No / Two Cylindrical Dielectric Resonators DR asymmetrically placed on a thin dielectric substrate and fed by a single rectangular slot for wideband wireless applications are presented. Optimized design procedures were applied within a well-known electromagnetic solver to achieve the improved elements dimensions of the antenna geometry. The simulated and measured results show that the proposed DRA can achieve 29% relative bandwidth at 10 dB return loss covering the spectrum range from 9.62 GHz to 12.9 GHz with a maximum gain of 8 dB.

No / This paper considers both the linear elastic and creep buckling of polymeric pipe linings used for the rehabilitation of gravity pipes, for which external groundwater pressure has been identified as the prime source of loading. Theoretically perfect and imperfect conditions are considered, with the imperfections taken to be in the form of a concentric or eccentric annulus between the rigid host pipe (cylindrical constraint) and polymeric lining. Under these conditions two recently obtained mathematical procedures for the prediction of linearly and non-linearly elastic buckling are compared with the results of complementary laboratory testing. Linear elastic conditions are shown to be well approximated by undertaking short-term (¿30 min) testing under increasing pressure to failure. Controlled imperfections are introduced into the laboratory tests and excellent correlation with the theoretical predictions is obtained. In particular, the dominant geometrical imperfections are shown to be major influences on the obtained buckling pressure. The mathematical models are then adapted to simulate the creep buckling process under long-term constant pressure. The results obtained are again compared with those provided by complementary physical testing, and appropriate conclusions are made.

No description available.

No description available.

Solid rocket motors consist of a thin metallic or composite shell filled with a soft rubbery propellant. Such motors are vulnerable and prone to buckling due to sudden external pressures produced by nearby detonation. The stability conditions of rocket motors subjected toaxisymmetric, external pressure loading are examined. The outer cases of motors are considered as isotropic (metallic) or anisotropic (composite), thin and high-strength shells, which are the main structures of interest in the stability analyses. The inner, low-strength elastic cores are modeled as linear and nonlinear elastic foundations. A general, refined, Sanders' nonlinear shell theory, which accounts for geometric nonlinearity in the form of von Karman type of nonlinear strain-displacement relations, is used to model thin-walled, laminated,composite cylindrical shells. The first order shear deformable concept is adopted in the analyses to include the transverse shear flexibility of composites. A winkler-type of linear and nonlinear elastic foundation is applied to model the internal foundations. Pasternak-foundation constants are also chosen tomodify the proposed elastic foundation model for the purpose of shear interactions. A set of displacement-based finite element codes have been formulated to determine critical buckling loads and mode shapes. The effect of initial imperfections on the structural responses are also incorporated in the formulations. A variety of numerical examples are investigated to demonstrate the validity and efficiency of the purposed theory under various boundary condiitions and loading cases. First, linear eigenvalue analysis is used to examine approximate buckling loads and buckling modes as well as symmetric conditions. An iterative solution procedure, either Newton-Raphson or Riks-Wempner method is employed to trace the nonlinear equilibrium paths for the cases of stress, buckling and post-buckling analyses. Both ring and shell-type models are applied for the structural analyses with different internal elastic foundations and initial imperfections. / Ph. D.

No / This paper considers both the linear elastic and creep buckling of polymeric pipe linings used for the rehabilitation of gravity pipes, for which external groundwater pressure has been identified as the prime source of loading. Theoretically perfect and imperfect conditions are considered, with the imperfections taken to be in the form of a concentric or eccentric annulus between the rigid host pipe (cylindrical constraint) and polymeric lining. Under these conditions two recently obtained mathematical procedures for the prediction of linearly and non-linearly elastic buckling are compared with the results of complementary laboratory testing. Linear elastic conditions are shown to be well approximated by undertaking short-term (¿30 min) testing under increasing pressure to failure. Controlled imperfections are introduced into the laboratory tests and excellent correlation with the theoretical predictions is obtained. In particular, the dominant geometrical imperfections are shown to be major influences on the obtained buckling pressure. The mathematical models are then adapted to simulate the creep buckling process under long-term constant pressure. The results obtained are again compared with those provided by complementary physical testing, and appropriate conclusions are made.

