Evolution mechanism of motion modality in three-degree-of-freedom flutter for engineering structures with various frequency relationships

Engineering structures suffering from flutter, e.g., long-span bridges, airfoils, cable-supported photovoltaic systems, and bundled conductors, display distinct flutter characteristics due to the different coupling mechanisms affected by the frequency relationships among different degrees of freedom (DOFs). Flutter modality, describing the relative motion relationships between different DOFs, is a fundamental indicator to understand flutter, but its evolution mechanism has long been obscured by numerous interconnected parameters. This study derives explicit analytical expressions for flutter modality, including amplitude ratio and phase difference, of a heaving-lateral-torsional 3DOF system with all frequency relationships. Through quantity order analyses, theoretical conclusions are systematically summarized and intuitively presented. The implications for the design of flutter structures and energy harvesting systems are then discussed. Numerical studies are conducted for validation and detailed illustration. The expressions reveal that the heaving motion contribution is much higher than torsional motion in the close heaving-torsional frequency cases due to significant lift force; special attention is needed in structural safety design and spatial arrangement for such structures. For energy harvesting, the heaving motion is more favorable for extracting energy than the torsional motion due to its higher vibration energy, and the larger phase difference can increase harvesting efficiency. The flutter modality of systems with close heaving-lateral frequencies is highly sensitive to aerodynamic parameters, and the modal vector may span a wide range, posing challenges to structural design. The phase difference magnitude is around 0°, 90°, or 180° for weakly coupled branches and around 45° or 135° for strongly coupled branches involving torsional motion. This study offers a systematic view and new insights into 3DOF flutter modality, serving as a reference in the design and studies of various engineering structures.