Sentence examples for the present formulae from inspiring English sources
It is shown that the present formulae are extremely efficient by cutting the CPU time by orders of magnitude in comparison with the traditional numerical integration scheme.
Finally, two simulations are conducted to validate the present formula.
The present formulas can provide references for estimation of the transmission coefficient in engineering practice.
The present formula employs a fundamental solution that eliminates the discretization of the top ground surface.
The rationality of the present formulas was verified by their comparison with existing empirical and analytical formulas.
It is verified that those formulas may be obtained readily from the present formulas by considering their certain assumptions.
Comparative analysis shows that the results of the present formulas agree with the numerical flume results as well as available experimental data, and the present formulas are superior to the existing empirical and analytical expressions in estimating the transmission coefficient.
The validities of the present formulas are confirmed by comparing them with demagnetization coefficients estimated in earlier works.
This paper ends with usefulness of the present formula in examining the structural characteristic of ship's hull.
The 3D finite element numerical simulation has validated the present formulas of natural frequencies and mode shapes.
The 3D finite element numerical simulations have verified the present formulas of natural frequencies and mode shapes.
