NEAR THE RESONANCE BEHAVIOR OF A PERIODICALY FORCED PARTIALLY DISSIPATIVE THREE‐DEGREES‐OF‐FREEDOM MECHANICAL SYSTEM
IN THIS PAPER, A NONLINEAR THREE-DEGREES-OF-FREEDOM DYNAMICAL SYSTEM CONSISTING OF A VARIABLE-LENGTH PENDULUM MASS ATTACHED BY A MASSLESS SPRING TO THE FORCED SLIDER IS INVESTIGATED. NUMERICAL SOLUTION IS PRECEDED BY APPLICATION OF EULER-LAGRANGE EQUATION. VARIOUS TECHNIQUES LIKE TIME HISTORIES, PHASE PLANES, POINCARÉ MAPS AND RESONANCE PLOTS ARE USED TO OBSERVE AND IDENTIFY THE SYSTEM RESPONSES. THE RESULTS SHOW THAT THE VARIABLE-LENGTH SPRING PENDULUM SUSPENDED FROM THE PERIODICALLY FORCED SLIDER CAN EXHIBIT QUASI-PERIODIC, AND IN A RESONANCE STATE, EVEN CHAOTIC MOTIONS. IT WAS CONCLUDED THAT NEAR THE RESONANCE THE INFLUENCE OF COUPLING OF BODIES ON THE SYSTEM DYNAMICS CAN LEAD TO UNPREDICTABLE DYNAMICAL BEHAVIOR
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