general form employing the parameters of the uncut system. A solution in this form has been obtained by the writer for a lumped-parameter system, and the extension of the results to a continuous system follows readily from a subsequent paper by the writer. The application of a displacement excitation at a cut introduces an easily-visualized initial discontinuity in slope with simplifies the analysis of the free and forced modes that are characterized by discontinuities in slope at the hinges.