Three-dimensional Finite Element Analysis of Sound Transmission Performance of Honeycomb Sandwich Structures

Abstract: Due to the lighter weight of honeycomb structures compared with a cuboid of similar material, honeycomb is widely used in applications requiring a high stiffness to weight ratio. One important honeycomb meta-structure is sandwich composites designed with a honeycomb core between two thin panel layers. The geometry of the honeycomb is formed from periodically spaced, non-overlapping unit cells. An important advantage of cellular materials such as honeycomb is that vibration and acoustic properties can be changed simply by changing the unit cell geometry variables such as included angle, cell wall thickness and length, while keeping the overall dimensions of the structure unchanged. Previous investigators have studied the vibration and sound transmission loss (STL) properties of honeycomb sandwich structures subjected to in-plane loading. In these studies, two-dimensional (2D) finite element models were sufficient to obtain solutions. In the present work, the sound transmission performance of honeycomb for out-of-plane loading is investigated, requiring a complete three-dimensional (3D) structural-acoustics model. In order to obtain efficient finite element solutions for a 3D model, a prolate spheroidal impedance boundary is used to truncate the unbounded acoustic region. The impedance boundary is designed to approximate the far-field acoustic radiation condition and absorb outgoing waves without reflection. The accuracy of this impedance boundary depends on the distance from the sound source, in this case the vibrating honeycomb structure, and frequency. In the present work, a 2D structural-acoustic finite element model with an elliptical non-reflecting impedance boundary is used to provide guidelines for generalization to the 3D model with a prolate spheroidal boundary. The 2D model provides fast STL solutions, for multiple model design evaluations, for selection of the smallest dimension which provides a reduced computational domain, while still maintaining similar accuracy to a circular (spherical) boundary with a much larger distance. Using the 3D finite element modeling procedure developed, natural frequencies and mode shapes are calculated to determine frequency ranges of interest for a steady-state analysis of a honeycomb sandwich panel coupled with the acoustic region subject to a time-harmonic pressure load. The effects of honeycomb unit cell geometry; both positive cell wall (regular) and negative angles (auxetic), on the sound transmission performance are compared. Relationships are observed between the number and frequency locations of peak amplitudes in STL response to the number of positive and negative normal amplitude regions in the mode shapes of the honeycomb structure. It is found that peaks in STL occur only when the number of positive amplitude mode shape regions is different from the number of negative regions. When the numbers of positive and negative amplitude regions are different, the amount of sound transmitted through the honeycomb structure is large. In contrast, when the numbers of positive and negative regions are the same, there is cancellation, and the amount of sound transmission is small (high STL). The first STL peak amplitude always occurs at the first natural frequency with a corresponding mode shape with a single positive or negative region. The second and third peak amplitudes occur at the closely spaced natural frequencies associated with the first pair of mode shapes which have different numbers of positive and negative amplitudes in reversed order. In some cases, even when the numbers of positive and negative regions are unequal, the incomplete shape of one amplitude region partially split into two, results in weaker peak amplitude. Comparing results for auxetic honeycomb cells with negative angles, the frequencies at peak amplitudes are observed to increase as the included angles of the unit cells are increased. For regular honeycombs with positive unit cell angles, the differences in the STL curves are small, and the width between the 2nd and 3rd peaks increases as the included angle of the cell is increased. Also, the average frequencies between the second and third peaks are similar for each of the regular honeycomb unit cell geometries, a property not observed for the auxetic honeycombs.