11 Hybrid Systems

Basically, we have already applied the hybrid theory in preceding sections, for example Section 7.4. In many cases there were deterministic systems in the junction, for example a plate that we have considered as deterministic connection between the two cavity SEA systems and using the deterministic transfer matrix of the plate.

The twin chamber is an excellent test case for the hybrid method, as it constitutes a clear separation between random and deterministic subsystems and provides all the details of how to deal with each single step of hybrid FEM/SEA simulation.

11.1 Hybrid SEA Matrix

For pure SEA models the matrix from equation (6.113) is applied. The hybrid SEA matrix is similar except one additional damping contribution caused by the damping from the connected FEM-subsystems.

StartLayout 1st Row with Label Start 1 By 1 Matrix 1st Row upper L Superscript prime Baseline EndMatrix equals Start 4 By 4 Matrix 1st Row 1st Column n 1 left-parenthesis eta 11 Superscript alpha Baseline plus sigma-summation Underscript n equals 1 Overscript upper N Endscripts eta Subscript 1 n Baseline right-parenthesis 2nd Column minus n 2 eta 21 3rd Column midline-horizontal-ellipsis 4th Column minus n Subscript upper N Baseline eta Subscript upper N Baseline 1 Baseline 2nd Row 1st Column minus n 1 eta 12 2nd Column n 2 left-parenthesis eta 22 Superscript alpha Baseline plus sigma-summation Underscript n equals 1 Overscript upper N Endscripts eta Subscript 2 n Baseline right-parenthesis 3rd Column Blank 4th Column vertical-ellipsis 3rd Row 1st Column vertical-ellipsis 2nd Column Blank 3rd Column down-right-diagonal-ellipsis 4th Column Blank 4th Row 1st Column minus n 1 eta Subscript 1 upper N Baseline 2nd Column midline-horizontal-ellipsis 3rd Column Blank 4th Column n Subscript upper N Baseline left-parenthesis eta Subscript upper N upper N Superscript alpha Baseline plus sigma-summation Underscript n equals 1 Overscript upper N Endscripts eta Subscript upper N n Baseline right-parenthesis EndMatrix EndLabel Blank EndLayout  (7.35)

All other impacts of the FE parts of the hybrid model are hidden in the hybrid coupling loss factors or an additional power input that may come from radiation of FE-subsystems into the SEA-subsystems.

11.2 Twin Chamber

Figure 11.1 Twin chamber arrangement for TL tests of panel.Source: Alexander Peiffer.

The twin chamber set-up is such a perfect example for the hybrid method, because both chambers are designed to be random by the large size and irregular shape. So, the ...

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