Experimental verification of the modified spring-mass theory of fiber Bragg grating accelerometers using transverse forces

A fiber Bragg grating (FBG) accelerometer using transverse forces is more sensitive than one using axial forces with the same mass of the inertial object, because a barely stretched FBG fixed at its two ends is much more sensitive to transverse forces than axial ones. The spring-mass theory, with the assumption that the axial force changes little during the vibration, cannot accurately predict its sensitivity and resonant frequency in the gravitational direction because the assumption does not hold due to the fact that the FBG is barely prestretched. It was modified but still required experimental verification due to the limitations in the original experiments, such as the (1) friction between the inertial object and shell; (2) errors involved in estimating the time-domain records; (3) limited data; and (4) large interval ∼5 Hz between the tested frequencies in the frequency-response experiments. The experiments presented here have verified the modified theory by overcoming those limitations. On the frequency responses, it is observed that the optimal condition for simultaneously achieving high sensitivity and resonant frequency is at the infinitesimal prestretch. On the sensitivity at the same frequency, the experimental sensitivities of the FBG accelerometer with a 5.71 gram inertial object at 6 Hz (1.29, 1.19, 0.88, 0.64, and 0.31 nm/g at the 0.03, 0.69, 1.41, 1.93, and 3.16 nm prestretches, respectively) agree with the static sensitivities predicted (1.25, 1.14, 0.83, 0.61, and 0.29 nm/g, correspondingly). On the resonant frequency, (1) its assumption that the resonant frequencies in the forced and free vibrations are similar is experimentally verified; (2) its dependence on the distance between the FBG’s fixed ends is examined, showing it to be independent; (3) the predictions of the spring-mass theory and modified theory are compared with the experimental results, showing that the modified theory predicts more accurately. The modified theory can be used more confidently in guiding its design by predicting its static sensitivity and resonant frequency, and may have applications in other fields for the scenario where the spring-mass theory fails.

Non-linear refined finite element elastic analysis of steel frames with generalized transverse member loads

In the finite element modelling of steel frames, external loads usually act along the members rather than at the nodes only. Conventionally, when a member is subjected to these transverse loads, they are converted to nodal forces which act at the ends of the elements into which the member is discretised by either lumping or consistent nodal load approaches. For a contemporary geometrically non-linear analysis in which the axial force in the member is large, accurate solutions are achieved by discretising the member into many elements, which can produce unfavourable consequences on the efficacy of the method for analysing large steel frames. Herein, a numerical technique to include the transverse loading in the non-linear stiffness formulation for a single element is proposed, and which is able to predict the structural responses of steel frames involving the effects of first-order member loads as well as the second-order coupling effect between the transverse load and the axial force in the member. This allows for a minimal discretisation of a frame for second-order analysis. For those conventional analyses which do include transverse member loading, prescribed stiffness matrices must be used for the plethora of specific loading patterns encountered. This paper shows, however, that the principle of superposition can be applied to the equilibrium condition, so that the form of the stiffness matrix remains unchanged with only the magnitude of the loading being needed to be changed in the stiffness formulation. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. The results are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple structural frames.

A nonlinear observer for estimating transverse stability parameters of marine surface vessels

This paper presents a nonlinear observer for estimating parameters associated with the restoring term of a roll motion model of a marine vessel in longitudinal waves. Changes in restoring, also referred to as transverse stability, can be the result of changes in the vessel's centre of gravity due to, for example, water on deck and also in changes in the buoyancy triggered by variations in the water-plane area produced by longitudinal waves -- propagating along the fore-aft direction along the hull. These variations in the restoring can change dramatically the dynamics of the roll motion leading to dangerous resonance. Therefore, it is of interest to estimate and detect such changes.

Interaction of transverse electromagnetic waves with counterpropagating surface waves at a plasma-dielectric interface

The nonlinear interaction of high-frequency transverse electromagnetic waves normally incident from a plasma region on to a dielectric with two surface waves (SWs) propagating in the opposite directions along the interface is studied. This interaction is found to be stable causing a slight modulation to the SWs in contrast to the decay instability for longitudinal plasma waves. The corresponding nonlinear frequency shift of the SWs is obtained and analyzed.

