Date of Award

12-2012

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering

Advisor

Thompson, Lonny L

Committee Member

Summers, Joshua D

Committee Member

Fadel, Georges M

Abstract

Cellular materials with macro effective properties defined by repeated meso-structures are increasingly replacing conventional homogeneous materials due to their high strength to weight ratio, and controllable effective mechanical properties, such as negative Poisson's ratio and tailored orthotropic elastic properties. Honeycomb structures are a well-known cellular material that has been used extensively in aerospace and other industries where the premium on the weight reduction with high-strength is required. Common applications of honeycomb cellular structures are their use as the core material in sandwich plates and plates between two face sheets. Honeycomb structures are built from repetition of a common hexagonal unit cell tessellation defined by four independent geometric parameters; the hexagonal unit cell side lengths, h, and l, cell wall thickness, t and orientation of the angle between the cell walls . These parameters can be controlled to achieve desirable effective properties.
Another important application of honeycomb sandwich structures is the ability to adjust the unit cell geometric parameters to increase the Sound Transmission Loss (STL); a metric for measurement of noise cancellation for acoustic waves passing though the panel structure, while maintaining a low mass, and controllable effective stiffness and strength properties. Previous research has been limited to parametric studies exploring the effect of change in a single unit cell parameter on the Sound Transmission Loss (STL). To obtain an optimal STL result and to determine sensitivities, the present work presents a novel technique to control all four of the unit cell parameters while maintaining constant overall dimensions and mass of the honeycomb sandwich plate. These two constraints are necessary to ascertain that the high STL occurs only due to the change in geometric properties of honeycomb unit cell, as the STL increases with increase in mass and change in overall dimensions.
An optimization problem has been set-up with the design variables as hexagonal interior angle, number of unit cells in the horizontal direction, and number of unit cells in the vertical direction for a representative plate model with in-plane acoustic pressure wave transmission analysis. These variables indirectly control the other unit cell lengths and cell-wall thickness parameters while satisfying the aforementioned constraints. All three of the design variables are restricted to integers to ensure the resulting geometry is regular and manufacturable. The STL response is optimized over a frequency range of 200-400 Hz, within a typical resonance region of the frequency response function. The goal of the optimization is to maximize the area under the STL curve over the frequency range of interest, with constraints on fixed mass and overall plate dimensions.
The optimization process required a complete design automation workflow of geometry creation based on changes in number of cells, constraints on overall dimensions and mass, output results extraction, construction of response surface to expedite the optimization using genetic algorithms. The process involved a coupled structural-acoustic finite element model with direct steady-state analysis and natural frequency extraction created and solved using the commercial finite element software package ABAQUS. The model is used to obtain acoustic pressure values for calculation of the STL of the honeycomb sandwich plate. Quadratic Timoshenko beam elements have been used to discretize the thin-walled honeycomb cellular structures for increased accuracy at higher frequencies. The elastic structure model is coupled with acoustic elements by applying surface based tie-constraints to transfer normal plate surface accelerations as input to calculate radiated sound pressure. The entire process of finite element model creation and solution has been parameterized and automated by extensive use of Python scripts directly interfaced with the ABAQUS solver. A detailed workflow has been set-up in the optimization package modeFRONTIER that generates the input variables using a genetic algorithm, NSGA-II, controls the Python scripts to create and solve the finite element Abaqus model, calls the Python scripts to extract results for post-processing needed to generate the STL vs. Frequency plots and finally optimizes the geometric unit cell parameters to maximize STL over a typical frequency range, all while respecting constraints on overall dimensions and mass. The frequency range from 200 Hz to 400 Hz was used to demonstrate the design automation and optimization process developed. The same workflow can be used to optimize STL for other frequency ranges.
To speed-up the optimization process, approximation functions have been generated utilizing the Response Surface Methodology (RSM) in modeFRONTIER. The Shepherd K-Nearest algorithm was found to be the most accurate of five alternative RSM functions considered. It has been shown that interpolation with this function accurately predicts the output with less than 1% error and significantly speeds up the optimization process compared to a complete finite element solution at each iteration.
Results of the optimization process show that although a single design with the highest STL measure was found, in general, the designs with less than-25o , number of horizontal cells greater than 60 and the ratio of unit cell lengths h/lgreater than 1 also give relatively high STL values over the frequency range studied. The designs with the highest STL measure show close to 70 % improvement over the designs with the lowest measured STL. Design trends have also been observed for the stiffness properties of honeycomb core. The designs with highest value of STL have low and in comparison to the designs with the lowest STL. However the is high for designs with high STL and low for designs with low STL.
To determine the most important design variables affecting STL results a sensitivity analysis has been conducted using the Pareto-chart of standardized effects. The results indicate that all the three design variables have a significant impact on the output. The significance in the descending order is the number of vertical cells, the number of horizontal cells and the unit cell wall orientation . This result is noteworthy given that was the only design variable considered for the parametric studies conducted previously.

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