This thesis is a numerical study of fields within ion traps having segmented electrodes1. The focus is on two cylindrical ion trap structures, two Orbit rap structures and one planar structure which mimics the field of the Orbit rap. In all these geometries, the segments which comprise the electrodes are easily Machin able rings and plates. By applying suitable potential to the different segments, the fields within these geometries are made to mimic the fields in the respective ideal structures. This thesis is divided into 6 chapters. Chapter 1 presents introduction and background information relevant to this work. A brief description of the Quadrupole Ion Trap (QIT) and the Orbit rap is given. The role of numerical simulations in the design of an ion trap geometry is briefly outlined. The motivation of this thesis is presented. The chapter ends by describing the scope of the thesis. Chapter 2 presents a general description of computational methods used throughout this work. The Boundary Element Methods (BEM) is first described. Both 2D and 3D BEM are used in this work. The software for 3D BEM is newly developed and hence 3D BEM is described in more detail. A verification of 3D BEM is presented with a few examples. The Runge-Kutta method used to compute the trajectory of ion is presented. A brief overview of the Nelder-Mead method of function minimization is given. The computational techniques specifically used to obtain the results in Chapter 3, 4 and 5 are presented in the respective chapters. Chapter 3 presents segmented electrode geometries of the Cylindrical Ion Trap (CIT). In these geometries, the electrodes of the CIT are split into number of mini-electrodes and different voltages are applied to these segmented electrodes to achieve the desired field. Two geometries of the segmented electrode CIT will be investigated. In the first, we retain the flat end cap electrodes of the CIT but split the ring electrode into five mini-rings. In the second configuration, we split the ring electrode of the CIT into three mini-rings and 1The term ‘segmented electrode’ used in this thesis has the same connotation as the term ‘split-electrode’ used in Sonalikar and Mohanty (2013). also divide the end caps into two mini-discs. By applying different potentials to the mini-rings and mini-discs of these geometries we will show that the field within the trap can be optimized to desired values. Two different types of fields will be targeted. In the first, potentials are adjusted to obtain a linear electric field and, in the second, a controlled higher order even multipole field are obtained by adjusting the potential. It will be shown that the different potentials to the segmented electrodes can be derived from a single RF generator by connecting appropriate capacitor terminations to segmented electrodes. The field within the trap can be modified by changing the value of the external capacitors. Chapter 4 presents segmented electrode geometries which are possible alternatives for the Orbitrap. Two segmented-electrode structures, ORB1 and ORB2, to mimic the electric field of the Orbitrap, will be investigated. In the ORB1, the inner spindle-like electrode and the outer barrel-like electrode of the Orbitrap are replaced by rings and discs of fixed radii, respectively. In this structure two segmented end cap electrodes are added. In this geometry, different potentials are applied to the different electrodes keeping top-bottom symmetry intact. In the second geometry, ORB2, the inner and outer electrodes of the Orbitrap are replaced by an approximate step structure which follows the profile of the Orbitrap electrodes. For the purpose of comparing the performance of ORB1 and ORB2 with that of the Orbitrap, the following studies will be undertaken: (1) variation of electric potential, (2) computation of ion trajectories, (3) measurement of image currents. These studies will be carried out using both 2D and 3D Boundary Element Method (BEM), the 3D BEM is developed specifically for this study. It will be seen in these investigations that ORB1 and ORB2 have performance similar to that of the Orbitrap, with the performance of the ORB1 being seen to be marginally superior to that of the ORB2. It will be shown that with proper optimization, geometries containing far fewer electrodes can be used as mass analysers. A novel technique of optimization of the electric field is proposed with the objective of minimizing