Etude approchee d'un systeme a hysteresis

On the basis of a geometrical interpretation of the method of first harmonic of Haag—Krylov—Bogolioubov—Mitropolski, a new dynamical study of an oscillator with hysteresis is made. This consists in replacing the equation of motion by another approximate equation which conserves the nonlinearity of the original equation. This method is valid in the case of sinusoidal excitation, but it can be extended to the case of random excitation. In particular, in the case when this excitation is white noise the Fokker—Planck equation for the system can be written down with the help of certain assumptions which are physically realisable. Hence, all useful information concerning the response can be derived.