Analysis and Experiments on Stress Waves in Planar Trusses

The dynamics of planar trusses are investigated in terms of axial (longitudinal) stress waves, which propagate along structural members and scatter at the joints. The scattering coefficients representing the reflection and transmission of axial waves at each joint are derived from the dynamics and compatibility conditions of the joint. The complex multiple reflections of waves within the structure are evaluated in the frequency domain with a newly developed reverberation matrix, which is formulated from the scattering coefficients and propagating phase factors. Transient waves are then derived by Fourier synthesis, and evaluated by a Fast Fourier Transform algorithm. Experimental results of propagating broad band pulses are presented for a truss model excited by a step loading. Comparison between theoretical results and transient wave records indicate that the axial wave theory is valid only for the response at the very early time. The discrepancy is much reduced if the scattering coefficients are modified to allow mode conversion from axial to flexural waves at the joint.