Gust Buffeting and Aerodynamic Admittance of Structures with Arbitrary Mode Shapes. II: A POD-Based Interpretation

Studies carried out on gust buffeting and aerodynamic admittance show that mode shape represents a sort of watershed. If the mode does not change sign along the structure axis, the problem admits a robust conceptual interpretation based on energy cascade and a simple closed-form solution. If, instead, the mode changes sign, the solution calls for numerical tools, and its physical interpretation definitely is unclear. The companion paper investigated this issue within the novel framework of the enhanced equivalent spectrum technique and derived a closed-form solution of the aerodynamic admittance that can be applied to any mode using quasi-steady theory. This solution is precise and simple for modes with a few changes of sign, but it becomes laborious with increasing mode shape complexity; in addition, it provides a partial conceptual interpretation. Both these limitations were overcome in this paper, in which the application of proper orthogonal decomposition led to a full conceptual interpretation of aerodynamic admittance and to a simple and general closed-form solution. Analyses were limited here to single modes; multiple arbitrary modes are left for future research, as is the generalization of these concepts to arbitrary influence functions.

Automated summary

Studies have shown that mode shape plays a significant role in determining the type of solution for gust buffeting and aerodynamic admittance problems. A simple closed-form solution is possible if the mode does not change sign, while a numerical approach is required if the mode changes sign. Proper orthogonal decomposition can provide a full conceptual interpretation and a simple closed-form solution for these problems.