Date of Award

8-2012

Document Type

Thesis

Degree Name

Master of Science (MS)

Legacy Department

Mechanical Engineering

Advisor

Thompson, Lonny L

Committee Member

Li , Gang

Committee Member

Daqaq , Mohammed

Abstract

Sandwich panel structures constructed with cellular honeycomb cores allow for control of acoustic performance due to their ability to optimize effective orthotropic material properties with changes in cell geometry. By modification of topology and geometric parameters of a unit cell, desirable effective properties can be obtained and used to design lightweight structures with reduced vibration and increased sound transmission loss properties. Thus investigating the relation between the geometric configuration of the honeycomb core and vibration and acoustic behavior is important to optimize design of sandwich panels.
In this work, a finite element model is developed in MATLAB to evaluate the resonance frequencies, vibration frequency response and structural behavior of general honeycomb sandwich panels undergoing in-plane loading. Bernoulli-Euler beam element stiffness and mass matrices are computed with coordinate transformations to assemble for two-dimensional frame dynamic analysis. The developed MATLAB finite element program is written to allow the user to specify any unit cell geometry together with the number of repeated cells along the longitudinal and transverse direction of a honeycomb sandwich panel. This automation allows for rapid studies of the effects of the cell geometry and number of cells for optimization and parametric studies. In addition, the user can specify the size of elements for cell length subdivision to ensure mesh convergence analysis. The developed MATLAB code was verified by comparing dynamic results to finite element models created using the commercial software ABAQUS using both cubic Bernoulli-Euler and quadratic Timoshenko beam elements. Natural vibration frequencies of the structure and vibration amplitude frequency response for honeycomb structures are computed between 1~1000 Hz, corresponding to low to medium frequency ranges. In addition, the ABAQUS finite element model is used to simulate the acoustic behavior of the sandwich panel mounted in a rigid baffle resulting from an incident plane pressure wave. This required the coupling of an acoustic finite element model tied to the sandwich panel model to model sound radiation from the vibrating panel. To model the infinite acoustic region on one side of the sandwich panel, the acoustic finite element mesh is truncated using a founded ellipse non-reflecting boundary condition (NRBC). Previous studies used a circular nonreflecting boundary condition. The use of an ellipse for the NRBC allows for a reduced size computational region surrounding the elongated sandwich panel structure. The accuracy of the NRBC's was also studied as a function of distance from the vibrating panel source.
Various core configurations of different geometric and effective material properties for regular and auxetic honeycomb cell geometries with two different orthogonal orientations were studied. Constant mass property is applied for sandwich panels with different number of longitudinal and transverse cell numbers to identify the effects of core geometry, cell truncation at face sheets, and effective properties on structural and acoustic behavior. Flexural and local dilatational vibration modes for the various configurations were identified. The influence of natural frequencies on the acoustic performance of the sandwich panels is also studied.

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