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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.
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By linearization about a trim condition, a decoupled model made of four dynamic modes is derived.
The modes were derived in turn from the 14 murchanas seven pairs of ascending seven-note series beginning on each of the notes of two closely related heptatonic (seven-note) parent scales, called sadjagrama and madhyamagrama.
Analytical expressions for five possible failure modes were derived considering not only stretching and bending deformation but also shear deformation of struts.
Based on numerical results, a semi analytical boundary that separates the slab's flexural and shear failure modes is derived as a function of peak reflected pressure and duration of blasting wave.
The method for obtaining the short-time narrow-banded modes is derived by minimizing an objective function comprised of three criteria: smoothness of the instantaneous amplitude envelope, smoothness of the instantaneous frequency and complete reconstruction of the signal data.
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