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Dynamic Condensation for Efficient Band-Structure Calculations of 2D Periodic Structures

AIAA JOURNAL 2025年第2期63卷 439-452页

作者： Hagos, Robel Weldebrhan Han, Jae-Hung Korea Adv Inst Sci & Technol Smart Struct & Hardware Syst Lab Dept Aerosp Engn Daejeon 34141 South Korea

Efficient band-structure calculations are essential for understanding the mechanical behaviors of periodic materials, with significant implications in material design and phononic engineering. This paper introduces the application of the improved reduced system (IRS) technique to expedite elastic band-structure calculations. The IRS, a dynamic condensation method, partitions the unit cell degrees of freedom (DOFs) into primary and secondary sets. A strategic selection of primary DOFs retains a subset of interior DOFs alongside all exterior DOFs while truncating the remaining interior DOFs. The integration of IRS with the Craig-Bampton method for additional reduction and the imposition of Bloch boundary conditions yields a notable decrease in computational overhead. Additionally, for structures with a high number of interior DOFs, a substructuring scheme can be implemented to further enhance efficiency. This approach offers a compelling combination of accuracy and expedited computation, making it applicable across diverse periodic materials.

关键词： Finite Element Method structural dynamics and characterization Quasiparticles Metamaterials Wavenumber Computing and Informatics Phononic Engineering Dynamic Condensation Band Structure Periodic Structure

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Guaranteed Cost Gain-Scheduled Control of Typical Aeroelastic Section Model

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JOURNAL OF GUIDANCE CONTROL AND dynamics 2025年第3期48卷 714-722页

作者： Pereira, Renan L. Gonzalez, Pedro J. Silvestre, Flavio J. Aeronaut Inst Technol Elect Engn Div BR-12228900 Sao Jose Dos Campos Brazil Tech Univ Berlin Flight Control & Aeroelast FMRA D-10587 Berlin Germany Tech Univ Berlin Flight Control & Aeroelast FMRA Marchstr 12 D-10587 Berlin Germany

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Parametric Investigation of Vibratory Responses for Reduced-Order Models of Rotating Bladed Disks

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AIAA JOURNAL 2023年第4期61卷 1839-1848页

作者： Kurstak, Eric D'Souza, Kiran Ohio State Univ Dept Mech & Aeronaut Engn Gas Turbine Lab Columbus OH 43210 USA

Attempting to predict the physical response of a complex system under realistic conditions is extremely challenging. In this work, a parametric reduced-order model (PROM) of a bladed disk is briefly presented that allows for the quick and efficient modeling of rotational speed effects and mistuning effects in bladed disks. This computational model is tuned to match experimental data. The tuned PROM is then investigated through a parametric study. Three internal parameters investigated are i) forcing magnitude, ii) mistuning value magnitude, and iii) damping magnitude, and four external parameters are iv) forcing location, v) forcing radius, vi) probe placement error, and vii) arrival time error. These parameters are common in the structural analysis of turbomachines. Each internal parameter is increased and decreased by 10, 20, and 50%, while external parameters are changed by varying amounts due to geometric and practical limitations. The model is time integrated to simulate the conditions present in the experimental test rig. The maximum blade amplitudes are then compared to the baseline case and analyzed. The damping, followed by the forcing, is shown to cause the greatest impact on the final system response. This indicates a greater need to accurately measure the damping compared to other parameters.

