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In this thesis we are concerned with studying some stress wave propagation problems in solids consisting of two dissimilar isotropic homogeneous elastic half-spaces (or semi infinite cylinders) bonded together along their common plane boundary as well as some electromagnetic wave propagation problems in waveguides filled with two different dielectric materials. The problems considered are (i) the torsional oscillations of a rigid circular disk symmetrically situated at the interface of two different infinite elastic half-spaces and is in welded contact with them, (ii) the diffraction of normally incident plane harmonic torsion stress waves by an immovable rigid circular disk securely attached to the interface of two different elastic half-spaces, (iii) problem (i) with the infinite half-spaces replaced by semi infinite cylinders, (iv) problem (ii) with the same restriction as in (iii), and finally (v) the diffraction of a normally incident electromagnetic field with no electric component in the direction of propagation, i. e. a TE-wave, (or with no magnetic component in this direction, i,e. a TM-wave) by a very thin perfectly conducting circular disk situated centrally in a circular waveguide filled with two different dielectric materials on either side of the disk. Using Hankel transforms in the solution of Problems (i) and (ii) and applying the mixed boundary conditions at the interface yield a pair of dual integral equations. The solution of these dual integral equations is reduced to that of a Fredholm integral equation of the second kind for an auxiliary function. The iterative solution of the integral equation at low frequencies is used to give approximations for some quantities of physical interest such as the stress at the disk-elastic medium interface, the torque acting on the disk and the forward and back-scatter coefficients. The results obtained when the parameters of the two different materials are set equal are in agreement with the known results whenever they exist. For problems (iii) and (iv) the solution is represented in the form of a Fourier-Bessel series when the cylindrical surface is rigidly clamped (case (a) ) and in the form of a Dini series when this surface is stress-free (case (b) ). The mixed boundary-value problem is formulated as a pair of dual relations of Fourier-Bessel series (case (a) ) or Dini series (case (b) ). The solution of the dual relations is then reduced to that of a Fredholm integral equation of the second kind for an auxiliary function. The iterative solution of the integral equation when the frequency and the ratio of the disk radius to that of the medium are small is employed as in problems (i) and (ii) to find approximate expressions for some relevant quantities. In problem (v) the electromagnetic diffracted field arising from a TE[01] mode incident field is given in terms of a Hertz vector. The mixed boundary-value problem for the determination of this Hertz vector is formulated as a pair of Fourier-Bessel series similar to one obtained in the solution of problem (iv). The equivalent circuit for the discontinuity in the waveguide is described. We also attempt to present a mathematical formulation for the problem of the diffraction of a general TE incident field. The problem of the diffraction of a TM[01]-mode is reduced to a Fredholm integral equation of the second kind which can be solved iteratively in the low frequency range when the ratio of disk radius to that of the waveguide is small compared with unity.

The diffraction and propagation problems presented here fall broadly into the two categories of high frequency diffraction of electromagnetic waves by smooth objects and of low frequency diffraction of electromagnetic waves by objects with edges. In the former category the geometry of the problems is such that the variables may be separated and a solution obtained in the form of an eigenfunction expansion which is suitable at low frequencies. The Watson Transformation which is then employed enables the high frequency case (i.e. the case when the wave number is large) to be considered. In the latter category an integral equation approach is adopted and a solution to the boundary value problems is shown to rest upon the solution of a Fredholm integral equation of the first kind. Using a technique employed by W.E., Williams, the Fredholm integral equation of the first kind is reduced to a Fredholm integral equation of the second kind for which, after ensuring that edge conditions are satisfied, an approximate solution is obtained. This solution is useful at low frequencies (i.e. when the wave number is small) and when certain separation distances are considered large. In both classes of problems attention is, amongst other things, focused on the field at large distances from the scattering obstacles so that expressions for scattering coefficients and transmission coefficients, where appropriate, may be obtained.

The spillover from a normal symmetrical Cassegrain aerial, particularly when the aerial is directed towards a. low elevation stationary satellite, is equally distributed towards the sky and the local hot Earth. In order to direct this radiation more toward the sky, both the subreflector and its feed horn have to be tilted in the appropriate direction. The consequences of this procedure are complex. The subreflector requires considerable redesign and the primary radiation pattern can therefore suffer serious degradation. The study has been aimed at optimizing the design and assessing the consequences in such a way as to achieve a considerable reduction in the Earth-directed spillover without undue decrease in gain or deterioration in secondary radiation performance. Theoretical analysis has been shown to be in good agreement with experimental patterns and computer programs have been produced which enable all systems of this type to be predictably analysed.

