Monte Carlo model of the uncertainty of SEA loss factors

Abstract

Finite Element Methods are widely used to model vibro-acoustic systems, but as the modal density becomes higher this type of model becomes inaccurate and impractical. This is why in the high modal density region the use of Statistical Energy Analysis (SEA) models has become increasingly popular. SEA has some obvious advantages such as its simple formal expression, being based on linear equation systems or the reduced number of variables involved. But SEA has drawbacks as well, such as the absence of local information or the necessity of frequency averaging. A key quantity in SEA models is the loss factor. This takes into account the energy dissipated within a given subsystem or when power flows from one subsystem to another. Even though analytical expressions exist for a number of subsystems of differing nature, the measurement of the loss factor is still advisable and a necessity for a large number of cases. The most commonly used method of measuring loss factors is the Power Injection Method. This method is based on the injection of power into every single subsystem in sequence while the energy in each subsystem is measured. In spite of its simplicity, there remain a number of problems where the accuracy of the results is influenced by various practical issues. In this paper, a Monte Carlo model is used to describe the uncertainty of a two subsystemproblem consisting of two planar elements connected along one side. The influence of the input variables is studied and the conditioning of the coefficient matrix that model the system is also taken into account