Reflection, Transmission and Coupling of Longitudinal and Flexural Waves at Beam Junctions. Part I: Measurement Methods

This paper presents measurement methods for the scattering matrix terms of beam junctions. The case of flexural and longitudinal waves travelling on prismatic beams and interacting with a structural discontinuity is considered. Reflection, transmission and wave coupling coefficients between these two waves are obtained from structural response functions measured by in-plane and out-of-plane laser vibrometers. Three measurement methods are developed and compared. They are based on different sets of assumptions for the junction: geometrical axial symmetry, reciprocity and conservation of the energy. The third method is iterative and is the most efficient way to obtain all coefficients: reflection and transmission coefficients are first estimated ignoring the wave coupling coefficients, which are computed in a second step. The measured coefficients are used to determine stiffness parameters of the junctions which are key parameters to predict response functions of beam assemblies using a wave superposition method.