Biaxial fiber Bragg grating accelerometer using axial and transverse forces

We demonstrate the first biaxial fiber Bragg grating (FBG) accelerometer using axial and transverse forces. An inertial object is fixed at the middle of two FBGs inscribed in one fiber. The difference between the resonant wavelengths of the two FBGs can distinguish the acceleration in the axial direction, while being insensitive in the transverse direction. The average of the resonant wavelengths of the two FBGs can distinguish the acceleration in the transverse direction, while being insensitive in the axial direction. In the experiments, when the transverse direction was vertical, the crest-to-trough sensitivity at 5 Hz and resonant frequency of the average were 0.545 nm/g and 34.42 Hz, respectively. When the axial direction was vertical, those of the difference were 0.0454 nm/g and 900 Hz, respectively. For each FBG, the crest-to-trough sensitivity at 5 Hz and resonant frequency in the transverse/vertical direction were 24 and 1/26 times those in the axial/vertical direction, respectively.

Tendinopathy alters cumulative transverse strain in the patellar tendon postexercise.

Introduction This research evaluated the effect of tendinopathy on the cumulative transverse strain response of the patellar tendon to a bout of resistive quadriceps exercise. Methods Nine adults with unilateral patellar tendinopathy (age 18.2±0.7 years, height 1.92±0.06 m and weight 76.8±6.8 kg) and ten healthy adults free of knee pain (age 17.8±0.8 years, height 1.83±0.05 m and weight 73.2±7.6 kg) underwent standardised sagittal sonograms (7.2–14 MHz linear–array transducer) of both patellar tendons immediately prior and following 45 repetitions of a double–leg decline–squat exercise performed against a resistance of 145% bodyweight. Tendon thickness was determined 5–mm and 25–mm distal to the patellar pole. Transverse Hencky strain was calculated as the natural log of the ratio of post– to pre–exercise tendon thickness and expressed as a percentage. Measures of tendon echogenicity were calculated within the superficial and deep aspects of each tendon site from gray–scale profiles. Intratendinous microvessels were evaluated using power Doppler ultrasound. Results The cumulative transverse strain response to exercise in symptomatic tendinopathy was significantly lower than that of asymptomatic and healthy tendon (P<.05). There was also a significant reduction (57%) in the area of microvascularity immediately following exercise (P=.05), which was positively correlated (r=0.93, P<.05) with VISA-P score. Conclusions This study is the first to show that patellar tendinopathy is associated with an altered morphological and mechanical response of the tendon to exercise, which is manifest by a reduction in cumulative transverse strain and microvascularity, when present. Research directed toward identifying factors that influence the acute microvascular and transverse strain response of the patellar tendon to exercise in the various stages of tendinopathy is warranted.

Numerical studies on CFRP strengthened steel columns under transverse impact

Strengthening of metallic structures using carbon fibre reinforced polymer (CFRP) has become a smart strengthening option over the conventional strengthening method. Transverse impact loading due to accidental vehicular collision can lead to the failure of existing steel hollow tubular columns. However, knowledge is very limited on the behaviour of CFRP strengthened steel members under dynamic impact loading condition. This paper deals with the numerical simulation of CFRP strengthened square hollow section (SHS) steel columns under transverse impact loading to predict the behaviour and failure modes. The transverse impact loading is simulated using finite element (FE) analysis based on numerical approach. The accuracy of the FE modelling is ensured by comparing the predicted results with available experimental tests. The effects of impact velocity, impact mass, support condition, axial loading and CFRP thickness are examined through detail parametric study. The impact simulation results indicate that the strengthening technique shows an improved impact resistance capacity by reducing lateral displacement of the strengthened column about 58% compared to the bare steel column. Axial loading plays an important role on the failure behaviour of tubular column.

Effect of partial H2O-D2O replacement on the anisotropy of transverse proton spin relaxation in bovine articular cartilage

Anisotropy of transverse proton spin relaxation in collagen-rich tissues like cartilage and tendon is a well-known phenomenon that manifests itself as the "magic-angle" effect in magnetic resonance images of these tissues. It is usually attributed to the non-zero averaging of intra-molecular dipolar interactions in water molecules bound to oriented collagen fibers. One way to manipulate the contributions of these interactions to spin relaxation is by partially replacing the water in the cartilage sample with deuterium oxide. It is known that dipolar interactions in deuterated solutions are weaker, resulting in a decrease in proton relaxation rates. In this work, we investigate the effects of deuteration on the longitudinal and the isotropic and anisotropic contributions to transverse relaxation of water protons in bovine articular cartilage. We demonstrate that the anisotropy of transverse proton spin relaxation in articular cartilage is independent of the degree of deuteration, bringing into question some of the assumptions currently held over the origins of relaxation anisotropy in oriented tissues.