Following a critique of previous theories of the dielectric aerial, a theoretical model is proposed based on the concepts of scattering theory. It is shown that the model is essentially an extension of the theory of polarization of dielectric materials. Application of the scattering model yields an inhomogeneous Fredholm integral equation, the solution of which is the aerial radiation pattern. Explicit equations are deduced for both TM01 and HE11 mode excitation of solid dielectric rods and numerical solutions have been obtained. The solutions compare favourably with those of previous methods. Extensions of the theory to other dielectric structures, such as tubes and inhomogeneous rods, are also discussed.

A survey is given of the literature concerning the scattering properties of infinite plane wire gratings when illuminated by plane electromagnetic waves. As an introduction, a summary of the applications of wire gratings is included. A description is given of some alternative methods of treating the scattering problem, with particular reference to the application of Green's function to the single cylinder and its application to the plane grating. The literature concerned with multiple grating configurations is also surveyed. A polarisation cascade matrix is derived which describes the transmission of a normally incident elliptically polarised wave through a grating of parallel wires whose angle is arbitrary. The terms of the matrix contain the well-established complex reflection and transmission coefficients for a linearly polarised plane wave incident upon a grating. Hence the matrix can be adapted for gratings of strips or Wires of non-circular cross-section. The product of a series of matrices representing a series of gratings whose wires are at different angles to a fixed direction gives the total complex transmission and reflection coefficients. The results are shown to be in agreement with previously published work on a double grating system and experimentally verified for configurations of two and five gratings. These results confirm that such a series of gratings can be used to design either broad-band polarisation rotators for linear polarization, or broad-band circular or elliptical polarisers or analysers. A sharp resonance reflection condition when gratings are separated by approximately half a wavelength can also be used in the design of frequency filters.

Parametrically excited systems, where defining system parameters vary periodically with an independent variable (time), are a popular research topic in engineering. Cable-stayed bridges, free hanging marine flexible risers, planetary gear systems and other engineering structures are often subject to parametric excitation. Due to the high amplitude of responses as a result of parametric amplification, parametric excitation can be disastrous if not account. Parametric amplification in mechanical and electrical systems can be exploited for designing vibration energy harvesters and electrical filters. This thesis contains various work on Linear and Nonlinear Parametrically Excited (LPE) and (NPE) systems. The system of interest is a clamped-free cantilever beam which is modelled as a single degree of freedom system. An electromagnetic system is used to generate time-periodic stiffness and control nonlinearities. The forces applied from the electromagnetic system are found analytically in order to compare this work to similar systems and to conduct parametric studies. The nonlinear electromechanical coupling, electrical damping, and the induced current is implemented in the analytical model. The free responses of LPE and NPE systems are investigated analytically with the method of averaging and harmonic balance, with particular attention paid to the stability of these systems. The effect of cubic and cubic parametric nonlinearity on the NPE systems is demonstrated through some analytical and experimental investigations. This study on the NPE system is employed to show the effect of time-periodic stiffness and stiffness nonlinearities on attenuating or amplifying the response. Increasing the response amplitude of amplifiers and filters with an electromagnetic system can be achieved by tuning the system at the parametric resonance. Furthermore, the electromagnetic system can be configured to reduce the electrical damping, or to control the nonlinearities and consequently increase the parametric amplification. The responses and stability of the NPE system subject to a harmonic base excitation are investigated analytically and experimentally. Unlike previous studies, the parametric excitation is independent of the base excitation. A careful selection of system parameters, such as parametric amplitude, relative phase and cubic parametric nonlinearity, can result in significant parametric amplification, and can prevent the jump between stable solutions. Parametric attenuation can also be achieved by controlling the phase difference between the base and the parametric excitation. This study has successfully demonstrated the importance of nonlinearity in parametrically excited systems.

