7 Coupled Systems
When systems of similar physics are connected, the situation is relatively simple. The degrees of freedom of the coupling zone are shared, and the state variables, for example pressure and displacement, are equal. The situation changes for coupled deterministic systems of different wave types and physics. Here, conditions must be defined that link, for example, the pressure of one subsystem to the displacements of the other subsystem. The zone where the coupling dynamics takes place is called a junction.
However, simulating sound and vibration propagation in realistic systems means coupling systems of different types of wave propagation and different topology. This can be, for example, a fluid cavity that is connected to several plates surrounding it or a beam that is connected to other beams or plates. Hence, simulating the coupling dynamics can become a complicated task even for pure deterministic subsystems. However, the dynamics can be finally described by a large set of equations of motion with different degrees of freedom.
When random subsystems are connected, the description becomes more complicated. How can the coupling physics between random subsystems be described? If the state of random systems is given by energy, the power flow between the systems must be determined, given by the so-called coupling loss factor.
As shown in section 6.1, the boundary load of random systems is defined by a cross spectral density function that acts on the junction. ...
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