| Numerous mechanical phenomena demonstrate the cyclical nonlinear behavior known as hysteresis. A literature review highlights the applicability of hysteretic analysis to a wide variety of mechanical systems and provides a historical overview of mathematical models developed for the most commonly referenced hysteretic phenomenon; plastic stress-strain in the dynamic behavior of solids. Modeling hysteresis in strength of materials involves capturing a wide variety of physical properties exhibited in materials, while retaining a tractability for analytical methods used extensively for random vibration and reliability analysis as well as system identification of physical systems. Computational tools are developed and exercised in this research which aid in the analysis of SDOF hysteretic systems, and advance the capabilities of current mathematical models.; The well-known method of equivalent linearization is modified to a format that is specifically derived for rate-type hysteretic systems, resulting in a computational approach which eliminates the significant analytic effort associated with earlier methods. The direct linearization approach allows for quick, accurate and robust analysis of many general hysteresis models, under stochastic excitation. This procedure enables a departure from traditional differential equation models in lieu of a Boolean model definition. The Boolean Model is a piecewise nonlinear set of analytic functions, supported by Boolean logical operator expressions explicitly defined by computer codes. The features of this modeling method are explored in detail.; Finally, the Boolean Model is expanded to a database format that is similar to a finite element approach, where the basic shape functions defining the hysteresis pattern are simple linear expressions, but are discretized to many small finite regions of the overall cycle. A computer software program is developed to implement the Boolean Material Property Database. This database is shown to offer high definition patterns, and significant potential for system identification and health monitoring of hysteretic systems. |