关键词： Turbomachinery structural Analysis Finite Element Modeling Mechanical and structural Vibrations structural dynamics and characterization Singular Value Decomposition Gas Turbine Finite Element Software Compressor Blades

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Fixed- and Free-Mode Flutter Derivatives During Aeroelastic Optimization

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AIAA JOURNAL 2024年第12期62卷 4645-4653页

作者： Stanford, Bret K. Thelen, Andrew S. Jacobson, Kevin E. NASA Langley Res Ctr Aeroelasticity Branch Res Aerosp Engineer Hampton VA 23681 USA

Aeroelastic flutter design derivatives may be approximated by ignoring the sensitivity of the structural mode shapes. This fixed-mode derivative is less expensive to compute than the exact free-mode derivative (which accommodates the mode shape dependency) but also may provide inaccurate sensitivities for optimization. This work formulates both fixed- and free-mode flutter derivatives and demonstrates the conditions under which they are equivalent. Two different types of fixed-mode derivatives are also developed in this work. Using a cantilevered-plate demonstration problem with both shape and sizing design parameters, the accuracy of the free-mode derivative and the two fixed-mode derivatives is demonstrated via gradient-based optimization.

关键词： High Aspect Ratio Finite Element Analysis Low Aspect Ratio Wings structural dynamics and characterization Aerodynamic Force Aircraft Design Software Computational Fluid dynamics Subsonic Flow Aircraft Wing Design Computing and Informatics

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Mistuning Identification of Blisks Using Mass Detuning and Influence Coefficients

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AIAA JOURNAL 2023年第8期61卷 3682-3691页

作者： Cimpuieru, Mihai Kelly, Sean T. T. Lupini, Andrea Keener, Christopher D'Souza, Kiran Epureanu, Bogdan I. I. Univ Michigan Dept Mech Engn Ann Arbor MI 48109 USA Ohio State Univ Dept Mech & Aeronaut Engn Columbus OH 43210 USA

Integrally bladed disks, also known as blisks, are important components in the operation of gas turbines. To study the dynamics of these structures, several computational techniques approximate blisks as tuned systems, where all blades have the same characteristics. In reality, manufactured blades have small variations from their intended design, thus creating so-called mistuned systems. Previous work has shown that such small variations can cause high response amplifications that can result in blisk structural failure. Therefore, it is essential to identify mistuning to ensure the safe operation of these systems. Several methods utilize cantilever blade frequencies in their procedure to model mistuning and calculate blisk vibration response. A previously developed mistuning identification method uses mass detuning to isolate the cantilever blade frequencies and a set of influence coefficients to quantify the blade-to-blade couplings. However, the mistuning is calculated with respect to an arbitrary mistuning value that later needs to be identified through a trial-and-error procedure that can affect the accuracy of the final mistuning values. This paper focuses on updating the method to eliminate this additive error that cannot precisely be determined. Furthermore, the updated procedure is applied to an as-manufactured blisk using experimental ping test results. An additional analysis is performed on the effect of adding multiple sets of influence coefficients to capture the blade-to-blade couplings more accurately.

关键词： Gas Turbine Mechanical Properties Computing and Informatics structural dynamics Nonlinear dynamics Turbomachinery Modal Analysis Aircraft Engines Vibration Isolation structural dynamics and characterization

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High-Fidelity Gradient-Based Wing structural Optimization Including Geometrically Nonlinear Flutter Constraint

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AIAA JOURNAL 2023年第7期61卷 3045-3061页

作者： Jonsson, Eirikur Riso, Cristina Monteiro, Bernardo Bahia Gray, Alasdair C. Martins, Joaquim R. R. A. Cesnik, Carlos E. S. Univ Michigan Dept Aerosp Engn 1320 Beal Ave Ann Arbor MI 48109 USA Univ Michigan Ann Arbor MI 48109 USA Georgia Inst Technol Daniel Guggenheim Sch Aerosp Engn 275 Ferst Dr Northwest Atlanta GA USA

