Non-prismatic beams have received great attention from engineers due to their capability in optimizing the strength and weight of the structure. In recent years, many researchers have worked on engineering problems related to static and dynamic analysis of either Euler–Bernoulli [1–3] or Timoshenko [4,5] beams. For short thick beams and rotating machineries, the Timoshenko beam theory presents ...

The equilibrium position of an Euler-Bernoulli beam is investigated. Using the discrete Euler-Lagrange and Lagrange-d’Alembert principles, the behavior of the beam is simulated using variational integrators and, in particular, AVIs (Asynchronous Variational Integrators). Special emphasis is placed on the discrete mechanics and geometric structure underlying stress resultant beam models.

the static pull-in instability of beam-type micro-electromechanical systems is theoretically investigated. two engineering cases including cantilever and double cantilever micro-beam are considered. considering the mid-plane stretching as the source of the nonlinearity in the beam behavior, a nonlinear size-dependent euler-bernoulli beam model is used based on a modified couple stress theory, c...

In this paper, the modified Euler-Bernoulli beam model is presented to examine the influence of surface elasticity and residual surface tension on the critical force of axial buckling of nanotubes in the presence of rotary inertia. An explicit solution is derived for the buckling loads of microscaled Euler beams considering surface effects. The size-dependent buckling behavior of the nanotube d...

the vibration of cable-stayed bridges subjected to the passage of high-speed trains is studied in this article. the moving train includes a number of wagons, each of which is modeled as a four-axle system possessing 48 degrees of freedom. the car model is nonlinear and three-dimensional and includes nonlinear springs and dampers of primary and secondary suspensions, dry friction between differe...

This paper presents a way of using He’s variational iteration method to solve free vibration problems for an Euler–Bernoulli beam under various supporting conditions. By employing this technique, the beam’s natural frequencies and mode shapes can be obtained and a rapidly convergent sequence is obtained during the solution. The results obtained are the same as the results obtained by the Adomia...

We show that a non-dissipative feedback that has been shown in the literature to exponentially stabilize an Euler-Bernoulli beam makes a Rayleigh beam and a Timoshenko beam unstable.

Finite element formulations based generally on classical beam theories such as Euler-Bernoulli or Timoshenko. Sometimes, these two formulations could be problematic expressed in terms of restrictions of Euler-Bernoulli beam theory, in case of thicker beams due to non-consideration of transverse shear; phenomenon that is known as shear locking characterized the Timoshenko beam theory, in case of...

In this paper, the modified Euler-Bernoulli beam model is presented to examine the influence of surface elasticity and residual surface tension on the critical force of axial buckling of nanotubes in the presence of rotary inertia. An explicit solution is derived for the buckling loads of microscaled Euler beams considering surface effects. The size-dependent buckling behavior of the nanotube d...