Date of Award

5-2013

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

Honeycomb structures are widely used in many areas for their material characteristics such as high strength-to-weight ratio, stiffness-to-weight, sound transmission, and other properties. Honeycomb structures are generally constructed from periodically spaced tessellations of unit cells. It can be shown that the effective stiffness and mass properties of honeycomb are controlled by the local geometry and wall thickness of the particular unit cells used. Of particular interest are regular hexagonal (6-sided) honeycomb unit cell geometries which exhibit positive effective Poisson's ratio, and modified 6-sided auxetic honeycomb unit cells with Poisson's ratio which is effectively negative; a property not found in natural materials. One important honeycomb meta-structure is sandwich composites designed with a honeycomb core bonded between two panel layers. By changing the geometry of the repetitive unit cell, and overall depth and material properties of the honeycomb core, sandwich panels with different vibration and acoustic properties can be designed to shift resonant frequencies and improve intensity and Sound Transmission Loss (STL).
In the present work, a honeycomb finite element model based on beam elements is programmed in MATLAB and verified with the commercial finite element software ABAQUS for frequency extraction and direct frequency response analysis. The MATLAB program was used to study the vibration and acoustic properties of different kinds of honeycomb sandwich panels undergoing in-plane loading with different incident pressure wave angles and frequency. Results for the root mean square intensity IRMS based on normal velocity on the transmitted side of the panel measure vibration magnitude are reported for frequencies between 0 and 1000 Hz. The relationship between the sound transmission loss computed with ABAQUS and the inverse of the intensity of surface velocity is established. In the present work it is demonstrated that the general trend between the STL pressure response and the inverted intensity metric have similar response characteristics over both the stiffness frequency region and the resonance frequency region, showing that an increase in IRMS corresponds to a decrease in STL. The ABAQUS model was used to verify the MATLAB program for natural frequencies and mode shapes, and to compute the STL on the top surface of the honeycomb sandwich structure. Resonant peaks in the frequency response of intensity and STL are identified with natural frequencies and mode shapes of the honeycomb sandwich structure.
A unique feature of this research is the ability to apply the time-harmonic acoustic pressure as a load on the transmitting surface of the honeycomb sandwich panel with variable incident angle ranging between 0¡ to 90¡. When the incident angle is nonzero, the pressure load is complex valued, with sinusoidal distribution, and frequency dependent. The finite element implementation of the complex-valued variable incident pressure distribution is programmed in MATLAB to give complete control of the angle, frequency and distribution. Commercial finite element software such as ABAQUS has limited ability to directly apply frequency dependent and distributed real and imaginary pressure distributions in a direct steady state frequency analysis over a large number of frequency evaluations.
In the present work, IRMS results for a family of honeycomb sandwich panels with systematic increment in internal cell wall angle, subject to incremental changes in incident angle pressure loads are studied and compared. Results show that for honeycomb sandwich panels with both positive and negative internal cell wall angle, on average, intensity for the nonzero incident angles is higher than the 0¡normal incident angle. For the honeycomb sandwich panels with positive internal angle, the intensity consistently increases with larger nonzero incident angles. Furthermore, under the same incident angle pressure load, the intensity of honeycomb panel with positive internal angle is consistently larger than honeycomb panels with negative internal angles.

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