the dependence of axial frequency of ion motion on the initial position of an ion. The results on the optimization of 9 and 15 segmented-electrode trap having the same design as ORB1 show that it can provide accurate mass analysis. Chapter 5 presents a segmented electrode planar geometry named as PORB used to mimic the electric field of the Orbit rap. This geometry has two planes, each plane consisting of 30 concentric ring electrodes. Although the geometry of PORB does not have conventional inner and outer electrodes of the Orbit rap, it will be shown that by selecting appropriate geometry parameters and suitable potentials for the ring electrodes, this geometry can trap the ions into an orbital motion similar to that in the Orbit rap. The performance of the planar geometry is studied by comparing the variation of potential, ion trajectories and image current in this geometry with that in the Orbit rap. The optimization of applied potentials is performed to correct the errors in the electric field so that the variation of axial frequency of ions with their initial position is minimized. Chapter 6 presents the summary and a few concluding remarks

Axisymmetric analysis of cylindrical contacts is considered in the context of axisymmetric assemblies such as shrink-fits. Fretting fatigue induces sub-critical cracks along the contact interface of press fits especially when they are subjected to vibration. The surface and near surface stresses play a major role in the fretting fatigue crack initiation process. Assuming near surface contact stresses to be largely independent of the actual geometry of components in contact, half-plane analyses and experimental results obtained from a strip configuration are often cited in the literature to predict and understand crack initiation in the actual components (ASTM STP 1425). This thesis starts with half plane and strip models for cylindrical contact such as in a shrink fitted shaft. Different traction profiles underpinning a typical fretting contact constitute a study of different geometrical parameters and friction coefficients. The cylindrical shrink fitted contact is considered using mixed boundary formulation. The different cases of contact such as full slip, partial stick-slip and full stick are considered. A formulation for cyclically varying tractions is attempted using dynamic elasticity. Finally, the problem of cylindrical cracks is highlighted to understand interface delamination in a fiber reinforced composite. Stress functions in conjunction with Fourier transforms are used for analysis. Dynamic potentials based on Helmholtz decomposition are used for dynamic loading.For static loading Love’s stress function is used for axisymmetric problems while Airy’s stress function is used for 2D problems. Solution procedures for solving traction boundary and mixed boundary conditions are described. Preliminary experiments are described to appreciate the contact stresses and crack initiation in cylindrical contact. Photoelastic fringes in a cylinder under a band of pressure illustrate fretting contact stresses concentrated close to the surface with the core of the cylinder relatively unstressed. Further, some material testing experiments using a specially designed cylindrical fretting rig demonstrated typical features of fretting fatigue crack initiation for providing the theoretical motivation. Fretting fatigue induces the initiation of a number of sub critical cracks along the contact interface of components in mechanical assemblies especially under vibration. The dominant crack among the initiated cracks may grow in size to the critical length in the presence of bulk cyclic loading finally resulting in fracture of the entire component. Fretting fatigue leads to unexpected failure of the component well below the expected life. It is therefore, critical to analyse, detect and control fretting. The blade root-disk joint in gas turbines as a critical example of fretting fatigue has spurred extensive research effort. There is relatively little literature available on cylindrical fretting in shrink fitted joint focused in this thesis. Analytical solutions for static fretting tractions are presented using both axisymmetric and plane elastic stress functions for later comparison. While Fourier transforms in conjunction with Airys stress functions are exploited for attacking plane problems, Loves axisymmetric stress functions are explored for