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Full 2×2 impedance matrices are included in the derivation of the reflection matrix of an arbitrary structural junction.
An active impedance load is introduced in order to match a discontinuity at the junction, i.e. to force the reflection matrix to zero.
This equation is numerically integrated using an adaptive Runge Kutta Fehlberg method, yielding the frequency- and spatially-dependent impedance matrix of the beam, from which the reflection matrix is obtained.
The approximation properties of PMDL quantified through its reflection matrix is used to derive simple bounds on the PMDL parameters necessary for the accurate absorption of all outgoing anti-plane and in-plane wavemodes – including those with cpxcgx<0.
By deriving a multiband k⋅p Riccati equation for the envelope function matrix, it is shown how to obtain the reflection matrix through a simple numerical integration of the Riccati equation.
Note that there are degenerate cases where det(V U T ) = -1, which means that V U T is a reflection matrix.
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be generalized reflection matrices.
Reflection matrices are presented for the plate domain.
Firstly, the propagation and reflection matrices for nanobeams are derived.
Firstly, the propagation and reflection matrices are derived for circular annular nanoplates.
The transmission and reflection matrices for various discontinuities on an axially loaded Timoshenko beam are derived.
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