Analytical relations between the critical buckling load of a functionally graded material (FGM) Timoshenko beam and that of the corresponding homogeneous Euler–Bernoulli beam subjected to axial compressive load have been derived for clamped–clamped (C–C), simply supported–simply supported (S–S) and clamped–free (C–F) edges. However, no such relation is found for clamped–simply supported (C–S) b...

In this work, the dynamic response of Euler–Bernoulli beams four different boundary conditions with fractional order internal damping under a traversing moving load is investigated. The assumed to be values constant velocity. A proposed approach obtain closed-form solution problem based on Green’s functions combined decomposition technique in Laplace transform domain introduced. Several cases a...

The vibration problems of uniform and nonuniform Euler-Bernoulli beams have been solved analytically or approximately [1-5] for various end conditions. In order to calculate fundamental natural frequencies and related mode shapes, well known variational techniques such as Rayleigh_Ritz and Galerkin methods have been applied in the past. Besides these techniques, some discretized numerical metho...

Analysis of the free and forced vibration responses beams is one most critical problems to be examined in design step these structural members. The finite-element method which solves boundary value can applied efficiently problems. In this study, natural frequency damped undamped transient analyses pinned-pinned are investigated. well-known software packages, ANSYS SAP2000, used. 2-D elastic be...

We study in this paper the stability of a system type Rao–Nakra sandwich beam whole line $\mathbb{R}$ under linear frictional dampings acting on two wave equations. prove that $L^2(\mathbb{R})$-norm solutions and their higher order derivatives with respect to space variable converge polynomially zero as time goes infinity. These decay estimates are obtained independently parameters spite fact E...

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...