A novel view on the composition of energy flow in multi-modal waveguides

In waveguide theory calculating the energy flowing through the guide is often of prime interest and especially within elastodynamics the energy partition between the different transmission paths such as axial, torsion, shear etc. is also of interest. In this paper, we show that the definition of state variables is not unique which make conclusions on energy partition between the various transmission paths somewhat ambiguous. On the other hand, we show that for the various definitions of state variables they all have in common what we denote essential state variables which is the part of the states variables that is responsible for the transmission of energy. The essential variables, therefore, correspond to what can be interpreted as the unique, or essential, part of any definition of the state variables. To illustrate this we use an infinite elastic plate strip simply supported at the edges as an example.