Search results for "beam"
showing 10 items of 2126 documents
Finite element method for a nonlocal Timoshenko beam model
2014
A finite element method is presented for a nonlocal Timoshenko beam model recently proposed by the authors. The model relies on the key idea that nonlocal effects consist of long-range volume forces and moments exchanged by non-adjacent beam segments, which contribute to the equilibrium of a beam segment along with the classical local stress resultants. The long-range volume forces/moments are linearly depending on the product of the volumes of the interacting beam segments, and their relative motion measured in terms of the pure beam deformation modes, through appropriate attenuation functions governing the spatial decay of nonlocal effects. In this paper, the beam model is reformulated wi…
A one-dimensional model for dynamic analysis of generally layered magneto-electro-elastic beams
2013
Abstract A new one-dimensional model for the dynamic problem of magneto-electro-elastic generally laminated beams is presented. The electric and magnetic fields are assumed to be quasi-static and a first-order shear beam theory is used. The electro-magnetic problem is first solved in terms of the mechanical variables, then the equations of motion are written leading to the problem governing equations. They involve the same terms of the elastic dynamic problem weighted by effective stiffness coefficients, which take the magneto-electro-mechanical couplings into account. Additional terms, which involve the third spatial derivative of the transverse displacement, also occur as a result of the …
Fractional visco-elastic Timoshenko beam from elastic Euler-Bernoulli beam
2014
The Euler–Bernoulli beam theory is well established in such a way that engineers are very confident with the determination of the stress field or deflections of the elastic beam based on this theory. In contrast, Timoshenko theory is not so much used by engineers. However, in some cases, Euler–Bernoulli theory, which neglects the effect of transversal shear deformation, yields unacceptable results. For instance, when dealing with visco-elastic behavior, shear deformations play a fundamental role. Recent studies on the response evaluation of a visco-elastic Euler–Bernoulli beam under quasi-static and dynamic loads have been stressed that for better capturing of the visco-elastic behavior, a …
Fractional visco-elastic Timoshenko beam deflection via single equation
2015
SUMMARY This paper deals with the response determination of a visco-elastic Timoshenko beam under static loading condition and taking into account fractional calculus. In particular, the fractional derivative terms arise from representing constitutive behavior of the visco-elastic material. Further, taking advantages of the Mellin transform method recently developed for the solution of fractional differential equation, the problem of fractional Timoshenko beam model is assessed in time domain without invoking the Laplace-transforms as usual. Further, solution provided by the Mellin transform procedure will be compared with classical Central Difference scheme one, based on the Grunwald–Letni…
A mechanically based approach to non-local beam theories
2011
A mechanically based non-local beam theory is proposed. The key idea is that the equilibrium of each beam volume element is attained due to contact forces and long-range body forces exerted, respectively, by adjacent and non-adjacent volume elements. The contact forces result in the classical Cauchy stress tensor while the long-range forces are modeled as depending on the product of the interacting volume elements, their relative displacement and a material-dependent distance-decaying function. To derive the beam equilibrium equations and the pertinent mechanical boundary conditions, the total elastic potential energy functional is used based on the Timoshenko beam theory. In this manner, t…
Mathematical model for the adsorption-induced nonlocal frequency shift in adatoms-nanobeam system
2017
Abstract This paper models and investigates the resonance frequency shift induced by the adsorption phenomena for an adatoms-nanobeam system including the small scale effect as well as rotary inertia and shear distortion effects. The Lennard-Jones (6–12) type potential is used to determine the adsorption-induced energy owing van der Waals (vdW) interaction mechanism between adatom-adatom and adatom-substrate. The small scale effect is introduced by using Eringen's nonlocal elasticity theory while the explicit expressions of inertia moment and shear force are derived from the standard Timoshenko beam equations in which the residual stress effect is accounted as an additive axial load. Numeri…
Finite-Element Formulation of a Nonlocal Hereditary Fractional-Order Timoshenko Beam
2017
AbstractA mechanically-based nonlocal Timoshenko beam model, recently proposed by the authors, hinges on the assumption that nonlocal effects can be modeled as elastic long-range volume forces and moments mutually exerted by nonadjacent beam segments, which contribute to the equilibrium of any beam segment along with the classical local stress resultants. Long-range volume forces/moments linearly depend on the product of the volumes of the interacting beam segments, and on pure deformation modes of the beam, through attenuation functions governing the space decay of nonlocal effects. This paper investigates the response of this nonlocal beam model when viscoelastic long-range interactions a…
A new displacement-based framework for non-local Timoshenko beams
2015
In this paper, a new theoretical framework is presented for modeling non-locality in shear deformable beams. The driving idea is to represent non-local effects as long-range volume forces and moments, exchanged by non-adjacent beam segments as a result of their relative motion described in terms of pure deformation modes of the beam. The use of these generalized measures of relative motion allows constructing an equivalent mechanical model of non-local effects. Specifically, long-range volume forces and moments are associated with three spring-like connections acting in parallel between couples of non-adjacent beam segments, and separately accounting for pure axial, pure bending and pure sh…
Analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem
2009
Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the def…
Timoshenko vs Euler-Bernoulli beam: fractional visco-elastic behaviour
2013
The Euler-Bernoulli beam theory is well established in such a way that engineers are very confident with the determination of stress field or def lections of the elastic beam based on this theory. Conversely Timoshenko theory is not so much used by engineers. However in such cases Euler-Bernoulli theory that n eglects the effect of transversal shear deformation leads to unacceptable results. For inst ance when dealing with the visco-elastic behaviour the shear deformations play a fundamental role. Recent studies [1]-[2] on the response evaluation of visco-elastic Euler-Bernoulli beam under quasi-static and dynamic loads, have been stressed that for better capturing the visco-elastic behavio…