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The article presents the mathematical model allowing to investigate longitudinal and flexural vibrations of stepped flexible waveguides with transitional section without regard to various vibration modes interaction.
On the other hand, it is the utilization of the SPP modes interaction in multi-interface system, for example, the excitation of long-range SPP [8, 9] and channel SPP [10].
The low energy band at 2.45 eV does not correspond to dipole mode interaction and can appear at higher levels of aggregation, as a result of high-order modes interaction (quadrupole, octupole, etc).
Using a double scale perturbative approach including modes interaction, we establish that the evolution of amplitudes of instability patterns is governed by a non-homogeneous second order system of three non-linear complex equations.
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This model applies in the instability mode interaction.
Therefore their binding mode interaction is more or less closer to each other.
Multimode simulations are used to self-consistently model the optical mode interaction with the electron beam.
Some evidence of mode interaction is recorded by the clustering of eigenvalues/eigenmodes.
However, in all cases of mode interaction the dynamic tension is greatly amplified.
We compute the critical aspect ratio and Rayleigh number corresponding to the (ℓ, ℓ+1) mode interaction.
This is especially true for resonance, high forcing frequency and mode interaction cases.
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