Search results for " Timoshenko beam"
showing 6 items of 6 documents
On the dynamics of non-local fractional viscoelastic beams under stochastic agencies
2018
Abstract Non-local viscoelasticity is a subject of great interest in the context of non-local theories. In a recent study, the authors have proposed a non-local fractional beam model where non-local effects are represented as viscoelastic long-range volume forces and moments, exchanged by non-adjacent beam segments depending on their relative motion, while local effects are modelled by elastic classical stress resultants. Long-range interactions have been given a fractional constitutive law, involving the Caputo's fractional derivative. This paper introduces a comprehensive numerical approach to calculate the stochastic response of the non-local fractional beam model under Gaussian white no…
On the vibrations of a mechanically based non-local beam model
2012
The vibration problem of a Timoshenko non-local beam is addressed. The beam model involves assuming that the equilibrium of each 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 taken as depending on the product of the interacting volume elements and on their relative displacement through a material-dependent distance-decaying function. To derive the motion equations and the related mechanical boundary conditions, the Hamilton's principle is applied The vibration problem of a Timoshenko non-local beam …
Hamiltonian structural analysis of curved beams with or without generalized two-parameter foundation
2013
The solution of curved Timoshenko beams with or without generalized two-parameter elastic foundation is presented. Beam can be subjected to any kind of loads and imposed external actions, distributed or concentrated along the beam. It can have external and internal restraints and any kind of internal kinematical or mechanical discontinuity. Moreover, the beam may have any spatial curved geometry, by dividing the entire structure into segments of constant curvature and constant elastic properties, each segment resting or not on elastic foundation. The foundation has six parameters like a generalized Winkler soil with the addition of other two parameters involving the link between settlements…
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 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…