Sentence examples for utilized the equations of from inspiring English sources

For the model herein utilized, the equations of motion, in terms of displacements and rotation, take into account shearing and axial deformations and rotary inertia.

Thereafter, the required curing time to achieve a particular rate of change of the compressive strength has been predicted utilizing the equation derived from the variation of the rate of change of compressive strength with the curing time, prior to the optimization of the curing time (at the 99.99% confidence level) using the Weibull distribution model.

To calculate the duration of ground motion, we utilized the empirical equation of Nojima (2014), which predicts the duration of a specific JMA seismic intensity under given values of predicted or observed JMA seismic intensity.

In order to consider the sub-grid scale (SGS) effects of the gas velocity and scalar fluctuation transport and evaporation, we utilized the transport equation of the velocity scalar joint filtered density function (VSJFDF) of the gas flow experienced by the droplets.

The investigations are carried out within the framework of the piecewise homogeneous body model by utilizing the exact equations of motion and relations of the linear theory of electro-elasticity.

Formation of potential tetrahedral blocks has been algebraically discerned by utilizing the plane equations of discontinuities.

Hamilton's principle is utilized to derive the equations of motion.

Hamilton's principle is utilized in deriving the equations of motion.

Then, weak form formulation and spatial approximations of variables are utilized to discretize the equations of motion.

The equations of motion and boundary conditions are derived by applying Hamilton's principle, and the general Galerkin method is utilized to convert the equations of motion into a set of coupled Hill's equations with complex coefficients in the time domain.

The investigations are made by utilizing the exact equations of linear viscoelasto-dynamics.