Mathematical Methods in Electro-Magneto-Elasticity

The mechanics of Coupled Fields is a discipline at the edge of modern research connecting Continuum Mechanics with Solid State Physics. It integrates the Mechanics of Continuous Media, Heat Conductivity and the theory of Electromagnetism that are usually studied seperately. For an accurate description of the influence of static and dynamic loadings, high temperatures and strong electromagneticfields in elastic media and constructive installations, a new aproach is required; an approach that has the potential to establish a synergism between the above-mentioned fields. Throughout the book a vast number of problems are considered: two-dimensional problems of electro-magneto-elasticity as well as static and dynamical problems for piecewise homogenous compound piezoelectric plates weakened by cracks and openings. The boundary conditions, the constuctive equations and the mathematical methods for their solution are thoroughly presented, so that the reader can get a clear quantative and qualitative understnding of the phenomena taking place.

This book is for the specialists in Continuous Mechanics, Acoustics and Defectoscopy, and also for advanced undergraduate and graduate -level students in Applied Mathematics, Physics, Engineering Mechanics and Physical Sciences.

Fills Many gaps in the theoretical literature which arise due to the complexity of the problem

Inhalt
Physical Fields in Solid Bodies.- Basic Equations of the Linear Electroelasticity.- Static Problems of Electroelasticity for Bimorphs with Stress Concentrators.- Diffraction of a Shear Wave on Tunnel Cracks in Media of Various Configurations (Antiplane Deformation).- Scattering of a Shear Wave by Cylindrical Inhomogeneities in Piezoceramic Media of Various Configurations (Antiplane Deformation).- Mixed Dynamic Problems of Electroelasticity for Piezoelectric Bodies with Surface Electrodes.- Harmonic Oscillations of Continuous Piezoceramic Cylinders with Inner Defects (Antiplane Deformation).- Electroacoustic Waves in Piezoceramic Media with Defects (Plane Deformation).- Fundamentals of Magnetoelasticity.- Influence of the Induced Currents on the Dynamic Intensity of Piecewise-Uniform Electro-Conductive Bodies in Magnetic Fields.- Influence of Magnetizability of Material on the Stress State of a Ferromagnetic Medium with Heterogeneities.- Optimal Control of Physical Fields in Piezoelectric Bodies with Defects.