On the flexural vibration of cylinders under axial loads:Numerical and experimental study

The flexural vibration of a homogeneous isotropic linearly elastic cylinder of any aspect ratio is analysed in this paper. Natural frequencies of a cylinder under uniformly distributed axial loads acting on its bases are calculated numerically by the Ritz method with terms of power series in the coordinate directions as approximating functions. The effect of axial loads on the flexural vibration cannot be described by applying infinitesimal strain theory, therefore, geometrically nonlinear strain–displacement relations with second-order terms are considered here. The natural frequencies of free–free, clamped–clamped, and sliding–sliding cylinders subjected to axial loads are calculated using the proposed three-dimensional Ritz approach and are compared with those obtained with the finite element method and the Bernoulli–Euler theory. Different experiments with cylinders axially compressed by a hydraulic press are carried out and the experimental results for the lowest flexural frequency are compared with the numerical results. An approach based on the Ritz formulation is proposed for the flexural vibration of a cylinder between the platens of the press with constraints varying with the intensity of the compression. The results show that for low compressions the cylinder behaves similarly to a sliding–sliding cylinder, whereas for high compressions the cylinder vibrates as a clamped–clamped one.

Influence of the Second Flexural Mode on the Response of High-Speed Bridges

This paper deals with the assessment of the contribution of the second flexural mode to the dynamic behaviour of simply supported railway bridges. Alluding to the works of other authors, it is suggested in some references that the dynamic behaviour of simply supported bridges could be adequately represented taking into account only the contribution of the fundamental flexural mode. On the other hand, the European Rail Research Institute (ERRI) proposes that the second mode should also be included whenever the associated natural frequency is lower than 30 Hz]. This investigation endeavours to clarify the question as much as possible by establishing whether the maximum response of the bridge, in terms of displacements, accelerations and bending moments, can be computed accurately not taking account of the contribution of the second mode. To this end, a dimensionless formulation of the equations of motion of a simply supported beam traversed by a series of equally spaced moving loads is presented. This formulation brings to light the fundamental parameters governing the behaviour of the beam: damping ratio, dimensionless speed $ \alpha$=VT/L, and L/d ratio (L stands for the span of the beam, V for the speed of the train, T represents the fundamental period of the bridge and d symbolises the distance between consecutive loads). Assuming a damping ratio equal to 1%, which is a usual value for prestressed high-speed bridges, a parametric analysis is conducted over realistic ranges of values of $ \alpha$ and L/d. The results can be extended to any simply supported bridge subjected to a train of equally spaced loads in virtue of the so-called Similarity Formulae. The validity of these formulae can be derived from the dimensionless formulation mentioned above. In the parametric analysis the maximum response of the bridge is obtained for one thousand values of speed that cover the range from the fourth resonance of the first mode to the first resonance of the second mode. The response at twenty-one different locations along the span of the beam is compared in order to decide if the maximum can be accurately computed with the sole contribution of the fundamental mode.

Fadiga cíclica flexural de instrumentos Hyflex CM e TF Adaptive em diferentes situações experimentais

O presente estudo teve como objetivo avaliar a resistência à fadiga cíclica flexural dos instrumentos de níquel- titânio, Hyflex CM (Coltène, EUA) e TF Adaptive (SybronEndo, EUA) em diferentes situações experimentais. Todas as limas que foram selecionadas possuíam conicidade 0,04 e diâmetro de ponta 35. Utilizou-se um dispositivo desenvolvido especificamente para realizar o ensaio flexural dinâmico. Os instrumentos TF Adaptive foram divididos em 3 grupos de acordo com o ângulo de curvatura do ensaio: 45º, 60º e 90º e cada grupo subdividido em 2 subgrupos de acordo com o tipo de movimento: rotação contínua e Adaptive. Cada subgrupo era composto por 15 instrumentos TF Adaptive, totalizando 90 instrumentos. Quinze instrumentos Hyflex CM formavam o grupo 4, no ensaio com ângulo de curvatura 90 graus e rotação contínua. A simulação foi realizada em canais artificiais de aço com ângulo de 45, 60, 90 graus e raio 5m m. O número de ciclos e o tempo em segundos até a fratura foram tabulados e analisados. Entretanto, a fadiga cíclica flexural foi significante maior nos três grupos em movimento Adaptive. E as limas TF Adaptive em seu próprio movimento tiveram maior número de ciclos e tempo até a fratura quando comparadas as Hyflex CM no ensaio de 90 graus. Portanto, conclui-se que o sistema Adaptive (limas TF Adaptive + movimento Adaptive) foi mais seguro à resistência á fadiga flexural, e no ensaio de 90 graus o sistema Adaptive foi mais resistente quando comparado com as limas Hyflex CM no movimento de rotação contínua.

