Gust Buffeting and Aerodynamic Admittance of Structures with Arbitrary Mode Shapes. I: Enhanced Equivalent Spectrum Technique

The loading and response of structures due to gust buffeting is a dominant topic of wind engineering. One of its crucial aspects is the shape of vibration modes. Although numeric solutions are available for any mode, conceptual interpretations and closed-form solutions mainly are limited to the case in which the sign of the mode does not change along the structural axis. For modes that change sign, it is difficult, if not impossible, to recognize the physical role of the parameters that govern the problem and judge analysis results in qualitative form. This paper addressed this issue in the framework of quasi-steady theory by clarifying the relationship linking aerodynamic admittance with mode shape, showed that any mode may be brought back to a piecewise ensemble of regular modes with constant sign, and used this concept to obtain a closed-form expression for any aerodynamic admittance. This solution is simple for modes with few changes of sign, but becomes laborious as mode complexity increases. In addition, it provides a partial conceptual interpretation. Both of these limits were overcome in the companion paper, in which the use of proper orthogonal decomposition led to a full conceptual interpretation of aerodynamic admittance and a simple and general closed-form solution.