cylindrical fretting. Near surface stresses are of great interest in fretting fatigue research. Although two dimensional models provide general understanding of stresses caused during fretting, these models become inadequate to explain the interaction of local stresses with the bulk stresses inevitably present in cylindrical components. Global stress analysis tools are desirable for estimating the fatigue life of components experiencing fretting. While numerical techniques immensely aid fatigue life estimation they have their limitation when it comes to coated components. Stress analysis of coated cylinders unveils the intricate influence of the elastic mismatch as well as the width of the loading for varying friction coefficients. Comparison of results obtained from axisymmetric elasticity with plane elasticity is discussed in detail. The validity and scope of relying on plane fretting results to cylindrical fretting contacts is examined by comparing the results obtained for three different traction profiles. Fretting is generally modeled as a stress boundary value problem wherein the normal and frictional shear stresses are prescribed on the cylindrical surface. In reality fretting generally turns out to be a mixed boundary value problem with unknown regions of stick and slip requiring prescribing traction and displacement simultaneously. This belongs to a formidable class of unsolved contact mechanics problems in cylindrical axisymmetric elasticity. The famous spherical axisymmetric Hertz problem has no cylindrical counterpart except in the limiting case of a cylinder of large radius. These aspects are investigated for studying the hub-shaft interfacial geometry. A conformal contact profile is considered to model a shrink fit; the contact pressure is zero at the ends of contact. The case of full slip condition is analysed assuming a frictionless contact. With friction, partial stick-slip condition is analysed. The unknown contact traction is resolved in terms of Chebyshev expansions whose unknown coefficients are solved using Schmidt method. The unknown contact length and stick zone length are determined through an iterative procedure. A rigid uneven undulating axisymmetric hub in total contact over an elastic shaft under full stick condition is analysed for obtaining the near surface stresses for a given value of hub penetration. Even though the stresses oscillate in fretting, almost all the analyses reported in the literature use static formulation. Understanding this need, a dynamic analysis for modeling fretting of a cylinder subjected to harmonic pressure and shear is attempted. The Pochhammer dispersion relation becomes a prerequisite for a dynamic analysis. The results show that the stresses do not decay away from the contact, in contrast to the static results. This shows the propagation of stresses along the axial direction. Further extension of the dynamic analysis to a layered cylinder is also described. The results obtained on contact stresses and contact tractions under the cylindrical contact represent a significant advance to the literature for modeling fretting fatigue crack initiation and propagation. Formulating cylindrical crack problems is somewhat similar to cylindrical contacts. Such cylindrical cracks arise from the debonding along the fiber-matrix interface of a composite. A unified formulation for the problem of a pressurised cylindrical crack as also a pair of 2D parallel cracks in infinite media is attempted using Love’s stress function in conjunction with Fourier transforms. The results obtained for stress intensity factors, strain energy release rate, mode mixity, crack opening and sliding displacements are compared with that of a 2D pair of parallel cracks obtained using the unified formulation. The asymptotic situation of a large crack length to spacing ratio is examined in detail. In the case of a pair of parallel cracks, this implies a single crack in mode-I as far as the total energy release rate is concerned while at the same time retaining an asymptotic value for the mode mixity. This unique feature of near field mixed mode blending smoothly to mode-I in the far field is also seen for the stress field around a symmetrically branched crack. Thus, this thesis presents a collection of cylindrical elastostatic and elastodynamic axisymmetric solutions to provide better understanding of fretting and delamination problems encountered in press fit assemblies.