Efficient intrinsic spin relaxation in graphene due to flexural distortions

We propose an intrinsic spin scattering mechanism in graphene originated by the interplay of atomic spin-orbit interaction and the local curvature induced by flexural distortions of the atomic lattice. Starting from a multiorbital tight-binding Hamiltonian with spin-orbit coupling considered non-perturbatively, we derive an effective Hamiltonian for the spin scattering of the Dirac electrons due to flexural distortions. We compute the spin lifetime due to both flexural phonons and ripples and we find values in the 1-10 ns range at room temperature. The proposed mechanism dominates the spin relaxation in high mobility graphene samples and should also apply to other planar aromatic compounds.

Anisotropic intrinsic spin relaxation in graphene due to flexural distortions

We propose an intrinsic spin scattering mechanism in graphene originated by the interplay of atomic spin-orbit interaction and the local curvature induced by flexural distortions of the atomic lattice. Starting from a multiorbital tight-binding Hamiltonian with spin-orbit coupling considered nonperturbatively, we derive an effective Hamiltonian for the spin scattering of the Dirac electrons due to flexural distortions. We compute the spin lifetime due to both flexural phonons and ripples and we find values in the microsecond range at room temperature. Interestingly, this mechanism is anisotropic on two counts. First, the relaxation rate is different for off-plane and in-plane spin quantization axis. Second, the spin relaxation rate depends on the angle formed by the crystal momentum with the carbon-carbon bond. In addition, the spin lifetime is also valley dependent. The proposed mechanism sets an upper limit for spin lifetimes in graphene and will be relevant when samples of high quality can be fabricated free of extrinsic sources of spin relaxation.

Damping of flexural vibrations by alternate visco-elastic and elastic layers

"Materials Laboratory, Contract no. AF 33(616)-5426, Project no. 7360."

Flexural strength of plain concrete,

Mode of access: Internet.

Analysis of flexural isostasy of the northern Andes

The mode in which a lithosphere plate supports overlying topography is greatly driven by the strength of the plate. By analyzing the geophysical signature of lithosphere flexure, in the space and spectral domains, the strength of the plates that support the north Andean mountains and adjacent basins, and the topography of Kenya was investigated. In addition, the effect of windowing on elastic thickness estimates obtained via the coherence method was evaluated. ^ The coherence between the topography and Bouguer gravity spectra of northern South America suggests that the average elastic thickness of the lithosphere is 30 km. Although lateral variations were not resolved by the coherence implementation, these became apparent by modeling the foreland stratigraphy of the Llanos, Barinas and Maracaibo sub-Andean basins. Flexural models reveal a zone of lithosphere weakness beneath the eastern flank of the Eastern Cordillera and western flank of the Venezuelan Andes. The gravity anomaly calculated from these models is consistent with the observed Bouguer gravity anomaly. This zone of weakness appears to separate the strong, old Guyana shield lithosphere from the weaker and probably younger Andean lithosphere. The zone of weakness may correspond to a Paleozoic feature at the western margin of cratonic South America, or a Mesozoic rift arm that weakened the proto-Andean lithosphere. ^ Using synthetic data as well as the northern South America topography and gravity, this study demonstrates that lithosphere strength calculated from the coherence of mirrored data may overestimate the true lithosphere strength. As a result, many lithosphere plates may be weaker than currently thought. In light of this observation, gravity and topography data from Kenya were reevaluated using multitaper spectral techniques. The elastic thickness of this plate, currently undergoing rifting, was estimated at 7 to 8 km, a factor of 2 less than previously estimated. These estimates suggest that despite intense fracturing and sustained tensile stresses, continental lithosphere plates undergoing rifting are able to retain some strength. ^

