1,720,986 research outputs found
Variational Derivation of Truncated Timoshenko-Ehrenfest Beam Theory
No full textThe 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 both direct and variational methods. This formulation is important for using variational methods of Rayleigh, Ritz as well as the finite element method (FEM). Despite the fact that literature abounds with variational formulations of the original Timoshenko-Ehrenfest beam theory, since it was put forward in 1912-1916, until now there was not a single derivation of the version without the fourth derivative and without the slope inertia. This gap is filled by the present paper. It is shown that the differential equations and the corresponding boundary conditions, used to find the solution of the dynamic problem of a truncated Timoshenko-Ehrenfest via variational formulation, have the same form to that obtained via direct method. Finally, in order to illustrate the advantages of the variational approach and its adaptability to the finite element formulation, some numerical examples are performed. The calculations are implemented through a software developed in Mathematica language and results are validated by comparison with those available in the literature
Nonlocal frequency analysis of embedded single-walled carbon nanotube using the Differential Quadrature Method
No full textIn the present paper free vibrations of embedded single-walled carbon nanotubes based on local Euler
eBernoulli beam theory are investigated. The surrounding elastic medium is described as the Winkler
and Pasternak models, defined by the kw and kp coefficients. The Hamilton principle is applied to derive
the governing equations and boundary conditions, which are solved by using the well-known Differential
Quadrature Method (DQM). The influence of the elastic medium coefficients, nonlocal parameter and end
supports on the free vibrations characteristics of the single-walled carbon nanotube (SWCNT) is
described. Numerical examples are performed to show the accuracy of the proposed method
Intervallo di quarta. Reinventare la musica cinese in Occidente: uno sguardo retrospettivo sulla letteratura pianistica
No full textNonlocal Timoshenko frequency analysis of single-walled carbon nanotube with attached mass: An alternative hamiltonian approach
No full textIn the present paper, the nonlocal vibration analysis of single-walled carbon nanotube as nanosized mass-sensor is examined. The nanotube is modeled as a clamped-free Timoshenko beam carrying an attached mass at its free end. Using the nonlocal Timoshenko beam theory, a re-formulation of Hamilton's principle has been presented and the equations of motion and the general corresponding boundary conditions have been derived. The main purpose of this paper is to show the sensitivity of the nanotube to the values of added mass and the in presence of nonlocal parameter on the fundamental frequencies values. Some numerical examples have been performed and discussed and the obtained results are compared with those of available works in literature and listed in bibliography
Free-Vibration Analysis for Truncated Uflyand–Mindlin Plate Models: An Alternative Theoretical Formulation
No full textStatic analysis of a double-cap masonry dome
No full textThe present work is focused on the analysis of the double-cap dome of St. Januarius Chapel, in Naples (Italy). Three different approaches based on the limit analysis for unilateral (no-tension) material has been applied to evaluate the dome stability. In the first approach, the overall stability of the dome has been investigated through a method of graphical statics. The method is a generalization of the “thrust line analysis” used for arches and consists in finding a purely compressed membrane in equilibrium with the external loads and entirely contained in the thickness of the dome, in the spirit of safe theorem. In the second approach, which is concerned with the equilibrium of domes and vaults, a thrust surface in equilibrium with the assigned external loads is found by numerically solving the Pucher’s differential equation. This latter is nothing but the equilibrium of the unknown thrust surface along the direction of vertical, i.e. gravitational, loads, where generalized stresses are conveniently projected on the platform, that is in the horizontal plane. Again in the spirit of the safe theorem, the thrust surface must be entirely contained within the volume of the structure. The solution procedure is based on the finite difference technique and has been implemented in a Mathematica-based code. Finally, in the third approach, a three-dimensional rigid block model with no-tension, frictional interfaces is employed. The formulation and the solution procedure of the underlying limit analysis problem has been implemented in a MATLAB-based tool equipped with a graphical user interface. The obtained results allow to state that the dome, under ordinary load conditions, is safe
The influence of dowel-bearing strength in designing timber pegged timber joints
No full textThe employment of timber pegs in timber structure joints is a widespread technology in the field of timber frame building in the USA, where the Timber Frame Engineering Council has published a special Standard to supplement the National Design Specification for Wood Construction. The Authors have been studying the possibility of supplementing the Eurocode 5 design formulas, thought for timber joints with metal connectors, with specifications needed for a reliable design when employing timber pegs. The field of application envisaged is that of restoring timber structures and results obtained until now are quite encouraging. In this step of the research, more attention has been paid to deformation process: fir and chestnut samples have been tested to determine their dowel-bearing behaviour with steel and ash timber peg while double shear plane joints made of the same wood species, and fastened with steel as well as timber pegs, have been analysed
Reinforcing stop-splayed scarf joints with timber pegs: Role of slenderness
No full textRepairing stop-splayed scarf-joints in beams or truss-rods is a frequent occurrence in restoring ancient timber structures. Reinforcement of carpentry joints by means of metallic elements as well as unconventional materials is extensively investigated in literature, while timber pegs in timber to timber connections are studied referring mainly to new timber structures. In the present paper, authors' previous research analysing the mechanical behaviour of stop-splayed scarf joints reinforced with timber pegs has been carried on, focusing on the evaluation of ductility which can be achieved by reinforcement with timber pegs. Moreover, the role of slenderness, the rate between jointed timber thickness and peg diameter is analysed. An experimental program has been carried out testing in axial tension two samples of fir scarf joints with an ash key: one sample constituted of two simple scarf joints, and one constituted of three scarf joints reinforced with two ash pegs of 20 mm of diameter. Comparing experimental results has allowed to better understand the role played by timber pegs in reinforcement and to evaluate the influence of reinforcement on ductility of reinforced scarf joints behaviour. Experimental results have also been compared with those obtained in a previous experimental study where an analogous experimental program has been made on smaller scarf joints reinforced with two ash pegs of 8 mm of diameter. So, the role played by slenderness has been focused. The evaluation of the attained results, even if not exhaustive for a reliable theoretical formulation of timber peg behaviour in reinforcing stop-splayed joints, has allowed the identification of some interesting features, that is stiffness and reinforcement due to timber pegs
Equilibrium of masonry-like vaults treated as unilateral membranes: Where mathematics meets history
No full textIn this paper, we study the equilibrium of masonry vaults, assuming that the material has infinite friction and no cohesion (i.e. it is No-Tension in the sense of Heyman). With Heyman's assumptions, the equilibrium of a structure composed of this ideal masonry material, can be studied with limit analysis. In particular, the present study is concerned with the application of the safe theorem of limit analysis to masonrylike vaults, that is, curved constructions modelled as continuous unilateral bodies. On allowing for singular stresses in the form of line or surface Dirac deltas, statically admissible stress fields concentrated on surfaces (and on their folds) lying inside the masonry, are considered. Such surface and line structures are unilateral membranes/arches, whose geometry is described a la Monge, and their equilibrium can be formulated in Pucher form. It is assumed that the load applied to the vault is carried by such a (possibly folded) membrane structure S. The geometry of the membrane S, that is of the support of the singularities, is not fixed, in the sense that it can be displaced and distorted, provided that one keeps it inside the masonry. Two particular case studies are analyzed to illustrate the method: a cross vaults of the Gothic Cathedral of Caserta, and a modern timbrel spiral stair built by the Guastavinos in New York
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