Analytical expressions of Preisach Distribution Function

Summary form only given. Preisach model of scalar hysteresis has demonstrated his capability to represent hysteretic behaviour, but it requires the accurate identification of the Preisach Distribution Function (PDF). The identification of PDF, P/sub irr/(/spl alpha/,/spl beta/), can be obtained by assuming the factorisation property P/sub irr/(/spl alpha/,/spl beta/)=/spl phi/(/spl alpha/)/spl middot//spl phi/(-/spl beta/). Following this approach, PDF is related to the descending branch M/sub u/(H) of limit experimental cycle. The author has deduced an analytical relation between function /spl phi/(H) and experimental data M/sub u/(H). Moreover, if an analytical approximation of the descending branch M/sub u/(H) is available an analytical expression for the PDF can be obtained. In this work, starting from same analytical expressions of the saturation loop such as probability integral and hyperbolic tangent, the related PDFs are obtained. This method look attractive in view of the calculation of simple analytical expression of PDF.