Sentence examples for mode solutions of from inspiring English sources

In 1749 he went on to explain that if several normal mode solutions of the wave equation are superposed, the result is a solution of the form where the coefficients a1, a2, a3, … are arbitrary constants.

The higher EOF mode solutions of the non-seasonal OBP (ΔP) from the GRACE GAD+GSM dataset.

Apart from this, a remarkable feature of Orthomin(1) brought out in this paper is its utility to find higher mode solutions of the K-eigenvalue problem.

This particle creation is characterised by the Bogoliubov coefficients, where, are the m and n mode solutions of Eq. (5) given by the metrics in Eq. (10) and Eq. (9) respectively.

The limitations of the theory are discussed and its predictions are compared with the fundamental mode solutions of the convected wave equation, the Pridmore-Brown equation and measurements where available.

Fig. 2 The leading EOF mode solutions of the non-seasonal OBP from the GRACE datasets, where the spatial pattern shows the amplitude of fluctuation (with positive or negative polarity) at each location according to the corresponding time history, for the GRACE datasets of: a the GAD; b the GSM; and c the GAD+GSM.

The exact buckling mode solution of the column, as functions of four integration constants, and the corresponding exact buckling load equation for any number, position and intensity of the cracks are presented.

The algorithm was first used by Suetomi and Sekimoto [Conjugate gradient like methods and their application to eigenvalue problems for neutron diffusion equations, Annals of Nuclear Energy, 18(4) (1991) 205 227.] to find fundamental mode solution of K-eigenvalue problem based on multi-group neutron diffusion theory.

From the Navier equations we derive that the lowest resonant frequencies are associated with localised bending modes solutions of a fourth-order differential equation in thin-bridges, which are responsible for the appearance of a low frequency stop band.

The buckling mode shapes are obtained by substituting the nontrivial coefficient solutions into the mode shape solutions of the subproblems, followed by superposition.

Amplitude- and phase-modulated motion including chaotic vibrations appears on the branches of the frequency response curves, which correspond to the single mode solution, when some deviation of the internal resonance ratio exists.