Novel non-linear elastic structural analysis with generalised transverse element loads using a refined finite element

In the finite element modelling of structural frames, external loads such as wind loads, dead loads and imposed loads usually act along the elements rather than at the nodes only. Conventionally, when an element is subjected to these general transverse element loads, they are usually converted to nodal forces acting at the ends of the elements by either lumping or consistent load approaches. In addition, it is especially important for an element subjected to the first- and second-order elastic behaviour, to which the steel structure is critically prone to; in particular the thin-walled steel structures, when the stocky element section may be generally critical to the inelastic behaviour. In this sense, the accurate first- and second-order elastic displacement solutions of element load effect along an element is vitally crucial, but cannot be simulated using neither numerical nodal nor consistent load methods alone, as long as no equilibrium condition is enforced in the finite element formulation, which can inevitably impair the structural safety of the steel structure particularly. It can be therefore regarded as a unique element load method to account for the element load nonlinearly. If accurate displacement solution is targeted for simulating the first- and second-order elastic behaviour on an element on the basis of sophisticated non-linear element stiffness formulation, the numerous prescribed stiffness matrices must indispensably be used for the plethora of specific transverse element loading patterns encountered. In order to circumvent this shortcoming, the present paper proposes a numerical technique to include the transverse element loading in the non-linear stiffness formulation without numerous prescribed stiffness matrices, and which is able to predict structural responses involving the effect of first-order element loads as well as the second-order coupling effect between the transverse load and axial force in the element. This paper shows that the principle of superposition can be applied to derive the generalized stiffness formulation for element load effect, so that the form of the stiffness matrix remains unchanged with respect to the specific loading patterns, but with only the magnitude of the loading (element load coefficients) being needed to be adjusted in the stiffness formulation, and subsequently the non-linear effect on element loadings can be commensurate by updating the magnitude of element load coefficients through the non-linear solution procedures. In principle, the element loading distribution is converted into a single loading magnitude at mid-span in order to provide the initial perturbation for triggering the member bowing effect due to its transverse element loads. This approach in turn sacrifices the effect of element loading distribution except at mid-span. Therefore, it can be foreseen that the load-deflection behaviour may not be as accurate as those at mid-span, but its discrepancy is still trivial as proved. This novelty allows for a very useful generalised stiffness formulation for a single higher-order element with arbitrary transverse loading patterns to be formulated. Moreover, another significance of this paper is placed on shifting the nodal response (system analysis) to both nodal and element response (sophisticated element formulation). For the conventional finite element method, such as the cubic element, all accurate solutions can be only found at node. It means no accurate and reliable structural safety can be ensured within an element, and as a result, it hinders the engineering applications. The results of the paper are verified using analytical stability function studies, as well as with numerical results reported by independent researchers on several simple frames.

Effect of bond length on the behaviour of CFRP strengthened concrete-filled steel tubes under transverse impact

Concrete-filled steel tubular (CFST) columns have shown great potential as axial load carrying member and used widely in many mission critical infrastructures. However, attention is needed to strengthen these members where transverse impact force is expected to occur due to vehicle collisions. In this work, finite element (FE) model of carbon fibre reinforced polymer (CFRP) strengthened CFST columns are developed and the effect of CFRP bond length is investigated under transverse impact loading. Initially the numerical models have been validated by comparing impact test results from literature. The validated models are then used for detail parametric studies by varying the length of externally bonded CFRP composites. The parameters considered for this research are impact velocity, impact mass, CFRP modulus, adhesive type, and axial static loading. It has been observed that the effect of CFRP strengthening is consistent after an optimum effective bond length of CFRP wrapping. The effect of effective bond length has been studied for above parameters. The results show that, under combined axial static and transverse impact loads CFST columns can successfully prevent global buckling failure by strengthening only 34% of column length. Therefore, estimation of effective bond length is essential to utilise the CFRP composites cost effectively.

Deep transverse metatarsal ligaments mechanical response during landing

The deep transverse metatarsal ligaments play an important role in stabilizing the metatarsal bones and manipulating foot transverse arch deformation. However, the biomechanical research about transverse metatarsal ligaments in the foot maneuver is quite few. Due to the difficulties and lack of better measurement technology for these ligaments experimental monitor, the load transfer mechanism and internal stress state also hadn't been well addressed. The purpose of this study was to develop a detailing foot finite element model including transverse metatarsal ligaments tissues, to investigate the mechanical response of transverse metatarsal ligaments during the landing condition. The transverse metatarsal ligaments were considered as hyperelastic material model was used to represent the nonlinear and nearly incompressible nature of the ligament tissue. From the simulation results, it is clearly to find that the peak maiximal principal stress of transverse metatarsal ligaments was between the third and fourth metatarsals. Meanwhile, it seems the transverse metatarsal ligaments in the middle position experienced higher tension than the sides transverse metatarsal ligaments.

