Vibration characteristics of slender structures under human induced loads

This paper presents the outcome of investigations and studies of the vibratioon characteristics and response of low frequency structural systems for a composite concrete steel floor plate and a reverse profiled cable tensioned foot bridge. These highly dynamic and slender structure are the engineering response to planning, aesthetic and environmental influences, but are prone to excessive and complex vibration. A number of design codes and practice guides provided information to engineers for vibration mitigation However, they are limited to very simple load function applied to a few uncoupled translational modes of excitation. Motivated by the need to address the knowledge gaps in this area, the investigations described in this paper focused on synchronous multi-modal and coupled excitation of the floor plate and footbridge with considerations for torsinal effects. The results showed the potential for adverse dynamic response from multi-modal and coupled excitation influenced by patterned loading, structure geometry, stiffness distribution, directional effects, forcing functions based on activity frequency and duration of foot contact, and modal participation. It was also shown that higher harmonics of the load frequency can excite higher modes in the composite floor structure. Such responsive behaviour is prevalent mainly in slender and lightweight construction and not in stiffer and heavier structural systems. The analytical techniques and methods used in these investigations can supplement the current limited code and best practice provisions for mitigating the impact of human induced vibrations in slender structural systems.

Size and habit of mineral particles in bone and mineralized callus during bone healing in sheep

Bone healing is known to occur through the successive formation and resorption of various tissues with different structural and mechanical properties. To get a better insight into this sequence of events, we used environmental scanning electron microscopy (ESEM) together with scanning small-angle X-ray scattering (sSAXS) to reveal the size and orientation of bone mineral particles within the regenerating callus tissues at different healing stages (2, 3, 6, and 9 weeks). Sections of 200 µm were cut from embedded blocks of midshaft tibial samples in a sheep osteotomy model with an external fixator. Regions of interest on the medial side of the proximal fragment were chosen to be the periosteal callus, middle callus, intercortical callus, and cortex. Mean thickness (T parameter), degree of alignment (ρ parameter), and predominant orientation (ψ parameter) of mineral particles were deduced from resulting sSAXS patterns with a spatial resolution of 200 µm. 2D maps of T and ρ overlapping with ESEM images revealed that the callus formation occurred in two waves of bone formation, whereby a highly disordered mineralized tissue was deposited first, followed by a bony tissue with more lamellar appearance in the ESEM and where the mineral particles were more aligned, as revealed by sSAXS. As a consequence, degree of alignment and mineral particle size within the callus increased with healing time, whereas at any given moment there were structural gradients, for example, from periosteal toward the middle callus.

Spatial and temporal variations of mechanical properties and mineral content of the external callus during bone healing

After bone fracture, various cellular activities lead to the formation of different tissue types, which form the basis for the process of secondary bone healing. Although these tissues have been quantified by histology, their material properties are not well understood. Thus, the aim of this study is to correlate the spatial and temporal variations in the mineral content and the nanoindentation modulus of the callus formed via intramembranous ossification over the course of bone healing. Midshaft tibial samples from a sheep osteotomy model at time points of 2, 3, 6 and 9 weeks were employed. PMMA embedded blocks were used for quantitative back scattered electron imaging and nanoindentation of the newly formed periosteal callus near the cortex. The resulting indentation modulus maps show the heterogeneity in the modulus in the selected regions of the callus. The indentation modulus of the embedded callus is about 6 GPa at the early stage. At later stages of mineralization, the average indentation modulus reaches 14 GPa. There is a slight decrease in average indentation modulus in regions distant to the cortex, probably due to remodelling of the peripheral callus. The spatial and temporal distribution of mineral content in the callus tissue also illustrates the ongoing remodelling process observed from histological analysis. Most interestingly the average indentation modulus, even at 9 weeks, remains as low as 13 GPa, which is roughly 60% of that for cortical sheep bone. The decreased indentation modulus in the callus compared to cortex is due to the lower average mineral content and may be perhaps also due to the properties of the organic matrix which might be different from normal bone.

Raman spectroscopic study of the uranyl titanate mineral brannerite (U,Ca,Y,Ce)2(Ti,Fe)2O6 –Effect of Metamictization

Raman spectra of the uranyl titanate mineral brannerite were analysed and related to the mineral structure. A comparison is made with the Raman spectra of uranyl oxyhydroxide hydrates. Observed bands are attributed to the TiO and (UO2)2+ stretching and bending vibrations, U-OH bending vibrations, H2O and (OH)- stretching, bending and libration modes. U-O bond lengths in uranyls and O-H…O bond lengths are calculated from the wavenumbers assigned to the stretching vibrations. Raman bands of brannerite are in harmony with those of the uranyl oxyhydroxides. The mineral brannerite is metamict as is evidenced by the intensity of the UO stretching and bending modes being of lower intensity than expected and with bands that are significantly broader.

