The beam theory allowing for rotary inertia and shear deformation and without the fourth order derivative with respect to time as well as without the slope inertia, as was developed by Elishakoff through the dynamic equilibrium consideration, is derived here by means of bot...
An efficient method has been developed to analyze the natural frequencies of a Timoshenko-Ehrenfest beam with variable cross-sections undergoing free flexural vibration. The method uses a single element to discretize the beam and combines polynomial and trigonometric shape functions to represent the displ...
The main objective of this paper is to study the free vibration behaviour of single-walled carbon nanotubes (SWCNT) using the nonlocal truncated Timoshenko beam theory. According to the Hamilton principle, the equation of motion of Timoshenko single-walled carbon nanotubes is calculated taking into ...
The main objective of this paper is to study the free vibration behaviour of single-walled carbon nanotubes (SWCNT) using the nonlocal truncated Timoshenko beam theory. According to the Hamilton principle, the equation of motion of Timoshenko single-walled carbon nanotubes is calculated taking into ...
Beam modelMeccanica - The first-order shear deformable beam theory should be named after Stephen Timoshenko and Paul Ehrenfest in recognition of the significant contribution of both of them. The...doi:10.1007/s11012-022-01618-1Faghidian, S. Ali...
Bresse‐Timoshenko beam theoryintermingling phenomenonslope inertia based versiontruncated versionIn this study we analyze the free vibrations of a beam on Pasternak foundation by using three alternative beam theories in contrast to other studies which focus on original Bresse-Timoshenko equations only. ...
Here, we propose a variational framework to study the dynamics of the Langevin transducer based on the Timoshenko-Ehrenfest beam theory and Hamilton's principle. The variational equation derived from this model is then discretized by the standard finite element method with spectral elements. To ...
Intermediate Theory Between the Bernoulli–Euler and the Timoshenko–Ehrenfest Beam Theories: Truncated Timoshenko–Ehrenfest EquationsA simple equation is discussed which takes into account both shear deformation and rotary inertia in vibrating beams; it is not as simple as the Bernoulli–Euler equation,...
elasticity theoryTimoshenko-Ehrenfest theoremIn this paper, geometrical interpretation of the Timoshenko-Ehrenfest theorem is given. It is based on a vector-valued version of continuum mechanics, which considers the deformed body as a surface in extended coordinate space. Scalar parameters of the ...
Timoshenko–Ehrenfest beamThe numerical solution of boundary value problems in solid mechanics is dominated by the Finite Element Method (FEM). The present study provides an alternative numerical approach using the Theory of Functional Connections (TFC) for solving problems of this type. Here TFC is...