Finite element analysis of the statics of and vibrations in axisymmetric shells

The finite element process is now used almost routinely as a tool of engineering analysis. From early days, a significant effort has been devoted to developing simple, cost effective elements which adequately fulfill accuracy requirements. In this thesis we describe the development and application of one of the simplest elements available for the statics and dynamics of axisymmetric shells . A semi analytic truncated cone stiffness element has been formulated and implemented in a computer code: it has two nodes with five degrees of freedom at each node, circumferential variations in displacement field are described in terms of trigonometric series, transverse shear is accommodated by means of a penalty function and rotary inertia is allowed for. The element has been tested in a variety of applications in the statics and dynamics of axisymmetric shells subjected to a variety of boundary conditions. Good results have been obtained for thin and thick shell cases .

In-fibre directional transverse loading sensor based on excessively tilted fibre Bragg gratings

We report a distinctive polarization mode coupling behaviour of tilted fibre Bragg gratings (TFBGs) with a tilted angle exceeding 45°. The ex-45° TFBGs exhibit pronounced polarization mode splitting resulted from the birefringence induced by the grating structure asymmetry. We have fabricated TFBGs with a tilted structure at 81° and studied their properties under transverse load applied to their equivalent fast and slow axes. The results show that the light coupling to the orthogonally polarized modes of the 81°-TFBGs changes only when the load is applied to their slow axis, giving a prominent directional loading response. For the view of real applications, we further investigated the possibility of interrogating such a TFBG-based load sensor using low-cost and compact-size single wavelength source and power detector. The experimental results clearly show that the 81°-TFBGs plus the proposed power-measurement interrogation scheme may be developed to an optical fibre vector sensor system capable of not just measuring the magnitude but also recognizing the direction of the applied transverse load. Using such an 81°-TFBG based load sensor, a load change as small as 1.6 × 10-2 g may be detected by employing a standard photodiode detector.

Rolling bearing vibrations: the effects of varying compliance, manufacturing tolerances and wear

In this study some common types of Rolling Bearing vibrations are analysed in depth both theoretically and experimentally. The study is restricted to vibrations in the radial direction of bearings having pure radial load and a positive radial clearance. The general vibrational behaviour of such bearings has been investigated with respect to the effects of varying compliance, manufacturing tolerances and the interaction between the bearing and the machine structure into which it is fitted. The equations of motion for a rotor supported by a bearing in which the stiffness varies with cage position has been set up and examples of solutions,obtained by digital simulation. is given. A method to calculate amplitudes and frequencies of vibration components due to out of roundness of the inner ring and varying roller diameters has been developed. The results from these investigations have been combined with a theory for bearing/machine frame interaction using mechanical impedance technique, thereby facilitating prediction of the vibrational behaviour of the whole set up. Finally. the effects of bearing fatigue and wear have been studied with particular emphasis on the use of vibration analysis for condition monitoring purposes. A number of monitoring methods have been tried and their effectiveness discussed. The experimental investigation was carried out using two purpose built rigs. For the purpose of analysis of the experimental measurements a digital mini computer was adapted for signal processing and a suite of programs was written. The program package performs several of the commonly used signal analysis processes and :include all necessary input and output functions.

Polarisation mode coupling of excessively tilted fibre Bragg gratings with directional transverse loading

We report a distinctive polarisation mode coupling behaviour of tilted fibre Bragg gratings (TFBGs) with tilted angle exceeding 45°. The ex-45° TFBGs exhibit pronounced polarisation mode splitting resulted from grating structure asymmetry induced birefringence. We have studied and analysed the property of ex-45° TFBGs under transverse load applied to their equivalent fast- and slow-axis. The results show that the coupling between the orthogonally polarised modes takes place only when the load is applied to its fast-axis, giving a prominent directional loading response. This transverse load related polarisation property may be exploitable for implementation of optical fibre vector sensors capable of measuring the magnitude and orientation of the applied transverse load.