Single crystal Raman spectroscopy of natural leiteite ZnAs2O4 and in comparison with the synthesised mineral

The oriented single crystal Raman spectrum of leiteite has been obtained and the spectra related to the structure of the mineral. The intensities of the observed bands vary according to orientation allowing them to be assigned to either Ag or Bg modes. Ag bands are generally the most intense in the CAAC spectrum, followed by ACCA, CBBC, and ABBA whereas Bg bands are generally the most intense in the CBAC followed by ABCA. The CAAC and ACCA spectra are identical, as are those obtained in the CBBC and ABBA orientations. Both cross-polarised spectra are identical. Band assignments were made with respect to bridging and non-bridging As-O bonds.

Raman spectroscopic study of the uranyl titanate mineral euxenite (Y,Ca,U,Ce,Th) (Nb,Ta,Ti)2O6

Raman spectra of the uranyl titanate mineral euxenite were analyzed and related to the mineral structure. A comparison is made with the Raman spectra of uranyl oxyhydroxide hydrates. The obsd. bands are attributed to the Ti[n.63743]O and (UO2)2+ stretching and bending vibrations, as well as lattice vibrations of rare-earth ions. The Raman bands of euxenite are in harmony with those of the uranyl oxyhydroxides. The mineral euxenite is metamict as is evidenced by the intensity of the U[n.63743]O stretching and bending modes, which are of lower intensity than expected, and with bands that are significantly broader.

Vibrational spectroscopic study of the antimonate mineral bindheimite Pb2Sb2O6(O,OH)

Raman spectroscopy complimented with infrared spectroscopy has been used to characterise the antimonate mineral bindheimite Pb2Sb2O6(O,OH). The mineral is characterised by an intense Raman band at 656 cm-1 assigned to SbO stretching vibrations. Other lower intensity bands at 664, 749 and 814 cm-1 are also assigned to stretching vibrations. This observation suggests the non-equivalence of SbO units in the structure. Low intensity Raman bands at 293, 312 and 328 cm-1 are assigned to the OSbO bending vibrations. Infrared bands at 979, 1008, 1037 and 1058 cm-1 may be assigned to δ OH deformation modes of SbOH units. Infrared bands at 1603 and 1640 cm-1 are assigned to water bending vibrations, suggesting that water is involved in the bindheimite structure. Broad infrared bands centred upon 3250 cm-1 supports this concept. Thus the true formula of bindheimite is questioned and probably should be written as Pb2Sb2O6(O,OH,H2O)

A Raman spectroscopic study of the ‘cave’ mineral ardealite Ca2(HPO4)(SO4)•4H2O

The mineral ardealite Ca2(HPO4)(SO4)•4H2O is a ‘cave’ mineral and is formed through the reaction of calcite with bat guano. The mineral shows disorder and the composition varies depending on the origin of the mineral. Raman spectroscopy complimented with infrared spectroscopy has been used to characterise the mineral ardealite. The Raman spectrum is very different from that of gypsum. Bands are assigned to SO42- and HPO42- stretching and bending modes.

Thermal stability of the ‘cave’ mineral brushite CaHPO4•2H2O -mechanism of formation and decomposition

Thermogravimetry combined with evolved gas mass spectrometry has been used to ascertain the stability of the ‘cave’ mineral brushite. X-ray diffraction shows that brushite from the Jenolan Caves is very pure. Thermogravimetric analysis coupled with ion current mass spectrometry shows a mass loss at 111°C due to loss of water of hydration. A further decomposition step occurs at 190°C with the conversion of hydrogen phosphate to a mixture of calcium ortho-phosphate and calcium pyrophosphate. TG-DTG shows the mineral is not stable above 111°C. A mechanism for the formation of brushite on calcite surfaces is proposed, and this mechanism has relevance to the formation of brushite in urinary tracts.

The application of Raman spectroscopy to the study of the uranyl mineral coconinoite Fe2Al2(UO2)2(PO4)4(SO4)(OH)2•20H2O

Raman spectra of the uranyl containing mineral coconinoite, Fe2Al2(UO2)2(PO4)4(SO4)(OH)2•20H2O, are presented and compared with the mineral’s infrared spectra. Bands connected with (UO2)2+, (PO4)3- , (SO4)2-, (OH)- and H2O stretching and bending vibrations, are assigned. Approximate U-O bond lengths in uranyl, (UO2)2+, and O-H...O hydrogen bond lengths are calculated from the wavenumbers of the U-O stretching vibrations and (OH)- and H2O stretching vibrations, respectively, and compared with published data for similar natural and synthetic compounds.

