An Alternative Derivation of the Landau-Lifshitz-Gilbert Equation for Saturated Ferromagnets

The Landau-Lifshitz-Gilbert equation for rigid and saturated ferromagnets is derived using a two-continuum model constructed by H.F. Tiersten for elastic and saturated ferromagnets. The relevant basic laws of physics are applied systematically to the two continua or their combination. The exchange interaction is introduced into the model through surface distributed magnetic couples. This leads to a continuum theory with magnetization gradients in the stored energy density. The saturation condition of the magnetization functions as constraints on the energy density and has implications in the constitutive relations

Theoretical Analysis of Quartz Plate Acoustic Wave Resonators and Sensors Using Three-Dimensional Equations of Anisotropic Elasticity or Piezoelectricity

This is a review of theoretical results from the three-dimensional equations of anisotropic elasticity or linear piezoelectricity on waves and vibrations in quartz crystal plates. It covers both the classical results on acoustic wave resonators and the relatively new applications in acoustic wave sensors. It discusses the basic thickness modes with various complications due to electrodes, mass loading, contact with fluids, and air gaps, etc. as well as the more complicated transversely varying modes. These results are fundamental for the understanding and design optimization of the widely used quartz crystal plate resonators and sensors

Propagation of Coupled Acoustic, Electromagnetic and Spin Waves in Saturated Ferromagnetoelastic Solids

We study the propagation of plane waves in an unbounded body of a saturated ferromagnetoelastic solid. The equations by Tiersten for small fields superposed on finite initial fields in a saturated ferromagnetoelastic material are employed, with their quasistatic magnetic field extended to dynamic electric and magnetic fields for electromagnetic waves. Dispersion relations of the plane waves are obtained. The cutoff frequencies and long wave approximation of the dispersion curves are determined. Results show that acoustic, electromagnetic and magnetic spin waves are coupled in such a material. For YIG which is a cubic crystal without piezoelectric coupling, the acoustic and electromagnetic waves are not directly coupled but they can still interact indirectly through spin waves

Vibrating Flexoelectric Micro-Beams as Angular Rate Sensors

We studied flexoelectrically excited/detected bending vibrations in perpendicular directions of a micro-beam spinning about its axis. A set of one-dimensional equations was derived and used in a theoretical analysis. It is shown that the Coriolis effect associated with the spin produces an electrical output proportional to the angular rate of the spin when it is small. Thus, the beam can be used as a gyroscope for angular rate sensing. Compared to conventional piezoelectric beam gyroscopes, the flexoelectric beam proposed and analyzed has a simpler structure