The flow-reversal elliptical cylindrical end chamber mufflers of short length are used often in the modern day automotive exhaust systems. The conventional 1-D axial plane wave theory is not able to predict their acoustical attenuation performance in view of the fact that the chamber length is not enough for the evanescent 3-D modes generated at the junctions to decay sufficiently for frequencies below the cut-off frequency. Also, due to the large area expansion ratio at the inlet, the first few higher order modes get cut on even in the low frequency regime. This necessitates a 3-D FEM or 3-D BEM analysis, which is cumbersome and time consuming. Therefore, an ingenious 1-D transverse plane wave theory is developed by considering plane wave propagation along the major-axis of the elliptical section, whereby a 2-port axially short elliptical and circular chamber muffler is characterized by means of the transfer matrix [T] or impedance matrix [Z]. Two different approaches are followed: (1) a numerical scheme such as the Matrizant approach, and (2) an analytical approach based upon the Frobenius series solution of the Webster’s equation governing the transverse plane wave propagation. The convective effects of mean flow are neglected; however the dissipative effects at the ports are taken into account. The TL predicted by this 1-D transverse plane wave analysis is compared with that obtained by means of the 3-D analytical approach and numerical (FEM/BEM) methods. An excellent agreement is observed between this simplified 1-D approach and the 3-D approaches at least up to the cut-on frequency of the (1, 1) even mode in the case of elliptical cylindrical chambers, or the (1, 0) mode in the case of circular cylindrical chambers, thereby validating this 1-D transverse plane wave theory. The acoustical attenuation characteristics of such short chamber mufflers for various configurations are discussed, qualitatively as well as quantitatively. Moreover, the Frobenius series solution enables one to obtain non-dimensional frequencies for determining the resonance peak and trough in the TL graph. The use of this theory is, however, limited to configurations in which both the ports are located along the major axis in the case of elliptical chambers and along the same diameter for circular chambers. The method of cascading the [T] matrices of the 2-port elements cannot be used to analyze a network arrangement of 2-port elements owing to the non-unique direction of wave propagation in such a network of acoustic elements. Although, a few papers are found in the literature reporting the analysis of a network of 2-port acoustic elements, no work is seen on the analysis of a network of multi-port elements having more than two external ports. Therefore, a generalized algorithm is proposed for analyzing a general network arrangement of linear multi-port acoustic elements having N inlet ports and M outlet ports. Each of these multi-port elements constituting the network may be interconnected to each other in an arbitrary manner. By appropriate book-keeping of the equations obtained by the [Z] matrix characterizing each of the multi-port and 2-port elements along with the junction laws (which imply the equality of acoustic pressure and conservativeness of mass velocity at a multi-port junction), an overall connectivity matrix is obtained, whereupon a global [Z] matrix is obtained which characterizes the entire network. Generalized expressions are derived for the evaluation of acoustic performance evaluation parameters such as transmission loss (TL) and insertion loss (IL) for a multiple inlet and multiple outlet (MIMO) system. Some of the characteristic properties of a general multi-port element are also studied in this chapter. The 1-D axial and transverse plane wave analysis is used to characterize axially long and short chambers, respectively, in terms of the [Z] matrix. Different network arrangements of multi-port elements are constructed, wherein the TL performance of such MIMO networks obtained on the basis of either the 1-D axial or 1-D transverse plane wave theory are compared with 3-D FEA carried on a commercial software. The versatility of this algorithm is that it can deal with more than two external or terminal ports, i.e., one can have multiple inlets and outlets in a complicated acoustic network. A generalized approach/algorithm is presented to characterize rigid wall reactive multi-port chamber mufflers of different geometries by means of a 3-D analytical formulation based upon the modal expansion and the uniform piston-driven model. The geometries analyzed here are rectangular plenum chambers, circular cylindrical chamber mufflers with and without a pass tube, elliptical cylindrical chamber mufflers, spherical and hemispherical chambers, conical chamber mufflers with and without a co-axial pass tube and sectoral cylindrical chamber mufflers of circular and elliptical cross-section as well as sectoral conical chamber mufflers. Computer codes or subroutines have been developed wherein by choosing appropriate mode functions in the generalized pressure response function, one can characterize a multi-port chamber muffler of any of the aforementioned separable geometrical shapes in terms of the [Z] matrix, subsequent to which the TL performance of these chambers is evaluated in terms of