Sentence examples for closed form formulations from inspiring English sources

Thus a new analytical approach and corresponding closed form formulations are presented in this paper for evaluating impact energy and induced berthing forces in these piers.

The proposed analysis method addresses the shortcomings of other closed form formulations and results in restraint moments that are more sensitive to the girder age at continuity.

The assume mode/Lagrangian formulation of dynamics is employed to derive closed form equations of motion.

Analytical closed form solutions have been considered.

Closed form SW dispersion equations are introduced.

The explicit formulation of relations in Eq. (5), or equivalently in Eq. (6), can be expressed in closed form in the case of function (vartheta left( cdot right)) (whose details are provided in Sect. 3) and function (gamma left( cdot right)) (whose formulation is provided in Eq. 3).

This study addresses the estimation of buffeting response of overhead conductor based on random vibration theory with closed-form formulations.

Based on the state-space Levy solution, the deflections, stresses, natural frequencies and critical buckling loads are analytically solved for the closed-form formulations.

The aerodynamic modal damping ratios are estimated in closed-form formulations in which the influence of static swing of the conductor plane is explicitly accounted.

Numerical results of the mode mixity predicted by the present closed-form formulations correlate well with those numerically calibrated on the basis of the singular field and crack-tip force models.

Although N-bit phasing is not an optimal closed-loop method, it admits closed-form formulations for performance measures (e.g., the outage probability).