In recent years the electrocaloric effect has gained the substantial interest of researchers due to its potential applications in commercial cooling. The high theoretical effciency of electro-thermal conversion places this phenomenon as a potential alternative to commercial vapour-compression refrigerators. Success in such solid state cooling is anticipated to lead to global scale energy savings and reduction in the emission of greenhouse gases. Most of the focus has been directed towards the achievement of high values of the electrocaloric effect temperature change ∆T EC . High values of around 10 K and more have been reported. However little attention has been given to the methods of measurements and their uncertainties. This work aims to use a metrological approach to study the electrocaloric phenomenon, to compare certain methods and to explore these measurements and their uncertainties. There are various ways to quantify the electrocaloric effect and various parameters infuence the direct measurements of ∆T EC . Here a direct method using infrared imaging is employed for the spatial and time-resolved temperature measurements of electrocaloric bodies. A set of the parameters infuencing the∆T EC is determined. Based on these quantifed contributions, an uncertainty for such measurements is reported. The calibration of the imager is performed to validate the traceability of measurements, and a further set of characterisation apparatus was implemented to establish its performance. A bulk Ba 0.65 Sr 0.35 TiO 3 sample was employed as a cross reference specimen in an inter-laboratory comparison involving infrared imaging and two types of differential scanning calorimetry. Within the scope of this work, two commercial ceramic material compositions were characterised; a multilayer capacitor and a PMN-PT ceramic. First, BaTiO 3 in form of a multilayer ceramic capacitor was used to establish the optimal performance of such a structure and to investigate the in-situ measurements. In this measurement there were substantial differences in ∆T EC depending on where on the sample (surface vs. interior) the measurement was made and an explanation for this difference is suggested. Second, the polycrystalline Pb(Mg 1/3 Nb 2/3 )−PbTiO 3 ceramic sample was used investigate other sources of uncertainties arising from the mechanical coupling during electrocaloric measurements, estimated to account for up to 20% of the observed electrocaloric effect.

Piezoelectricity is the ability of certain, non-conductive, materials to generate an electrical charge when pressure is applied to them. The voltage produced is directly proportional to the applied stress. The amount of charge generated can depend on, for example, the applied strain rate or the temperature. Due to this ability, piezoceramics, such as PZT ceramics, find use in many different applications, primarily as sensors or actuators. Sensors work by detecting pressure, mechanically deforming and thus producing a voltage. Actuators, on the other hand, mechanically deform upon application of an electric field. To develop a better understanding of the piezoelectric ceramic lead zirconate titanate (PZT) 95/5, a range of studies including varying temperatures, porosities, and strain rates have been conducted. The effects on the voltage output and failure of poled PZT samples of different porosities have been investigated using different compressive strain rates (10^-4 – 10^4 s^-1), reached with quasi-static loading equipment, drop-weight towers, and Split Hopkinson Pressure Bars (SHPBs). The main cylindrical specimens were of 4.4 mm diameter, thickness 0.8 - 4.4 mm, and density 7.3 - 8.3 g cm^-3. The temperature range of -20°C to +80°C was achieved using purpose-built environmental chambers. The resulting stress-strain relationships are compared; all the samples ultimately displaying a brittle response at failure [1]. To support this work, ideal geometric specimen sizes were identified for the different types of loading experiment, by carrying out a range of strain-rate compression experiments on well-studied materials such as aluminium and copper. In addition, different experimental platforms were successfully developed in order to reach non-ambient temperatures in the Split Hopkinson Pressure Bar experiments. Finally, as piezoceramics, when used in real world applications, are often coated in protective layers of polymer, several different types of industrial polymer have been characterised across the full range of strain rates and temperatures.

Cold molecules are attractive for a wide range of scientific applications, including quantum computation, the study of chemical reactions, and tests of fundamental physics. Laser cooling has proved to be an invaluable technique in the cooling of atoms. This technique was once thought to be infeasible for molecules, because it is difficult to find a closed cycling transition due to their vibrational structure. Recently, laser cooling of several diatomic species has been demonstrated. These molecules possess electronic transitions with highly diagonal Franck-Condon matrices, which make it possible to drive a quasi-closed cycling transition. Ytterbium fluoride (YbF) molecules are amenable to laser cooling and are especially interesting because they are used to measure the electron's electric dipole moment (eEDM). Measurements of the eEDM test the prediction of theories that extend the Standard Model of particle physics. The sensitivity of an eEDM experiment could be greatly increased by using ultracold molecules produced by direct laser cooling. This thesis presents work done towards producing a laser-cooled beam of YbF for an eEDM experiment. This work includes the construction of the cooling experiment, a novel method for efficiently combining laser beams of very similar frequencies, results of spectroscopic measurements to find the required transitions for laser cooling, the results of initial optical cycling experiments, and the first laser cooling results of YbF. Using a one-dimensional optical molasses, a beam of molecules is Doppler cooled in one transverse direction to a temperature of approximately 70 mK. Preliminary evidence of cooling to lower temperatures through a Sisyphus mechanism is also presented. Finally, paths towards improving the laser cooling are suggested. The work opens the door to improved measurements of the eEDM using ultracold YbF molecules.