Sentence examples for derived by utilizing the from inspiring English sources

The receptance of the ring is derived by utilizing the modal expansion method.

The governing equations, initial conditions and boundary conditions are derived by utilizing the Hamilton's principle.

First, the existence of a switching rule for the system is derived by utilizing the Shilnikov heteroclinic criterion.

The maximum-likelihood (ML) estimators for the parameters are derived by utilizing the theory for growth curve models.

Based on the theory of surface piezoelectricity and nonlocal piezoelectricity, a novel two-dimensional theory of piezoelectric nanoplates and boundary conditions are derived by utilizing the Hamilton's principle.

The variational consistent equilibrium equations and boundary conditions in terms of both displacements and stress resultants are derived by utilizing the variational principle.

A full dynamical model is derived by utilizing Newton Euler formulation for the development of the flight control system.

In Section 4, a sharp threshold for global existence and blowup of the solutions are derived by utilizing two invariant manifolds, applying potential well argument and the concavity method.

The nonlinear translational dynamic model is derived by utilizing analytical mechanics theory; and analysis on the dynamic characteristics is put forward.

The eigenvalues and eigenfunctions for the instability problem are derived by utilizing a D2 Chebyshev tau method (J. J. Dongarra, B. Straughan, and D. W. Walker, 1996, Appl. Numer. Math.22, 399 435).

Firstly, based on the nonlinear relation between strain and displacement, a set of partial differential equations of the beam and the axial boundary condition for the sliding end are derived by utilizing Hamilton׳s principle, where both frictional force and temperature-dependent properties of material are taken into consideration.