Prediction of bending wave transmission across coupled plates affected by spatial filtering and non-diffuse vibration fields

Abstract

This thesis concerns models based on Statistical Energy Analysis (SEA) to predict bending wave vibration in heavyweight buildings from structure-borne sound sources such as machinery. These sources tend to inject most power in the low- and mid-frequency ranges where the walls and floors have low mode counts and low modal overlap for which calculated Coupling Loss Factors (CLFs) from semi-infinite plate theory can be in error. For machinery it is necessary to predict vibration on walls/floors that are remote from the source room. In this situation, propagation across successive structural junctions causes spatial filtering of the wave field and the assumption of a diffuse field in each plate subsystem breaks down. The predictive approach described in the European Standard EN12354 uses SEA path analysis which assumes that transmission is dominated by first-order paths. However the feasibility of extending the concept of path analysis to walls and floors of rooms that are distant from the source room(i.e. not adjacent) is unknown. These issues are addressed in the thesis. The feasibility of SEA path analysis was assessed by quantifying the total contribution to receiver subsystem energy from paths containing specified numbers of CLFs. For receiving subsystems which are attached directly to the source subsystem, the EN12354 approach was found to underestimate the energy levels. For rooms remote from the source room, path analysis was found to significantly underestimate the vibration of the walls/floors which form the receiver room. Alternative approaches to improve predictions in large heavyweight buildings were assessed through comparison with Monte-Carlo Finite Element Method (MCFEM) models which were validated on a small heavyweight building. Matrix SEA was used with CLFs calculated for L-, T- and X-junctions using analytical models for rectangular plates to try and incorporate modal features. For isolated junctions, there was good agreement with MCFEM but in large buildings. However, it was unable to predict the peaks and troughs in the vibration response to one-third octave band accuracy although it can estimate the envelope response for plates that are directly connected to the source plate. In general, matrix SEA using finite plate theory CLFs does not improve the prediction in one-third octave bands when the statistical mode count is less than unity. Ray tracing was therefore investigated which showed that the angular distribution of power incident on the plate edges differed significantly from a diffuse field. Computationally efficient ray tracing was then developed for inclusion in Advanced SEA (ASEA) models to account for indirect coupling between plate subsystems. ASEA gave significant improvements over matrix SEA when there were large numbers of structural junctions between the source and receiving plates.