Dynamic analysis of space frames: The method of reverberation-ray matrix and the orthogonality of normal modes

The formulation of reverberation-ray matrix analysis has been proposed to study wave propagation in planar frames. It is applied here to modal analysis of complex three-dimensional framed structures, optionally with lumped masses and/or elastic supports. Furthermore, by means of Betti's reciprocity theorem, orthogonal conditions are established for different natural modes, and hence transient response analysis based on mode superposition is developed. Both the reverberation-ray matrix analysis for free vibration and the mode superposition method for transient response are illustrated by numerical examples.