In this contribution we present a phenomenological mesoscopic thermodynamically consistent model for the description of switching processes in ferroelectric materials that is able to describe the fundamental electromechanical hysteresis effects. The main goal is to develop a representation using the set of independent variables, the strains and the electric field, in a coordinate-invariant setting. This formulation is particularly suitable for the treatment of a variety of complex boundary-value problems (BVP) with regard to the essential boundary conditions. Here we restrict ourselves to transversely isotropic solids. The anisotropic behavior is governed by isotropic tensor functions that depend on a finite set of invariants. Thus the material symmetry requirements are automatically fulfilled.

An overview of different techniques to monitor vibrations of the generator end winding (impact tests, online vibration measurements using fiber optic accelerometers or a laser vibrometer) are presented. Data from online vibration measurements to investigate the vibration modal shapes of the stator end winding basket during operation is correlated with the generator operation parameters. These analyses are compared to results of finite-element-model calculations of a stator end winding. To evaluate the vibrations of a generator stator end winding during operation, it is necessary to relate vibrational modes to the generator operation parameters. In situ recording of, i.e. local accelerations or strain together with generator operating parameters allows deeper insight into the correlation of operating parameters and vibrations of the stator end windings.

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A characteristic feature of ferroelectric crystals is the appearance of a spontaneous polarisation, where its direction can be reversed by an applied electric field. This quantity, that has a maximum value at high electric-fields, depends on the loading history of the material. In this paper we discuss a thermodynamic consistent phenomenological model for an assumed transversely isotropic ferroelectric crystal, where the history dependency is modelled by internal variables. The anisotropic behaviour is governed by isotropic tensor functions, depending on a finite set of invariants, that satisfy automatically the symmetry relationships of the considered body. The main goal of this investigation is to capture some characteristics of nonlinear ferroelectrica, such as the polarisation-electric-field and the strain-electric-field (butterfly) hysteresis loops.

In this contribution we discuss as imple phenomenological modelf or an assumedt ransversely isotropic ferroelectric crystal. We focusonthe theoreticalformulation andnumerical treatmentofthe coupledelectro-mechanical behaviour. The main goal of this investigation is to capturet he main characteristics of nonlinearf erroelectrica, such as the polarization-electric-field andt he quadratic strain-electric-field (butterfly) hysteresisl oops.T he history dependency is modelledv ia twoi nternal variables, thei rreversible polarization andi ts conjugated irreversible electric-field.