| The study of multiferroics, or ferroelectro-magnets, is nascent compared to other active materials. Discovered in the 1960s, multiferroics possess the ability to couple electroelastic and magnetoelastic responses as well as the additional ability to couple electromagnetic responses. To date, material scientists have identified over 100 of these materials. Absent from the progress in this field, however, are the analytical contributions that serve the design considerations for use of multiferroics. To fit this need, the following has as its focus analytical topics in the solid and wave mechanics of multiferroics, with particular attention paid throughout to the effect of the unique type of couplings that exist within multiferroic continua.; In the solid mechanical analysis contained herein, the governing and constitutive equations are derived and accompanied by proof that their solutions are unique. These sets of equations are plied to the case of a transversely isotropic, linear multiferroic under plane stress, the details and results of which are provided. From this analysis, an effective coupling factor is defined for determining the ability of a multiferroic material to convert energies.; The first type of wave phenomenon considered is the acousto-electromagnetic, or Bleustein-Gulyaev, wave for a linear electromagnetoelastically-coupled material. Using the aforementioned equations, an analytical model is developed to determine the velocity of Bleustein-Gulyaev waves in linear multiferroic. The effective coupling factor that was present in the mechanical analysis is found also in the case of the acoustical analysis of a transversely isotropic, linear multiferroic. The effect of its presence on the propagation of information within a multiferroics is discussed.; Also considered are electromagnetic waves; of particular interest is the ability of multiferroics to couple the rapidly altering electric and magnetic fields associated with such a wave. As such, the analytical development of a wave equation for real, rapidly altering fields in multiferroics is presented. With consideration given to phenomenology, crystal color symmetry and the laws of Ampere and Faraday, the analysis is applied to the case of an orthorhombic multiferroic. A velocity expression is obtained for a coupled wave. The implications of the expressions to modulated optical properties are discussed. |