Lightweight high-aspect-ratio wings make aircraft more energy efficient thanks to their lower induced drag. Because such wings exhibit large deflections, design optimization based on linear flutter analysis of the wing undeformed shape is inadequate. To address this issue, we develop a framework for integrating a geometrically nonlinear flutter constraint, which considers in-flight deflections, into a high-fidelity gradient-based structural optimization. The wing mass and stress constraints are evaluated on a linear built-up (detailed) finite element model to capture realistic structural features. The geometrically nonlinear flutter constraint is based on a condensed low-order beam representation of the built-up finite element model, which captures the impact of in-flight deflections with tractable computational effort for optimization. The flutter constraint is differentiated with respect to the detailed structural model sizing variables using the adjoint method to enable large-scale optimizations. The framework is demonstrated by minimizing the mass of a wingbox model subject to the geometrically nonlinear flutter constraint along with stress and adjacency constraints. The geometrically nonlinear flutter constraint adds a penalty of up to 60% of the baseline mass due to the impact of in-flight deflections on the flutter onset speed and its mechanism. In contrast, a linear flutter constraint evaluated on the undeformed wing adds a mass penalty of only 10%. This methodology can help design energy-efficient aircraft with high-aspect-ratio wings, which require geometrically nonlinear flutter analyses early in the design cycle.

关键词： structural Design and Development Finite Element Modeling structural dynamics and characterization Aircraft Components and Structure Nonlinear Aeroelastic Systems Aircraft Wing Design structural Optimization Flutter Analysis Nonlinear structural dynamics Dynamic Aeroelasticity

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Sharp Bounds for Natural Frequencies of Beams with Uncertain Spring Coefficients

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AIAA JOURNAL 2023年第10期61卷 4623-4631页

作者： Elishakoff, Isaac Ducreux, Baptiste Yvain, Nicolas Florida Atlantic Univ Dept Ocean & Mech Engn Boca Raton FL 33431 USA French Inst Adv Mech F-63170 Clermont Ferrand France SIGMA Clermont 27 Rue Roche Genes F-63170 Aubiere France

In this paper, we deal with both the static and dynamic behavior of uniform beams with uncertain boundary conditions. Uncertainty in spring constants is modeled as intervals, with specified lower and upper bounds. It is demonstrated that the classical interval analysis may lead to overestimation in the natural frequencies. A method is suggested to overcome the overestimation and obtain sharp bounds.

关键词： Mechanical and structural Vibrations Simply Supported Beams Mechanical Properties Rayleigh Ritz Method structural dynamics and characterization Frequency Response Functions structural Health Monitoring Monte Carlo Simulation Aircraft Wing Design Computer Programming and Language

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Enhanced Multimodal Nonparametric Probabilistic Method for Model-Form Uncertainty Quantification and Digital Twinning

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AIAA JOURNAL 2024年第11期62卷 4265-4279页

作者： Azzi, Marie Jose Farhat, Charbel Stanford Univ Dept Mech Engn 440 Escondido Mall Stanford CA 94305 USA Stanford Univ Dept Aeronaut & Astronaut Aircraft Struct Durand BldgRoom 257 Stanford CA USA Stanford Univ Inst Computat & Math Engn Durand Bldg Room 257 Stanford CA USA

The nonparametric probabilistic method (NPM) is a physics-based machine learning approach for model-form (MF) uncertainty quantification (UQ), model updating, and digital twinning. It extracts from reference data information not captured by a real-time computational model and infuses it into a "hyperparameterized," stochastic version of this model by solving an inverse statistical problem formulated using a loss function and a few hyperparameters. The loss function is designed such that the mean value and statistical fluctuations of some quantities of interest predicted using the real-time stochastic model match target values obtained from the reference data. NPM's performance hinges upon the efficient minimization of the loss function, which is unfortunately stochastic and nonconvex and thus prone to getting the optimization procedure trapped in suboptimal local minima. The latter scenario is exacerbated when the reference data is scarce. The paper addresses these issues by adopting the squared quadratic Wasserstein distance as the measure of dissimilarity between two different sets of data and by reformulating NPM's inverse statistical problem as a multimodal data-assimilation problem. The potential of the resulting enhanced NPM for MF-UQ, model updating, and digital twinning is demonstrated using numerical simulations relevant to applications in structural dynamics, including structural health monitoring.

