Sentence examples for using the present formulation from inspiring English sources

Results obtained using the present formulation are compared with previous classical equivalent linearization results.

A computer program is written using the present formulation for calculating the natural frequencies and harmonic response of composite plates without contact with elastic foundation and composite plates resting on non-homogenous foundations.

Numerical examples are presented using the present formulations to analyze dispersions and characteristics of waves in FGPM plates.

The numerical results calculated using the present formulations are then compared with those available in the literatures to validate the derived novel constituent equations.

Using the present formulations, an FG shaft composed of zirconia (ZrO2) and stainless steel (SS) is considered and the forward and backward whirl frequencies and critical speeds are determined.

Using the presented formulation, FG plates with arbitrary boundary conditions can be analyzed.

We compare our method with existing approaches based on the distribution of migrant tracts obtained through ancestry deconvolution, and we revisit the analysis of the Masai population using the presented formulation.

Under such "compressed gas" conditions, designers of partial condensation separation processes employing cooler-condensers can use the present formulation to account for all systematic departures from a familiar but degenerate limiting case: y1,satp1,saTdpdp)/p, no longer valid.

Numerical examples of the new quasi-3D HSDTs (non-polynomial, polynomial and hybrid) derived by using the present generalized formulation are compared with 3D exact solutions and with other HSDTs.

A Matlab programme has been developed using the present finite element formulation.

Isolation elements composed by rubber bearings are used in the present formulation.