Abueidda, Diab

Jasiuk, Iwona

Sobh, Nahil

English

Purdue E-Pubs

Purdue UniversityPurdue e-PubsIUTAM Symposium Architectured MaterialsMechanics Symposium ContributionsSep 17th, 12:00 AM - Sep 19th, 12:00 AMAcoustic Band Gaps, Sound Attenuation, andElastic Stiffness of PMMA Cellular Materials Basedon Triply Periodic Minimal SurfacesDiab AbueiddaUniversity of Illinois at Urbana Champaign, abueidd2@illinois.eduIwona JasiukNahil SobhFollow this and additional works at: https://docs.lib.purdue.edu/iutamPart of the Engineering CommonsThis document has been made available through Purdue e-Pubs, a service of the Purdue University Libraries. Please contact epubs@purdue.edu foradditional information.Recommended CitationAbueidda, D., Jasiuk, I., & Sobh, N. (2018). Acoustic Band Gaps, Sound Attenuation, and Elastic Stiffness of PMMA CellularMaterials Based on Triply Periodic Minimal Surfaces. In T. Siegmund & F. Barthelat (Eds.) Proceedings of the IUTAM SymposiumArchitectured Materials Mechanics, September 17-19, 2018 , Chicago, IL: Purdue University Libraries Scholarly Publishing Services,2018. https://docs.lib.purdue.edu/iutam/presentations/abstracts/1IUTAM Symposium Architectured Material Mechanics,  T. Siegmund, F. Barthelat, eds September 17-19, 2018, Chicago, IL, USA, , Chicago, IL, USA  Acoustic band gaps, sound attenuation, and elastic stiffness of PMMA cellular materials based on triply periodic minimal surfaces Diab W. Abueiddaa,b, Iwona Jasiuka,b, Nahil A. Sobhb a Department of Mechanical Science and Engineering, University of Illinois at Urbana-Champaign, 1206 West Green Street, Urbana, IL 61801-2906, USA, abueidd2@illinois.edu, ijasiuk@illinois.edu, b Beckman Institute for Advanced Science and Technology, University of Illinois at Urbana-Champaign, 405 N Mathews Ave, Urbana, IL 61801, USA, sobh@illinois.edu,  KEYWORDS:  Acoustic band gap, Elastic stiffness, Sound attenuation, Finite element method. The acoustic band structures, sound attenuation, and uniaxial elastic modulus of cellular materials (CMs) based on triply periodic minimal surfaces (TPMS) (see Figure 1) are presented. TPMS are defined as infinitely extending, smooth, and continuous surfaces that are attributed by local area minimizing [1, 2]. In addition, the sum of principal curvatures vanishes at each point on the TPMS; hence, the mean curvature of TPMS is zero. Moreover, TPMS divide the space into two congruent intertwined regions where each region is three-dimensionally (3D) periodic and possesses a volume fraction of 50%.  TPMS cellular materials have an advantage over other cellular materials available in the literature as they overcome the common drawbacks of truss/strut-based structures. Specifically, truss structures induce stress concentrations and usually have imperfections in their joints induced during manufacturing process which in turn cause them to collapse at lower applied loads [3].  Figure 1: TPMS surfaces: (a) Schwarz Primitive surface, (b) Schoen IWP surface, and (c) Neovius surface. In this paper, we investigate computationally responses of three polymeric cellular materials that are based on TPMS. These TPMS include Schwarz Primitive, Schoen IWP, and Neovius surfaces. The studied cellular materials are basically uniformly thickened TPMS where different wall thicknesses lead to different porosities/volume fractions. The finite element method (FEM) is adopted to calculate the acoustic band gaps (their width and location), sound attenuation, and (c) (b) (a) elastic stiffness of these three types of cellular materials. Moreover, the dependence of the band gaps and elastic stiffness on the porosity of the three TPMS cellular materials are investigated where the structures are assumed to be infinite (periodic boundary conditions are applied as shown in the equation below).     (1) where    are the components of Bloch wave vector, and  is the pressure. The eigenfrequencies and eigenmodes are attained through scanning the wave vector in the first irreducible Brillouin zone. The porosities considered in this study range from 28 to 92%. Since the elastic impedance of the cellular solids is higher than that of the air, it is expected that acoustic waves propagating in the air are reflected by the cellular solids and propagation takes place mainly in the air. Complete band gaps are obtained in these structure at low frequencies and low relative densities compared to the cellular structures available in the literature. Cellular material based on Neovius surface shows the highest robustness regarding the acoustic response. Furthermore, sound attenuation for the three TPMS-CMs is calculated along desired directions to verify the band gap analyses. We stack seven unit cells in the desired direction, and then we send an incident wave with a known power. The power at the outlet of the wave guide is calculated to find the transmitted power and sound attenuation.  TPMS-CSs promote complete band gaps, and the width of the band gap increases with the increase of the relative density. The humps appearing in the sound attenuation analysis are in a good agreement with the band gap analysis. The band gaps of TPMS-CSs are wider than the band gaps obtained for other structures mentioned in the literature. Also, all the band gaps obtained for TPMS-CSs lie in the audible range of frequencies.  Thus, TPMS-CSs show very promising acoustic response for use in many engineering applications including noise control. Furthermore, we discuss the variation of the elastic moduli of the three TPMS-CMs with their relative densities. In this paper, we study the elastic moduli for a wide range of relative density where periodic boundary conditions are applied to obtain the effective elastic moduli. Also, cellular materials based on TPMS have a mechanical behavior that is between stretching- and bending-dominated modes for the relative densities considered in this study.   References [1] D.W. Abueidda, M. Bakir, R.K.A. Al-Rub, J.S. Bergström, N.A. Sobh, I. Jasiuk, Mechanical properties of 3D printed polymeric cellular materials with triply periodic minimal surface architectures, Materials & Design, 122 (2017) 255-267. [2] D.W. Abueidda, R.K.A. Al-Rub, A.S. Dalaq, D.-W. Lee, K.A. Khan, I. Jasiuk, Effective conductivities and elastic moduli of novel foams with triply periodic minimal surfaces, Mechanics of Materials, 95 (2016) 102-115. [3] S. Khaderi, V. Deshpande, N. Fleck, The stiffness and strength of the gyroid lattice, International Journal of Solids and Structures, 51 (2014) 3866-3877.  1231 2 3 1 2 31 2 3 1 2 31 2 3 1 2 3( , , ) ( , , )( , , ) ( , , )( , , ) ( , , ) ,ik aik aik ap x a x x p x x x ep x x a x p x x x ep x x x a p x x x e+ =+ =+ =1 2 3( , , )k k k a p

Acoustic Band Gaps, Sound Attenuation, and Elastic Stiffness of PMMA Cellular Materials Based on Triply Periodic Minimal Surfaces

https://docs.lib.purdue.edu/cgi/viewcontent.cgi?article=1000&amp;context=iutam

Acoustic Band Gaps, Sound Attenuation, and Elastic Stiffness of PMMA Cellular Materials Based on Triply Periodic Minimal Surfaces

Abstract

Similar works

Full text

Available Versions

Purdue E-Pubs