Transverse load and orientation measurement with multicore fiber Bragg gratings

We demonstrate the sensitivity of Bragg gratings in a multicore fiber to transverse load. The Bragg peaks are split because of stress-induced birefringence, the magnitude of which depends upon the load and grating position relative to the load axis. Experiments show that a set of gratings in a four-core fiber can measure a load axis angle to ±5° and a load magnitude to ±15 N m-1 up to 2500 N m-1. We consider alternative designs of multicore fiber for optimal load sensing and compare experimental and modeled data. © 2005 Optical Society of America.

Transverse loading of multicore fibre gratings

We report experimental measurements of the reflection spectra of Bragg gratings inscribed in 4-core fibres under transverse loading. Broadening and splitting of the Bragg peaks from each core are observed as a function of load and fibre orientation.

Differential birefringence in Bragg gratings in multicore fiber under transverse stress

We present experimental measurements of the peak splitting of the reflection spectra of fiber Bragg gratings as a result of birefringence induced by transverse loading of a multicore fiber. Measurements show that the splitting is a function of the applied load and the direction of the load relative to the azimuth of the fiber. A model for calculating the stress in the fiber that is due to an applied load is in good agreement with our experimental observations.

Polarization effects in polymer FBGs:study and use for transverse force sensing

Bragg gratings photo-inscribed in polymer optical fibers (POFs) are more sensitive to temperature and pressure than their silica counterparts, because of their larger thermo-optic coefficient and smaller Young's modulus. Polymer optical fiber Bragg gratings (POFBGs) are most often photo-written in poly(methylmethacrylate) (PMMA) based materials using a continuous-wave 325 nm HeCd laser. In this work, we present the first study about birefringence effects in POFBGs manufactured in different types of fiber. To achieve this, highly reflective (> 90%) gratings were produced with the phase mask technique. Their spectral response was then monitored in transmission with polarized light. Polarization dependent loss (PDL) and differential group delay (DGD) were computed from the Jones matrix eigenanalysis using an optical vector analyzer. Maximum values exceeding several dB and a few picoseconds were obtained for the PDL and DGD, respectively. An inverse scattering technique applied to the experimental data provided an estimate of the photo-induced birefringence value arising from the side fabrication process. The response to lateral force was finally investigated for various incident directions using the PDL response of FBGs manufactured in step-index POFs. As the force induced birefringence adds to the photo-induced one, a force dependent evolution of the PDL maximum value was noticed, with a good temperature-insensitivity.

Polarisation mode coupling of excessively tilted fibre Bragg gratings with directional transverse loading

We report a distinctive polarisation mode coupling behaviour of tilted fibre Bragg gratings (TFBGs) with tilted angle exceeding 45°. The ex-45° TFBGs exhibit pronounced polarisation mode splitting resulted from grating structure asymmetry induced birefringence. We have studied and analysed the property of ex-45° TFBGs under transverse load applied to their equivalent fast- and slow-axis. The results show that the coupling between the orthogonally polarised modes takes place only when the load is applied to its fast-axis, giving a prominent directional loading response. This transverse load related polarisation property may be exploitable for implementation of optical fibre vector sensors capable of measuring the magnitude and orientation of the applied transverse load.

Convection induced by instabilities in the presence of a transverse seepage

The transition of laterally heated flows in a vertical layer and in the presence of a streamwise pressure gradient is examined numerically for the case of different values Prandtl number. The stability analysis of the basic flow for the pure hydrodynamic case ( Pr = 0 ) was reported in [1]. We find that in the absence of transverse pumping the previously known critical parameters are recovered [2], while as the strength of the Poiseuille flow component is increased the convective motion is delayed considerably. Following the linear stability analysis for the vertical channel flow our attention is focused on a study of the finite am- plitude secondary travelling-wave (TW) solutions that develop from the perturbations of the transverse roll type imposed on the basic flow and temperature profiles. The linear stability of the secondary TWs against three-dimensional perturbations is also examined and it is shown that the bifurcating tertiary flows are phase-locked to the secondary TWs.