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Daniel Guggenheim School of Aerospace Engineering
Daniel Guggenheim School of Aerospace Engineering
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ItemA Sliding-Window Matrix Pencil Method for Aeroelastic Design Optimization with Limit-Cycle Oscillation Constraints(Georgia Institute of Technology, 2023-12-15) Golla, TarunThis paper presents a new approach for constraining limit-cycle oscillations in aeroelastic design optimization. The approach builds on a gradient-oriented limit-cycle oscillation constraint that bounds the recovery rate to equilibrium, bypassing the need for bifurcation diagrams. Previous work demonstrated the constraint using recovery rates approximated via a conservative approach. This work introduces a new approach to accurately evaluate recovery rates from transient simulations. The approach uses the matrix pencil method within a time window that slides along the time history for the quantity of interest, allowing this damping identification method to resolve amplitude-variant nonlinear effects. The new sliding-window matrix pencil method is verified with reference recovery rates from envelope finite differencing of the dynamic responses induced with a large initial perturbation of a typical aeroelastic section. Sensitivity analyses identify optimal parameters to obtain accurate recovery rates while minimizing computational costs. The new developments are then demonstrated by optimizing the typical section subject to the proposed limit-cycle oscillation constraint along with flutter and side constraints. The results are compared with previous work that solved the same optimization problem by evaluating the limit-cycle oscillation constraint using approximate recovery rates. The limit-cycle oscillation constraint based on the new sliding-window matrix pencil method allows the optimizer to achieve a less conservative design solution while satisfying the constraints. This methodology was additionally extended through the optimization of a more complex 3-variable optimization. The implementation was further ported into a modular framework within which results were verified, allowing for future extensions to this methodology. This work is anticipated to pave the way for larger-scale aeroelastic design optimizations subject to limit-cycle oscillation constraints.
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ItemA Sliding-Window Matrix Pencil Method for Aeroelastic Design Optimization with Limit-Cycle Oscillation Constraints(Georgia Institute of Technology, 2023-12-13) Golla, TarunThis thesis presents a new approach to constraining limit-cycle oscillations (LCOs) in aeroelastic design optimization. LCOs are self-excited oscillations that can develop in nonlinear aeroelastic systems experiencing flutter, and they must be avoided during operation to keep safety and performance. One approach to addressing this problem is to design the system using an optimization process that includes an LCO constraint. Previous efforts have proposed various LCO constraints for aeroelastic design optimization but have not addressed realistic design applications. This gap persists because existing LCO constraints are not oriented toward scalable gradient-based optimization algorithms. The proposed approach builds on a recent LCO constraint that bounds the recovery rate to equilibrium and is suited to gradient-based optimization. The new contribution from this thesis consists of introducing a new matrix pencil method for accurately evaluating the recovery rate within the LCO constraint using output data from transient responses. The amplitude-varying behavior of the recovery rate in the presence of dynamic nonlinearities is captured using a sliding time window along the transient response for a chosen quantity of interest. This new approach differs from the conventional matrix pencil method, which considers an entire transient response at once under linearized assumptions. Sensitivity studies are conducted to identify the optimal singular-value decomposition tolerance, sliding window size, stride size, output data sampling step, and aggregation parameters for obtaining accurate results. The new sliding-window matrix pencil method is then used to optimize a typical aeroelastic section model with a subcritical LCO behavior, enforcing no flutter or LCOs at chosen operation conditions. Optimization results are compared with previous work that used the same LCO constraint formulation combined with an approximate, conservative method to evaluate the recovery rate. The LCO constraint evaluated using the new sliding-window matrix pencil method allows the optimizer to completely suppress subcritical LCOs within the specified operating conditions while minimizing design changes, achieving a less conservative optimized solution. This work is a step toward constraining LCOs in large-scale aeroelastic design optimization to enable higher-performance designs while avoiding undesirable dynamics, such as subcritical LCOs. Future work includes formulating adjoint derivatives of the LCO constraint and demonstrating the methodology for aeroelastic models of increasing physical and computational complexity.