TY - JOUR
T1 - Bloch wave framework for structures with nonlocal interactions
T2 - Application to the design of origami acoustic metamaterials
AU - Pratapa, Phanisri P.
AU - Suryanarayana, Phanish
AU - Paulino, Glaucio H.
N1 - Funding Information:
GP and PP acknowledge support from the National Science Foundation (NSF) through grant CMMI 1538830 , and from the endowment provided by the Raymond Allen Jones Chair at the Georgia Institute of Technology. We acknowledge useful interactions with Prof. Katia Bertoldi, which helped us in discovering the presence of bandgaps in 2D homogeneous Miura-ori sheets.
Publisher Copyright:
© 2018 Elsevier Ltd
PY - 2018/9
Y1 - 2018/9
N2 - We present a generalized Bloch wave framework for the dynamic analysis of structures with nonlocal interactions and apply it to the design of origami acoustic metamaterials. Specifically, we first discretize the origami structures using a customized structural bar-and-hinge model that minimizes the degrees of freedom in the associated unit cell, while being sufficiently accurate to capture the behavior of interest. Next, observing that this discretization results in nonlocal structural interactions—the stiffness matrix has nonzeros between nodes that are not nearest neighbors due to the coupled deformations arising during folding or bending—we generalize the standard Bloch wave approach used in structural analysis to enable the study of such systems. Utilizing this framework, choosing the geometry of the unit cell as well as the folded state of the structure as design variables, we design tunable and programmable Miura-ori and eggbox strips, sheets, and composites that are large band, low frequency acoustic switches. In doing so, we find that the number of bandgaps in the sheets is significantly smaller than their strip counterparts and also occur at relatively higher frequencies, a limitation which is overcome by considering composite structures that have individual panels made of different materials. Overall, we have found origami structures to be ideal candidates as acoustic metamaterials for noise control, vibration isolation, impact absorption, and wave guides.
AB - We present a generalized Bloch wave framework for the dynamic analysis of structures with nonlocal interactions and apply it to the design of origami acoustic metamaterials. Specifically, we first discretize the origami structures using a customized structural bar-and-hinge model that minimizes the degrees of freedom in the associated unit cell, while being sufficiently accurate to capture the behavior of interest. Next, observing that this discretization results in nonlocal structural interactions—the stiffness matrix has nonzeros between nodes that are not nearest neighbors due to the coupled deformations arising during folding or bending—we generalize the standard Bloch wave approach used in structural analysis to enable the study of such systems. Utilizing this framework, choosing the geometry of the unit cell as well as the folded state of the structure as design variables, we design tunable and programmable Miura-ori and eggbox strips, sheets, and composites that are large band, low frequency acoustic switches. In doing so, we find that the number of bandgaps in the sheets is significantly smaller than their strip counterparts and also occur at relatively higher frequencies, a limitation which is overcome by considering composite structures that have individual panels made of different materials. Overall, we have found origami structures to be ideal candidates as acoustic metamaterials for noise control, vibration isolation, impact absorption, and wave guides.
KW - Acoustic bandgap
KW - Bloch wave analysis
KW - Eggbox pattern
KW - Mechanical metamaterials
KW - Miura-ori
KW - Origami patterns
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U2 - 10.1016/j.jmps.2018.05.012
DO - 10.1016/j.jmps.2018.05.012
M3 - Article
AN - SCOPUS:85047602118
SN - 0022-5096
VL - 118
SP - 115
EP - 132
JO - Journal of the Mechanics and Physics of Solids
JF - Journal of the Mechanics and Physics of Solids
ER -