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Hence, one of the most important candidates for constructing ultra small ADFs without significant losses are photonic crystal ring-resonators (PCRRs), where the guided mode is coupled between two W1 waveguides.
In the Hamiltonian model of eq 11.5 the solvent mode is coupled to both the q and R coordinates.
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When a local (cable) and a global (structure) mode are coupled, even very small motion of the deck or tower may cause dynamic instability and extremely large vibration amplitudes of the stay cables.
When the tube cross section is perfectly circular, acoustic modes are coupled with structural modes having the same circumferential symmetry.
The bending coupled modes, in which shaft bending modes are coupled with one nodal diameter disk modes, are classified as the balanced and unbalanced modes.
If we set Q′ = 0 and B′ = 0 in Equations (11), (12), (13), the vertical oscillatory mode will be an independent mode, while two other modes are coupled yet.
Because of the swirling nature of the flow, the modes are coupled by pairs of nearly equal energy, hence mode 1 and 2 are similar, as well as 3 and 4, Fig. 5 (down).
In the general case with 3D ground conductivity variations the TE and TM modes are coupled to each other, but in 2D cases they can be separated into E-polarization and B-polarization modes by choosing the coordinate system appropriately.
In this case, the effect of damping is far more complicated since several modes are coupled both in terms of friction and damping.
These modes are coupled through gyroscopic and non-linear terms, while the parametric excitation originates by small periodic perturbations of the spin speed of the ring.
Prior to fabrication, simulation of modes was coupled to predict the performance of this chemosensor.
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