Hysteretic nonlinearity

However, even in quasi-static operation the actual displacement and desired displacement usually do not correspond. Internal imperfections such as complex hysteretic nonlinearities described by the operator Ia in Fig. 6.6 and external influences such as load reactions via the surrounding mechanical... 

This equation possesses a unique solution for time t if and only if the continuous y-F mapping is strongly monotonous for all X. In this case the different branches of hysteretic nonlinearities differ with respect to the actual hysteretic state of the operator /s. An additional consideration of this information allows us to solve (6.65) uniquely, and thus we can calculate the inverse mapping (6.58). 

The next step to extend the validity of the system model is carried out by the modeling of complex hysteretic nonlinearities by the so called complex hysteresis operators. These complex hysteretic nonlinearities are present in varying degrees in virtually all sohd-state actuators provided that they are driven with sufEciently high amphtudes [349],... 

Unfortunately, in addition to complex hysteretic nonlinearities, actuators and sensors based on the technologically important piezoelectric ceramics contain also log(t)-type creep dynamics to a degree which is not neglectable in wideband applications like positioning systems. 

The self-sensing actuator concept requires the powerful mathematical machinery of complex hysteresis operators - first for reconstructing the mechanical quantities by means of the measured values of electrical quantities and second for compensating the hysteretic nonlinearities and the load dependency. Whereas robust software tools exist for modeling, identifying and compensating scalar complex hysteretic nonlinearities in practical applications, a considerable amount of research activities is necessary in the field of vectorial hysteresis phenomena to obtain a similar status. 

Kuhnen, K. Janocha, H. Inverse feedforward controller for complex hysteretic nonlinearities in smart material systems. Control and Intel . Sys. 29, 3 (2001), pp. 74-83... 

Kuhnen, K. Modeling, Identification and Compensation of complex hysteretic Nonlinearities - A modified Prandtl-Ishlinskii approach. Eur. J. of Control 9, 4 (2003), pp. 407-418... 

The origin of the nonlinearity and hysteresis in the films is most likely due to displacement of domain walls [4], If domain walls move in a medium with a random distribution of pinning center, the response of the material can be described, in the first approximation by Rayleigh relations. We next demostrate how optical interferometry can be sued to verify whether this particular model applies to the investigated pzt thin film. In the case of the converse piezoelectric effect, when the driving field E is varied between — Eo and Eo, the piezoelectric strain x is hysteretic and can be expressed by the following Rayleigh relations ... 

Electro- and magnetooptical phenomena in colloids and suspensions are widely used for structure and kinetics analysis of those media as well as practical applications in optoelectronics [143,144]. The basic theoretical model used to study optical anisotropy of the disperse systems is the noninteracting Brownian particle ensemble. In the frame of this general approximation, several special cases according to the actual type of particle polarization response to the applied field may be distinguished (1) particles with permanent dipole moments, (2) linearly polarizable particles, (3) nonlinearly polarizable particles, and (4) particles with hysteretic dipole moment reorientation. 

The scanner controlling the tip position and tip scanning is made from piezoelectric materials. The intrinsic physical and mechanical properties of piezoelectric materials, such as nonlinear piezoelectricity, hysteretic piezoelectricity and creep deformation affect the performance of the scanner. Such properties can generate distortion of SPM imaging during scanning. 

Determination of these soil properties are well established with recent advances in the formulation of nonlinear hysteretic constitutive relations for soils and the characterization of stiffness degradation of saturated sands and clays with cycles of loading. The increasing interest in seafloor slope stability problems imder wave and earthquake loadings has also emphasized the need for data from cyclic tests simulating stress conditions on slopes. The application of cyclic test techniques in relation to the latter developments are discussed with reference to both test results and associated analytical approaches. 

Sorption by soils and sediments in aquatic surface and subsurface systems functions to retard the transport, regulate the toxicity, and constrain the bioavailability of organic contaminants (1-3). The process is frequently observed to be nonlinear, slow, and apparently hysteretic (4-23). Such behavior is often invoked to explain the ineffectiveness of various technologies to fully cleanup and remediate contaminated... 

The slow, nonlinear and apparently hysteretic behavior commonly observed for soils and sediments is phenomenologically and mechanistically incompatible with the linear partition model. The clear dependence of sorption properties on chemical structures and elemental compositions of SOM found by several investigators (77, 14, 19, 21-23, 32-36) confirms that SOM is in most cases neither homogeneous nor completely gel-like in character, as assumed implicitly by the linear partitioning model. 

Reggio, A., De Angelis, M.. Feasibility of a passive isolation system with nonlinear hysteretic behaviour for the seismic protection of critical equipment. In Proceedings of the XIV Covegno ANIDIS Associazione Nazionale Italiana di Ingegneria Sismica. Bari, Italy 2011. 

The equation (1.14) defines implicitly the dependence r o(h), which, as we will see below, has hysteretic character. The field decreases the symmetry of paraphase and induces order parameter po 0 for all the temperatures. It follows from Eq. (1.14) that order parameter is a nonlinear function of the field (see Fig. 1.5a for T > Tc) and at T = Tc it reads q =... 

Using a model with lumped masses at two characteristic levels (top and level 1), a nonlinear dynamic analysis was performed with a complex hysteretic (IZIIS) model (Fig. 8.5, Shendova 1998). To calibrate the computations in defining the capacity degradation in hysteretic models, the results from seismic shaking table testing of the model were used. With this, an attempt was made to model the dynamic response in a simple way, suitable for everyday analyses, resulting however in satisfactory final results on the behavior at individual levels. 

A nonlinear dynamic analysis has been performed for the three monuments (Sect. 8.2.3), with the masses lumped at characteristic levels and applying a corresponding storey hysteretic model obtained by summing up the elastoplastic characteristics of each of the bearing walls, with the load-bearing capacity of each of them limited to the bending and shear capacity, whichever is less. 

The analytical investigations involved definition of the seismic response of the structure in the nonlinear range of behavior. To model the behavior of the structural system in the elastic phase, at the beginning of nonlinearity (occurrence of cracks) and deep nonlinearity, the IznS three-linear hysteretic model with stiffness degradation and pinching effect was used (Fig. 8.5). 

Dynamic analysis With the masses lumped at two characteristic levels, a nonlinear dynamic analysis has been performed with storey hysteretic model obtained by summing up the elastoplastic characteristics of each of the bearing walls, whereas the load-bearing capacity of each of them has been limited to the lower value of bending and shear capacity (according to Sect. 8.3.3). To obtain the dynamic response, three different types of earthquake (Petrovac 1979, Ulcinj 1979 and El Centro 1940) with maximum input acceleration of 0.24g and return period of 1,000 years have been applied. Obtained as the results from the dynamic analysis are the storey displacements and ductility ratios required by the earthquake that have to comply with the design criteria defined in Sect. 8.3.4. 

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