关键词： structural dynamics and characterization structural Health Monitoring Machine Learning Cumulative Distribution Function Uncertainty Quantification Digital Twins Probabilistic Methods Model Updating Damage Detection Inverse Problems

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Aeroelastic Analysis of Highly Flexible Wings with Linearized Frequency-Domain Aerodynamics

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JOURNAL OF AIRCRAFT 2024年第2期61卷 365-374页

作者： Stanford, Bret K. Jacobson, Kevin E. Chwalowski, Pawel NASA Langley Res Ctr Hampton VA 23681 USA

Aeroelastic flutter analysis of configurations with geometric structural nonlinearities typically is done with time-domain analysis. The results from this process are computationally expensive and can yield cumbersome results that may be difficult to manage and interpret. Compared to time-domain methods, frequency-domain flutter analysis can provide additional insight into the characteristics of a flutter instability. By linearizing the aeroelastic problem about the nonlinear equilibrium state, this work applies frequency-domain aeroelastic analysis to the Pazy wing, the subject of the Large Deformation Working Group in the Aeroelastic Prediction Workshop. Generalized aerodynamic forces (GAFs) are computed with both a doublet-lattice method and a computational fluid dynamics solver at a range of reduced frequencies as well as a range of dynamic pressures to account for the dependence of the mode shapes on the nonlinear equilibrium state. These GAFs are used in a p-k flutter solver, which is modified to handle the nonlinear dependence of the stiffness matrix and GAFs on the dynamic pressure. The hump mode flutter mechanism predicted by the linear doublet-lattice method is found to underpredict the severity of the instability, relative to the computational fluid dynamics-based tool, though the overall static and dynamic aeroelastic mechanisms predicted by the two fidelities are similar.

关键词： Dynamic Aeroelastic Analysis Time Domain Analysis Aerodynamic Force Aircraft Wing Design structural dynamics and characterization Pressure Coefficient Influence Coefficients Computational Fluid dynamics structural Nonlinearities CFD Codes

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Noise and Jet Momentum of Synthetic Jet Actuators with Different Orifice Configurations

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AIAA JOURNAL 2024年第2期62卷 668-676页

作者： Arafa, Nadim Sullivan, Pierre Ekmekci, Alis Sheridan Coll Mech & Elect Engn Technol Sch Brampton ON L6Y 5H9 Canada Univ Toronto Mech & Ind Engn Dept Toronto ON M5S 3G8 Canada Univ Toronto Inst Aerosp Studies Toronto ON M5S 3G8 Canada

Sound pressure levels and flow characteristics of a synthetic jet actuator (SJA) are investigated experimentally using the following orifice configurations: a) a slender rectangular slot orifice and b) an array of circular orifices with two different orifice diameters. All configurations have similar total orifice neck area, orifice height, and cavity volume, resulting in a similar Helmholtz frequency. Experiments are conducted for orifices mounted on a flat plate under a quiescent condition. The mean jet velocity exhibits resonant peaks at several excitation frequencies, which also gave rise to the sound pressure levels. The resonant frequencies and peak jet velocities were found to depend on the excitation amplitude and orifice configuration. Investigation of the jet momentum penetration into the quiescent air above the different orifice configurations shows that the momentum issuing from the rectangular slot decays much quicker than that of the circular orifices, irrespective of whether the SJA is excited at resonance or not. The most favorable performance (i.e., the highest momentum in the jet core) was obtained with the array of circular orifices having a smaller orifice diameter, even at off-resonance excitations. The work herein shows the possibility of reducing the SJA noise by 8-10 dB by operating the SJA at a frequency away from the Helmholtz frequency while still achieving comparable levels of jet momentum penetration into the crossflow.

关键词： Adverse Pressure Gradient Actuators Overall Sound Pressure Level Mechanical and structural Vibrations Fluid Flow Properties High Aspect Ratio Vortex dynamics Acoustic Measurement structural dynamics and characterization

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