Sentence examples for by the classical plate from inspiring English sources

The vibrations of the plate are investigated both by the classical plate theory and by the improved plate theory (Mindlin plate theory).

To evaluate the effect of shear deformation, anisotropy and other problem parameters on the response, the numerical results obtained with this theory are compared with the results obtained by the classical plate theory.

The comparison of present results with the available molecular dynamics simulation data from the literature shows that the present formulation with appropriate values of surface and nonlocal parameters provides more accurate results than those obtained by the classical plate model.

The bending components (u_{b}) and (v_{b}) are assumed to be similar to the displacements given by the classical plate theory.

The displacements U in x-direction and V in y-direction consist of extension, bending, and shear components: U = u + u_{b} + u_{s},;V = v + v_{b} + v_{s} (2) The bending components (u_{b}) and (v_{b}) are assumed to be similar to the displacements given by the classical plate theory.

Equilibrium and compatibility equations for functionally graded plates are derived by using the classical plate theory taking into account both geometrical nonlinearity in von Karman sense and initial geometrical imperfection.

Here, the coupled dynamic model is derived by mixing the classical plate's theories (Mindlin and Kirchhoff models) and the specific behaviour law for the ultra-thin films, previously introduced in our published works in Applied Acoustics Journal [1], with an integral equation formulation for the acoustic radiation of the studied structure.

In this manuscript, we examined this issue by incorporating the nonlocal theory into the classical plate model.

This manner of variation is similar in form to that demonstrated elsewhere by analyses based on the use of the classical plate theory but the magnitudes of the present calculated frequencies are considerably reduced for moderately thick plates.

The motion equation is derived based on the classical plate theory and solved by using Galerkin method.

The effect of transverse shear and normal deformation on the plate natural frequencies is illustrated by comparing the frequencies of the two higher order theories and the classical plate theory for decreasing length-to-thickness ratio.