When does a Periodic Response Exist in a Periodically Forced\n Multi-Degree-of-Freedom Mechanical System?

2019/07/08 by Thomas Breunung, George Haller, Breunung, Thomas +1
Engineering · Physics and Astronomy · #Bladed Disk Vibration Dynamics #Dynamical Systems (math.DS) #FOS: Mathematics #Force Microscopy Techniques and Applications #Structural Health Monitoring Techniques

paper · pdf · doi:10.48550/arxiv.1907.03605

openalex publication_date 2019/07/08 · openalex created_date 2022/07/20 · openalex updated_date 2026/07/28

Abstract

While periodic responses of periodically forced dissipative nonlinear\nmechanical systems are commonly observed in experiments and numerics, their\nexistence can rarely be concluded in rigorous mathematical terms. This lack of\na priori existence criteria for mechanical systems hinders definitive\nconclusions about periodic orbits from approximate numerical methods, such as\nharmonic balance. In this work, we establish results guaranteeing the existence\nof a periodic response without restricting the amplitude of the forcing or the\nresponse. Our results provide a priori justification for the use of numerical\nmethods for the detection of periodic responses. We illustrate on examples that\neach condition of the existence criterion we discuss is essential.\n

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