The Effect of Foam Core Density on the Flexural and Axial Behaviour of Sandwich Panels of Varying Slenderness with Natural Flax-FRP and Glass-FRP Composite Skins

This study investigates the effect of foam core density and skin type on the behaviour of sandwich panels as structural beams tested in four-point bending and axially compressed columns of varying slenderness and skin thickness. Bio-composite unidirectional flax fibre-reinforced polymer (FFRP) is compared to conventional glass-FRP (GFRP) as the skin material used in conjunction with three polyisocyanurate (PIR) foam cores with densities of 32, 64 and 96 kg/m3. Eighteen 1000 mm long flexural specimens were fabricated and tested to failure comparing the effects of foam core density between three-layer FFRP skinned and single-layer GFRP skinned panels. A total of 132 columns with slenderness ratios (kLe/r) ranging from 22 to 62 were fabricated with single-layer GFRP skins, and one-, three-, and five-layer FFRP skins for each of the three foam core densities. The columns were tested to failure in concentric axial compression using pinned-end conditions to compare the effects of each material type and panel height. All specimens had a foam core cross-section of 100x50 mm with 100 mm wide skins of equal thickness. In both flexural and axial loading, panels with skins comprised of three FFRP layers showed equivalent strength to those with a single GFRP layer for all slenderness ratios and core densities examined. Doubling the core density from 32 to 64 kg/m3 and tripling the density to 96 kg/m3 led to flexural strength increases of 82 and 213%, respectively. Both FFRP and GFRP columns showed a similar variety of failure modes related to slenderness. Low slenderness of 22-25 failed largely due to localized single skin buckling, while those with high slenderness of 51-61 failed primarily by global buckling followed by secondary skin buckling. Columns with intermediate slenderness experienced both localized and global failure modes. High density foam cores more commonly exhibited core shear failure. Doubling the core density of the columns resulted in peak axial load increases, across all slenderness ratios, of 73, 56, 72 and 71% for skins with one, three and five FFRP layers, and one GFRP layer, respectively. Tripling the core density resulted in respective peak load increases of 116, 130, 176 and 170%.

Creep deflection of low-strength reinforced concrete flexural members strengthened with carbon fiber composite sheets

The low-strength concrete is defined as a concrete where the compressive cubic strength is less than 15 MPa. Since the beginning of the last century, many low-strength concrete buildings and bridges have been built all over the world. Being short of deeper study, composite sheets are prohibited in strengthening of low-strength reinforced concrete members (CECS 146; ACI 440). Moreover, there are few relevant information about the long-term behavior and durability of strengthened RC members. This fact undoubtedly limits the use of the composite materials in the strengthening applications, therefore, it is necessary to study the behaviours of low-strength concrete elements strengthened with composite materials (FRP) for the preservation of historic constructions and innovation in the strengthening technology. Deformability is one of criteria in the design of concrete structures, and this for functionality, durability and aesthetics reasons. Civil engineer possibly encounters more deflection problems in the structural design than any other type of problem. Many materials common in structural engineering such as wood, concrete and composite materials, suffer creep; if the creep phenomenon is taken into account, checks for serviceability limit state criteria can become onerous, because the creep deformation in these materials is in the same order of magnitude as the elastic deformation. The thesis presents the results of an experimental study on the long-term behavior of low-strength reinforced concrete beams strengthened with carbon fiber composite sheets (CFRP). The work has investigated the accuracy of the long-term deflection predictions made by some analytical procedures existing in literature, as well as by the most widely used design codes (Eurocode 2, ACI-318, ACI-435).