IRREGULAR VIBRATIONS IN MULTI-MASS DISCRETE-CONTINUOUS SYSTEMS TORSIONALLY DEFORMED

Abstract

IN THE PAPER IRREGULAR VIBRATIONS OF DISCRETE-CONTINUOUS SYSTEMS CONSISTING OF AN ARBITRARY NUMBER RIGID BODIES CONNECTED BY SHAFTS TORSIONALLY DEFORMED ARE STUDIED. IN THE SYSTEMS A LOCAL NONLINEARITY DESCRIBED BY THE POLYNOMIAL OF THE THIRD DEGREE IS INTRODUCED. IT IS ASSUMED THAT THE CHARACTERISTIC OF THE LOCAL NONLINEARITY IS OF A HARD TYPE. GOVERNING EQUATIONS ARE SOLVED USING THE WAVE APPROACH LEADING TO EQUATIONS WITH A RETARDED ARGUMENT. EXEMPLARY NUMERICAL CALCULATIONS ARE DONE FOR THE THREE-MASS SYSTEM. THE POSSIBILITY OF OCCURRING OF IRREGULAR VIBRATIONS IS DISCUSSED ON THE BASIS OF THE POINCARÉ MAPS, BIFURCATIONS DIAGRAMS AND THE EXPONENTS OF LYAPUNOV.