Computing reflection and transmission coefficients for plate reinforcement beams

In this paper, we investigate the possibility of obtaining experimentally the reflection and transmission coefficients for propagating bending waves in infinite thin plates caused by a reinforcing beam that is flexibly connected to the plate. A reinforced plate spectral element including the attachment flexibility effect was derived and implemented computationally for this purpose. The proposed technique was numerically verified by using a system consisting of a long simply supported rectangular plate wave-guide. The system was modeled using the derived spectral element, which was validated by comparison with a finite element model. The dynamic responses simulated at a few locations are used to compute the reflection and transmission coefficients. Theoretical expressions of the reflection and transmission coefficients were obtained by using a transfer matrix formulation for the plate and for the flexibly connected beam. The coefficients obtained by using the proposed method are compared with the theoretical values and good agreement is found. The proposed numerical model can be used to optimize the experimental conditions for extracting the reflection and transmission coefficients. The reflection and transmission coefficients obtained with the proposed technique can be used, for instance, in ray-tracing methods, which are currently under development.