Dynamic response and wave propagation in plane trusses and frames

The dynamics of planar frames and trusses is analyzed in terms of the propagation of axial (longitudinal) and flexural (transverse) stress waves being structural members. The waves are multiscattered at the joints, and scattering coefficients representing the reflection and transmission of both types of waves at each joint are derived from the dynamics and compatibility conditions of the joint. The complex multireflected waves within the structure are evaluated in the frequency domain by a newly developed reverberation matrix, which is formulated from scattering coefficients and propagating phase factors. Transient waves are then analyzed by Fourier synthesis and evaluated by a fast Fourier transform algorithm. Transient responses for the axial and bending strains in all structural members are calculated over a long duration for a model truss with rigid joints. Comparison to experimental data of the model truss under a step loading shows good agreement for the early as well as considerably long time responses.