A vibrational spectroscopic study of hydrated Fe3+ hydroxyl-sulphates; polymorphic minerals butlerite and parabutlerite

Raman and infrared spectra of two polymorphous minerals with the chemical formula Fe3+(SO4)(OH)•2H2O, monoclinic butlerite and orthorhombic parabutlerite, are studied and the spectra assigned. Observed bands are attributed to the (SO4)2- stretching and bending vibrations, hydrogen bonded water molecules, stretching and bending vibrations of hydroxyl ions, water librational modes, Fe-O and Fe-OH stretching vibrations, Fe-OH bending vibrations and lattice vibrations. The O-H...O hydrogen bond lengths in the structures of both minerals are calculated from the wavenumbers of the stretching vibrations. One symmetrically distinct (SO4)2- unit in the structure of butlerite and two symmetrically distinct (SO4)2- units in the structure of parabutlerite are inferred from the Raman and infrared spectra. This conclusion agrees with the published crystal structures of both mineral phases.

Vibrational spectroscopic study of the mineral tsumebite Pb2Cu(PO4,SO4) (OH)

The mineral tsumebite Pb2Cu(PO4)(SO4)(OH), a copper phosphate-sulfate hydroxide of the brackebuschite group has been characterised by Raman and infrared spectroscopy. The brackebuschite mineral group are a series of monoclinic arsenates, phosphates and vanadates of the general formula A2B(XO4)(OH,H2O), where A may be Ba, Ca, Pb, Sr, while B may be Al, Cu2+,Fe2+, Fe3+, Mn2+, Mn3+, Zn and XO4 may be AsO4, PO4, SO4,VO4. Bands are assigned to the stretching and bending modes of PO43- and HOPO3 units. Hydrogen bond distances are calculated based upon the position of the OH stretching vibrations and range from 2.759 Å to 3.205 Å. This range of hydrogen bonding contributes to the stability of the mineral.

Raman spectroscopy of newberyite Mg(PO3OH)•3H2O – a cave mineral

Newberyite Mg(PO3OH)•3H2O is a mineral found in caves such as from Moorba cave, Jurien Bay, Western Australia, the Skipton Lava tubes (SW of Ballarat, Victoria, Australia) and in the Petrogale Cave (Madura , Eucla, Western Australia). Because these minerals contain oxyanions, hydroxyl units and water, the minerals lend themselves to spectroscopic analysis. Raman spectroscopy can investigate the complex paragenetic relationships existing between a number of ‘cave’ minerals. The intense sharp band at 982 cm-1 is assigned to the PO43- ν1 symmetric stretching mode. Low intensity Raman bands at 1152, 1263 and 1277 cm-1 are assigned to the PO43- ν3 antisymmetric stretching vibrations. Raman bands at 497 and 552 cm-1 are attributed to the PO43- ν4 bending modes. An intense Raman band for newberyite at 398 cm-1 with a shoulder band at 413 cm-1 is assigned to the PO43- ν2 bending modes. The values for the OH stretching vibrations provide hydrogen bond distances of 2.728Å (3267 cm-1), 2.781Å (3374cm-1), 2.868Å (3479 cm-1), and 2.918Å (3515 cm-1). Such hydrogen bond distances are typical of secondary minerals. Estimates of the hydrogen-bond distances have been made from the position of the OH stretching vibrations and show a wide range in both strong and weak bonds.

Raman spectroscopy of stercorite H(NH4)Na(PO4)•4H2O – a cave mineral from Petrogale Cave, Madura, Eucla, Western Australia

Raman spectroscopy complimented with infrared spectroscopy has been used to characterise the mineral stercorite H(NH4)Na(PO4)·4H2O. The mineral stercorite originated from the Petrogale Cave, Madura, Eucla, Western Australia. This cave is one of many caves in the Nullarbor Plain in the South of Western Australia. These caves have been in existence for eons of time and have been dated at more than 550 million years old. The mineral is formed by the reaction of bat guano chemicals on calcite substrates. A single Raman band at 920 cm−1 defines the presence of phosphate in the mineral. Antisymmetric stretching bands are observed in the infrared spectrum at 1052, 1097, 1135 and 1173 cm−1. Raman spectroscopy shows the mineral is based upon the phosphate anion and not the hydrogen phosphate anion. Raman and infrared bands are found and assigned to PO43−, H2O, OH and NH stretching vibrations. The detection of stercorite by Raman spectroscopy shows that the mineral can be readily determined; as such the application of a portable Raman spectrometer in a ‘cave’ situation enables the detection of minerals, some of which may remain to be identified.