Sentence examples for using the linear theory from inspiring English sources

The properties like stability and controllability of nonlinear systems can be analyzed using the linear theory.

The highly nonlinear mass matrix because of the inertia coupling between the reference and the elastic displacements is approximated using the linear theory of elastodynamics.

The stress state of crimped pultruded composite rods subjected to traction has been investigated analytically using the linear theory of elasticity of anisotropic body and the superposition principle.

The particle velocity and acceleration components of the Morison equation were obtained using the linear theory of wind-generated waves from the directional wave spectrum obtained by measuring the wave elevation.

Using the linear theory, analytical solution of the critical length of a nanowire, below which there is no buckling, is obtained, which is dependent on the constraint of the ends of the nanowire and the volumetric strain of the nanowire at the fully lithiated state.

(5.21) Since (5.21) is the first order linear partial integro-differential equation with variable coefficients with respect to (F_{0} t,x)), one may prove the existence of a solution by using the linear theory.

Transmission of electric energy through an elastic hollow cylinder by acoustic waves is investigated using the linear theories of piezoelectricity and elasticity.

Although the interaction of a dense (n b > n 0), short proton beam (the wavelength of the plasma wave is of the order of the bunch length, σ z  ~ λ p) with a plasma is inherently nonlinear, we can use the linear theory which predicts the plasma response to either a short electron or proton beam [9, 28].

The thermal resistance of soil can be calculated using the linear source theory and cylindrical source theory, while that inside the borehole is more complicated due to the integrated resistance of fluid convection, and the conduction through pipe and grout.

The typical cases analyzed by Sternling & Scriven (AIChE J., 1959) using the linear instability theory were simulated by the finite difference method and good agreement between the theory and the numerical simulation was observed.

In this paper the design of thermoacoustic refrigerators, using the linear thermoacoustic theory, is described.