By linearization about a trim condition, a decoupled model made of four dynamic modes is derived.
In particular, expressions for the coverage probabilities with different sleeping policies and access modes are derived in closed forms.
The effects of the absorber tuning order on the modes are derived.
General properties of the dispersion relation (eigenvalue relation) for the neutrally stable acoustic modes are derived.
Lastly, the non-linear normal modes are derived again using the phase-closure principle.
The dispersion relation for the symmetric modes are derived by using a modal approach.
The characteristic equations for the natural frequencies of both in-plane and out-of-plane vibration modes are derived.
Thermodynamic criteria governing each of these four evolution modes are derived with respect to an initial sinusoidal perturbation.
Meanwhile, the extended stress intensity factors (SIFs) including two new fracture modes are derived in terms of the extended displacement discontinuities.
Based on the von Kármán nonlinear theory, Galerkin's method and the static condensation method, the coupled nonlinear differential equations with two modes are derived.
