Sentence examples for beam is obtained using from inspiring English sources

Finally, natural frequency of the FG nano beam is obtained using He's variational method.

Based on a mathematical model of the lateral buckling process which considers the geometric and boundary conditions, an optimal geometry of a cantilever beam is obtained using the calculus of variation.

Next, the response of a simply supported nonlinear Timoshenko beam is obtained using a variationally correct (VC) model for the beam [Marur, S., Prathap, G., 2005. Nonlinear beam vibration problems and simplification in finite element model. Comput. Mech. 35 5), 352 360.].

Closed-form expressions of the time-dependent interface stresses and deflection of the beam are obtained using Laplace transform.

In this paper, the natural frequencies and mode shapes of a cracked beam are obtained using the finite element method.

Closed-form expressions of the interface stresses and deflection of the beam are obtained using Laplace transform and calculated using the Zakian's numerical method.

Basis on the Timoshenko beam theory (TBT), the critical buckling load of 2D-FG beams is obtained using the Ritz method.

Stiffness matrix, consistent load vector, and mass matrix of a beam element is obtained using the exact solution of the governing equations.

The governing equation of a micro-beam deflection is obtained using Hamilton's principle and also the governing equations of thermo-diffusive elastic damping are established by using two dimensional non-Fourier heat conduction and non-Fickian mass diffusion models with one relaxation time based on continuum theory frame.

The beam profile at the target is obtained using a simulation.

Elevation beam profiles were obtained using a hydrophone, which showed that the measured −6 dB slice thickness was approximately 3 mm throughout the entire range of field of interest.