Experimental and numerical validation of Advanced Statistical Energy Analysis to incorporate tunneling mechanisms for vibration transmission across a grillage of beams

Abstract

Advanced Statistical Energy Analysis (ASEA) is used to predict vibrational response on a three-bay linear grillage of beams that supports multiple wave types when there is significant indirect coupling through tunneling mechanisms. For bending wave excitation where the component beams have identical material properties, there was agreement between measurements, ASEA and FEM (Finite Element Methods). The importance of indirect coupling was confirmed for bending-longitudinal and bending-torsional models due to ASEA predicting a higher response than SEA on beams that were distant from the source, and closer agreement between FEM and ASEA (rather than SEA) with only bending modes on all the beams or where beams supported longitudinal or torsional modes as well as bending modes. To investigate an imperfectly periodic, finite grillage that could exist due to engineering tolerances, numerical experiments with FEM were used to introduce uncertainty into the Young’s modulus for each beam. For beams modelled with Euler-Bernoulli or Timoshenko theory, the effect of this uncertainty was to reduce differences between FEM and ASEA to less than ≈3 dB. The results confirm the ability of ASEA to predict vibration transmission with significant indirect coupling across frameworks of beams that support local modes with multiple wave types.