Tracking Nonlinear Vibration Phenomena
Justin Porter, Rice University
Modern engineering structures for aerospace and energy generation are highly optimized requiring the consideration of nonlinear vibration phenomena. For instance, bolted joints are essential for large structures that are impractical or cost prohibitive to build as a single component. However, the friction introduced through jointed connections results in nonlinear vibration phenomena. Accurately characterizing vibration amplitudes and frequencies is essential to predicting the reliability and longevity of structures. Large unexpected vibrations can cause immediate failures or reduce the operating lifetime of structures. The present work considers superharmonic resonances of nonlinear vibrating systems. Superharmonic resonances occur when harmonics of the motion at an integer multiple of the forcing frequency respond with high amplitudes (e.g., on the order of the amplitude of the harmonic of the motion at the forcing frequency) resulting in potential failure of structures. Such phenomena do not occur in linear systems where the motion only occurs at the same frequency as the external forcing. Characterizing the responses of the higher harmonics is important for understanding potential failure points for nonlinear structures. The present work develops a method of tracking such nonlinear vibrations to reduce the required computational cost. Specifically, the tracking method only requires calculation of a single solution per forcing level compared to traditional methods that require calculation of many solutions at different forcing frequencies for each forcing amplitude. For the considered systems, the proposed method can identify key behavior up to 230 times faster than traditional methods. The developed method enables ongoing work considering larger structures utilizing computational models that require high performance computing. Utilizing better computational tools for nonlinear vibration has the potential to reduce the billions of dollars spent annually on vibration testing.
Abstract Author(s): Justin H. Porter and Matthew R. W. Brake