Nonlinear Electromechanical CouplingsOffers an updated and rigorous treatise on most manifestations of nonlinear electromechanical couplings in dielectric media with applications to piezoelectric and ferroelectric crystals, piezoelectric powders and solutions of electrodeformable macromolecules. Presents a variety of static and dynamic nonlinear effects which have important engineering applications. Contains an insight into the nonlinear behavior of such new substances as ceramics, powders and ferroelectrics. Rigorous mathematical treatment includes hyberbolic systems, asymptotic expansions, singular perturbations, convexity and soliton theory. |
Contents
Continuum and discrete models of electrodeformable continua | 47 |
Quasilinear dynamics of electroelasticity | 105 |
Nonlinear dynamics of electroelasticity | 161 |
Copyright | |
8 other sections not shown
Common terms and phrases
acoustic amplitude applied electric field barium titanate behaviour boundary conditions Chapter components consider constants constitutive equations continuum corresponding crystal curve defined deformation depends derivative dielectric dipoles dispersion displacement dissipation domain dynamic E₁ echo effects electric field electric polarisation electric susceptibility electroelastic electromechanical couplings electrostriction entropy equilibrium evolution expression ferroelastic ferroelectric Figure first-order free energy frequency function generalised given gradient grains hysteresis loop integral interaction jump kink Lagrangian linear macromolecules material Maugin mechanical mode motion nonlinear obtained order parameter oscillations P₁ perturbation phase transition piezoelectric plane polyelectrolytes Pouget & Maugin propagation pulse resonator response rotation second-order shock waves sine-Gordon equation solitary waves soliton solution spatial strain stress surface symmetry temperature tensor theory thermodynamic thermodynamic equilibrium transformation U₁ variable vector velocity wavenumber X₁ yields