On well-posedness for some thermo-piezoelectric coupling models

There is an increasing reliance on mathematical modelling to assist in the design of piezoelectric ultrasonic transducers since this provides a cost-effective and quick way to arrive at a first prototype. Given a desired operating envelope for the sensor the inverse problem of obtaining the associated design parameters within the model can be considered. It is therefore of practical interest to examine the well-posedness of such models. There is a need to extend the use of such sensors into high temperature environments and so this paper shows, for a broad class of models, the well-posedness of the magneto-electro-thermo-elastic problem. Due to its widespread use in the literature, we also show the well-posedness of the quasi-electrostatic case

Acoustic Waves

The concept of acoustic wave is a pervasive one, which emerges in any type of medium, from solids to plasmas, at length and time scales ranging from sub-micrometric layers in microdevices to seismic waves in the Sun's interior. This book presents several aspects of the active research ongoing in this field. Theoretical efforts are leading to a deeper understanding of phenomena, also in complicated environments like the solar surface boundary. Acoustic waves are a flexible probe to investigate the properties of very different systems, from thin inorganic layers to ripening cheese to biological systems. Acoustic waves are also a tool to manipulate matter, from the delicate evaporation of biomolecules to be analysed, to the phase transitions induced by intense shock waves. And a whole class of widespread microdevices, including filters and sensors, is based on the behaviour of acoustic waves propagating in thin layers. The search for better performances is driving to new materials for these devices, and to more refined tools for their analysis

An analytical solution for the magneto-electro-elastic bimorph beam forced vibrations problem

Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the definition of the bending moment. Moreover, the influences of the electro-mechanic, magneto-mechanic and electromagnetic coupling on the stiffness of the bimorph stem from the computation of the beam equivalent stiffness constants. Free and forced vibration analyses of both multiphase and laminated magneto-electro-elastic composite beams are carried out to check the effectiveness and reliability of the proposed analytic solution.Based on the Timoshenko beam theory and on the assumption that the electric and magnetic fields can be treated as steady, since elastic waves propagate very slowly with respect to electromagnetic ones, a general analytical solution for the transient analysis of a magneto-electro-elastic bimorph beam is obtained. General magneto-electric boundary conditions can be applied on the top and bottom surfaces of the beam, allowing us to study the response of the bilayer structure to electromagnetic stimuli. The model reveals that the magneto-electric loads enter the solution as an equivalent external bending moment per unit length and as time-dependent mechanical boundary conditions through the definition of the bending moment. Moreover, the influences of the electro-mechanic, magneto-mechanic and electromagnetic coupling on the stiffness of the bimorph stem from the computation of the beam equivalent stiffness constants. Free and forced vibration analyses of both multiphase and laminated magneto-electro-elastic composite beams are carried out to check the effectiveness and reliability of the proposed analytic solution

Sound and vibration analysis of compliant piezoelectric enabled structures

Ph.DDOCTOR OF PHILOSOPH

Modelling the Directional Response of Fabry-Pérot Ultrasound Sensors

Fabry-Pérot ultrasound sensors offer an alternative to traditional piezoelectric sensors for clinical and metrological applications, for example, measuring high intensity focused-ultrasound (HIFU) fields. In this thesis, a model of the frequency dependent directional response was developed based on the partial-wave method, treating the sensor as a multi-layered elastic structure. An open-source MATLAB toolbox called ElasticMatrix was developed to model acoustic and elastic-wave propagation in multi-layered structures with anisotropic material properties. The toolbox uses an object-oriented framework, giving it a simple scripting interface and allowing it to be expanded easily. The toolbox is capable of calculating and plotting reflection and transmission coefficients, slowness profiles, dispersion curves and displacement and stress fields. An additional MATLAB class is included to model the frequency-dependent directional response of Fabry-Pérot ultrasound sensors. The model was validated, tested and compared with directional response measurements made on two glass-etalon sensors: an air-backed cover-slip sensor with well-known acoustic properties, and an all-hard-dielectric sensor. Features of the directional response were investigated and attributed to the critical angles of the substrate backing, and Lamb- and Rayleigh-modes propagating in the sensor. The directional response of two sensors with Parylene C (a commonly used soft-polymer) were also investigated: a sensor with a Parylene C spacer, and a glass-etalon sensor with a thick Parylene C coating. X-ray diffraction and transmission electron microscope measurements indicated Parylene has a crystal structure and impedance measurements indicated that Parylene is acoustically anisotropic. Using the measured impedance values, the modelled and measured directivity had improved agreement compared with isotropic values based on the phase-speeds of guided modes. The developed modelling tools allow detailed analysis of the physical mechanisms affecting the frequency-dependent directional response of planar Fabry-Pérot sensors. This knowledge can be used to inform future sensor design, to aid with material selection, and for deconvolution of the sensor response from acoustic measurements

Homogenization Methods for Problems with Multiphysics, Temporal and Spatial Coupling

There are many natural and man-made materials with heterogeneous micro- or nanostructure (fine-scale structure) which represent a great interest for industry. Therefore there is a great demand for computational methods capable to model mechanical behavior of such materials. Direct numerical simulation resolving all fine-scale details using very fine mesh often becomes very expensive. One of alternative effective group of methods is the homogenization methods allowing to model behavior of materials with heterogeneous fine-scale structure. The essence of homogenization is to replace heterogeneous material with some equivalent effectively homogeneous material. The homogenization methods are proven to be effective in certain classes of problems while there is need to improve their performance, which includes extension of the range of applicability, simplification, usage with conventional FE software and reducing computational cost. In this dissertation methods extending the range of applicability of homogenization are developed. Firstly, homogenization was extended of the case of full nonlinear electromechanical coupling with large deformations, which allows simulating effectively behavior of electroactive materials such as composites made of electroactive polymers. Secondly, homogenization was extended on wave problems where dispersion is significant and should be accounted for. Finally, the homogenization was extended on the case where the size of microstructure. The distinctive feature of the methods introduced in this dissertation is that they don't require higher order derivatives and can be implemented with conventional FE codes. The performance of methods is tested on various examples using Abaqus

Wave Propagation in Materials for Modern Applications

In the recent decades, there has been a growing interest in micro- and nanotechnology. The advances in nanotechnology give rise to new applications and new types of materials with unique electromagnetic and mechanical properties. This book is devoted to the modern methods in electrodynamics and acoustics, which have been developed to describe wave propagation in these modern materials and nanodevices. The book consists of original works of leading scientists in the field of wave propagation who produced new theoretical and experimental methods in the research field and obtained new and important results. The first part of the book consists of chapters with general mathematical methods and approaches to the problem of wave propagation. A special attention is attracted to the advanced numerical methods fruitfully applied in the field of wave propagation. The second part of the book is devoted to the problems of wave propagation in newly developed metamaterials, micro- and nanostructures and porous media. In this part the interested reader will find important and fundamental results on electromagnetic wave propagation in media with negative refraction index and electromagnetic imaging in devices based on the materials. The third part of the book is devoted to the problems of wave propagation in elastic and piezoelectric media. In the fourth part, the works on the problems of wave propagation in plasma are collected. The fifth, sixth and seventh parts are devoted to the problems of wave propagation in media with chemical reactions, in nonlinear and disperse media, respectively. And finally, in the eighth part of the book some experimental methods in wave propagations are considered. It is necessary to emphasize that this book is not a textbook. It is important that the results combined in it are taken “from the desks of researchers“. Therefore, I am sure that in this book the interested and actively working readers (scientists, engineers and students) will find many interesting results and new ideas