the scattering matrix [S] parameters by making use of the relations between [Z] and [S] matrices derived earlier. Interestingly, the [Z] matrix approach combined with the uniform piston-driven model is indeed ideally suited for the 3-D analytical formulation inasmuch as regardless of the number of ports, one deals with only one area discontinuity at a time, thereby making the analysis convenient for a multi-port muffler configuration with arbitrary location of ports. The TL characteristics of SISO chambers corresponding to each of the aforementioned geometries (especially the elliptical cylindrical chamber) are analyzed in detail with respect to the effect of chamber dimensions (chamber length and transverse dimensions), and relative angular and axial location of ports. Furthermore, the analysis of SIDO (i.e., single inlet and double outlet) chamber mufflers is given special consideration. In particular, we examine (1) the effect of additional outlet port (second outlet port), (2) variation in the relative angular or axial location of the additional or second outlet port (keeping the location of the inlet port and the outlet ports of the original SISO chamber to be constant) and (3) the effect of interchanging the location of the inlet and outlet ports on the TL performance of these mufflers. Thus, design guidelines are developed for the optimal location of the inlet and outlet ports keeping in mind the broadband attenuation characteristics for a single inlet and multiple outlet (SIMO) system. The non-dimensional limits up to which a flow-reversal elliptical (or circular) cylindrical end chamber having an end-inlet and end-outlet configuration is acoustically short (so that the 1-D transverse plane wave theory is applicable) and the limits beyond which it is acoustically long (so that the 1-D axial plane wave theory is applicable) is determined in terms of the ratio or equivalently, in terms of the ratio. Towards this end, two different configurations of the elliptical cylindrical chamber are considered, namely, (1) End-Offset Inlet (located along the major-axis of the ellipse) and End-Centered Outlet (2) End-Offset Inlet and End-Offset Outlet (both the ports located on the major-axis of the ellipse and at equal offset distance from the center). The former configuration is analyzed using 3-D FEA simulations (on SYSNOISE) while the 3-D analytical uniform piston-driven model is used to analyze the latter configuration. The existence of the higher order evanescent modes in the axially long reversal chamber at low frequency (before the cut-on frequency of the (1, 1) even mode or (1, 0) mode) causes a shift in the resonance peak predicted by the 1-D axial plane wave theory and 3-D analytical approach. Thus, the 1-D axial plane wave analysis is corrected by introducing appropriate end correction due to the modified or effective length of the elliptical cylindrical chamber. An empirical formulae has been developed to obtain the average non-dimensional end correction for the aforementioned configurations as functions of the expansion ratio, (i.e., ), minor-axis to major-axis ratio, (i.e., ) and the center-offset distance ratio, (i.e., ). The intermediate limits between which the chamber is neither short nor long (acoustically) has also been obtained. Furthermore, an ingenious method (Quasi 1-D approach) of combining the 1-D transverse plane wave model with the 1-D axial plane wave model using the [Z] matrix is also proposed for the end-offset inlet and end-centered outlet configuration. A 3-D analytical procedure has also been developed which also enables one to determine the end-correction in axially long 2-port flow-reversal end chamber mufflers for different geometries such as rectangular, circular and elliptical cylindrical as well as conical chambers, a priori to the computation of TL. Using this novel analytical technique, we determine the end correction for arbitrary locations on the two end ports on the end face of an axially long flow-reversal end chamber. The applicability of this method is also demonstrated for determination of the end corrections for the 2-port circular cylindrical chamber configuration without and with a pass tube, elliptical cylindrical chambers as well as rectangular and conical chambers.

The Orbitrap is a mass analyzer that employs an electrostatic field to confine ions. The mass of an ion is determined from the frequency of its axial oscillations in the Orbitrap. The Orbitrap has high resolving power and accuracy. However, the electrodes of the Orbitrap have complicated curved shapes. As a consequence the Orbitrap is not easy to miniaturize. In this thesis we have proposed a class of easily machinable cylindrical-electrode structures to mimic the behavior of an Orbitrap. The proposed structure consists of a single cylinder and many coaxial equally spaced thick rings. A detailed numerical simulation of the cylindrical-electrode structure reveals that axial ion oscillations in it have many spurious frequency components in addition to the dominant frequency component. We have carried out a systematic shape optimization that adjusts the dimensions of the structure to minimize the amplitudes of the spurious frequency components of ion motion in the axial direction. The performance of the optimized structure was found to rival that of a practical Orbitrap.