A study is made of the free and forced oscillations in dynamicsystems with hysteresis, on the basis of a piecewise-linear, nonlinearmodel proposed by Reid. The existence, uniqueness, boundednessand periodicity of the solutions for a single degree of freedomsystem are established under appropriate conditions using topologicalmethods and Brouwer's fixed-point theorem. Exact periodic solutionsof a specified symmetry class are obtained and their stability is alsoexamined. Approximate solutions have been derived by the Krylov-Bogoliubov-Van der Polmethod and comparison is made with the exact solutions.
For dynamic systems with several degrees of freedom, consistingof "Reid oscillators", exact periodic solutions are derived undercertain restricted forms of "modal excitation" and the stability of theperiodic solutions has been studied. For a slightly more general formof sinusodial excitation, a simple way of obtaining approximate solutionsby "apparent superposition" has been indicated. Examples arepresented on the exact and approximate periodic solutions in a dynamicsystem with two degrees of freedom.
