Sentence examples for derived for free from inspiring English sources

Exact expressions for the displacement field are derived for free oscillation and forced oscillations with prescribed pressure differences.

The analytical model, originally derived for free vibration analyses and system identification applications, is extended in the present paper to earthquake response simulations.

Analytical solutions are derived for free vibrations of three-dimensional, linear anisotropic, magneto-electro-elastic, and multilayered rectangular plates under simply supported edge conditions.

Based on the Flory theory of polymer networks with constrained junctions, a novel expression is derived for free energy density of a swollen elastomer.

The frequency equations previously derived for free, axisymmetric vibrations of an elastic spherical shell submerged in a compressible viscous fluid is reduced to a simple polynomial expression.

First-known exact solutions are derived for free vibration of thick and moderately thick functionally graded rectangular plates with at least one pair of opposite edges simply-supported on the basis of a family of two-dimensional shear and normal deformation theories with variable order.

Closed-form solutions are derived for the free vibration problem of cylindrical microshells with simply supported ends and fixed ends respectively.

In this note, exact frequency and normal mode expressions are derived for the free torsional vibrations of circular shafts or piping systems constrained by unsymmetrical torsional springs and carrying unequal rotational masses at either end.

Originally the Kozeny equation was derived for clay-free sand with high porosity, and for that reason Walderhaug et al. (2012) suggested a modified Kozeny equation for predicting permeability in quartz-rich sandstones, even with high clay content.

The predicted horizontal flame extent also agrees well with existing experimental correlations, although some difference may indicate that the relation between the mean and continuous flame heights derived for an open free pool fire may no longer apply due to the presence of the ceiling which affects air entrainment and the turbulence of the ceiling flame jet.

Recall that the new model derived for predicting the free energy of formation of trinucleotide bulges has a parameter that was dependent upon the sequence of the bulge (Δ G°37, bulge).