Mechanical Energy Flux
The mechanical energy flux is a vector formed by the multiplication of the stress tensor and the velocity vector
The reason for the minus sign in the definition is that if you put a pressure on an external boundary, and it moves in the direction of the load, then a positive power input in the direction of the load is obtained.
In the time domain, the expression above is used. In frequency domain, two versions are supplied. The complex mechanical energy flux is the complex vector formed by multiplying the stress tensor by the complex conjugate of the velocity:
The mechanical energy flux is in the frequency domain defined as a real quantity, the cycle average of the complex mechanical energy flux.