Finite element analysis of deep transverse metatarsal ligaments mechanical response during landing

The deep transverse metatarsal ligaments (DTML) play an important role in stabilizing the metatarsal bones and manipulating foot transverse arch deformation. However, the biomechanical research about DTML in the foot maneuver is quite few. Due to the difficulties and lack of better measurement technology for these ligaments experimental monitor, the load transfer mechanism and internal stress state also hadn't been well addressed. The purpose of this study was to develop a detailing foot finite element model including DTML tissues, to investigate the mechanical response of DTML during the landing condition. The DTML was considered as hyperelastic material model was used to represent the nonlinear and nearly incompressible nature of the ligament tissue. From the simulation results, it is clearly to find that the peak maiximal principal stress of DTML was between the third and fourth metatarsals. Meanwhile, it seems the DTML in the middle position experienced higher tension than the sides DTML.

Towards a single crystal Raman spectrum of kaolinite at 77 K

The Raman spectra at 77 K of the hydroxyl stretching of kaolinite were obtained along the three axes perpendicular to the crystal faces. Raman bands were observed at 3616, 3658 and 3677 cm−1 together with a distinct band observed at 3691 cm−1 and a broad profile between 3695 and 3715 cm−1. The band at 3616 cm−1 is assigned to the inner hydroxyl. The bands at 3658 and 3677 cm−1 are attributed to the out-of-phase vibrations of the inner surface hydroxyls. The Raman spectra of the in-phase vibrations of the inner-surface hydroxyl-stretching region are described in terms of transverse and longitudinal optic splitting. The band at 3691 cm−1 is assigned to the transverse optic and the broad profile to the longitudinal optic mode. This splitting remained even at liquid nitrogen temperature. The transverse optic vibration may be curve resolved into two or three bands, which are attributed to different types of hydroxyl groups in the kaolinite.

Raman spectroscopy of kaolinites using different excitation wavelengths

The Raman spectra of both low- and high-defect kaolinites in the hydroxyl stretching and low-wavenumber region were obtained with excitation at three visible wavelengths of 633, 514 and 442 nm and a UV wavelength of 325 nm. The UV-excited spectra were comparable to those excited by the visible wavelengths. The Raman spectra show hydroxyl stretching bands at 3621 cm-1 attributed to the inner hydroxyl, at 3692 and 3684 cm-1 attributed to the longitudinal and transverse optic modes of the inner surface hydroxyls and at 3668 and 3653 cm-1 assigned to the out-of phase vibrations of the inner surface hydroxyls. Two bands were observed in the spectral profile at 3695 cm-1 for the high-defect kaolinite at 3698 and 3691 cm-1 and were assigned to TO/LO splitting. An increase in relative intensity of the transverse optic mode is observed with decrease in laser wavelength. The intensity of the out-of-phase vibrations at 3668 and 3653 cm-1 of the inner surface hydroxyls shows a linear relationship with the longitudinal and transverse optic modes. In the low-wavenumber region excellent correlation was found between the experimentally determined and the calculated band positions.

Raman spectroscopy of the copper chloride minerals nantokite, eriochalcite and claringbullite - implications for copper corrosion

The application of Raman spectroscopy to the study of the copper chloride minerals nantokite, eriochalcite and claringbullite has enabled the vibrational modes for the CuCl, CuOH and CuOH2 to be determined. Nantokite is characterised by bands at 205 and 155 cm-1 attributed to the transverse and longitudinal optic vibrations. Nantokite also has an intense band at 463 cm-1, eriochalcite at 405 and 390 cm-1 and claringbullite at 511 cm-1. These bands are attributed to CuO stretching modes. Water librational bands at around 672 cm-1 for eriochalcite have been identified and hydroxyl deformation modes of claringbullite at 970, 906 and 815 cm-1 are observed. Spectra of the three minerals are so characteristically different that the minerals are readily identified by Raman spectroscopy. The minerals are often determined in copper corrosion products by X-ray diffraction. Raman spectroscopy offers a rapid, in-situ technique for the identification of these corrosion products.