Session: 01-01-04: Elastic and Acoustic Metamaterial

Paper Number: 99559

99559 - Experimental Investigation of 3d Printed Viscoelastic Metamaterials 

We numerically and experimentally investigate the static and dynamic properties of novel designs of 3D printed viscoelastic metamaterial beams. We first examine the complex-valued Bloch dispersion relationship of the different periodic beam designs using two complementary formulations, known as the ω(k) and k(ω) formulations, to characterize the temporal and spatial damping of the beams, respectively and identify their band gap properties. For a Bloch wavenumber k, the ω(k) formulation results in a nonlinear eigenvalue problem (NLEP) over the unit cell that admits a complex-valued sequence of eigenfrequencies, whose imaginary parts determine the (temporal) damping ratios of the corresponding Bloch eigenmode.  Conversely, for a frequency ω, the k(ω) formulation results in a guadratic eigenvalue problem (QEP) over the unit cell that admits a complex-valued sequence of wavenumbers, whose imaginary parts quantify the spatial attenuation rate of the Bloch eigenmode. We consolidate the later damping characterization frameworks by investigating the natural frequencies and corresponding damping ratios of the periodic beam designs via finite element analysis (FEA) and experimental modal analysis (EMA) using a modal hammer actuator and a scanning laser Doppler vibrometer (LDV) sensing system. In these settings, we consider (i) three cylindrical phononic crystal (PC) beam designs that contain a periodic distribution of twisted viscoelastic inclusions, (ii) one periodic tetra-chiral metamaterial (TCM) beam design whose unit cell has a tetra-chiral geometry that is internally coated via a viscoelastic material, and (iii) one periodic PC beam with parallelepipedal inclusions that is used as a reference for the TCM beam study. We use VeroClear as the backbone material for the PC and TCM beams and use Agilus30 or TangoBlack Plus as the viscoelastic material for the inclusions or coating materials.  In the static regime, we assess the bending stiffness of the PC and TCM beam 3D printed samples in a cantilever setup, identify the stiffest cylindrical PC beam design and demonstrate that the TCM beam design has higher stiffness compared to the reference PC beam design. In the dynamic regime, (i) we find that using TangoBlack Plus (vs. Agilus30) as the inclusion (resp. coating) material for the PC (resp. TCM) beams results in higher (spatial and temporal) damping properties and larger band gaps of the beams, (ii) we numerically verify that the obtained spatial attenuation rate via the k(ω) formulation predicts well the beam’s vanishing response within the first flexural band gap, (iii) we find that the extracted natural frequencies and damping ratios of the PC and TCM beams from the EMA match well with their numerically evaluated counterpart, (iv) we demonstrate that the TCM beam design has globally higher damping properties compared to the baseline PC beam and (v) we prove how a particular twisting of the PC beam inclusion results in a neatly superior stiffness and damping properties compared to the other PC beams. The optimal PC and TCM beam designs have direct relevance to the design of high-precision, metadamped, and light-weight space structures.

Presenting Author: Othman Oudghiri-Idrissi University of Michigan Ann Arbor

Presenting Author Biography: Dr. Othman Oudghiri-Idrissi is currently a postdoctoral research fellow at the mechanical engineering department of the University of Michigan Ann Arbor. His research areas include dynamic homogenization of periodic structures, waves in complex media, origami engineering, inverse problems and non-destructive testing. His current research focuses on the design of metamaterials for space structures. <br/><br/>Dr. Oudghiri-Idrissi received his Engineering Diploma in Civil Engineering from Ecole Hassania des Travaux Publics, Morocco and his M.Sc. in Geotechnical Engineering from Ecole des Ponts ParisTech, France in 2016. He received his Ph.D. in Civil Engineering from University of Minnesota Twin Cities in 2022.

Authors:

Othman Oudghiri-Idrissi University of Michigan Ann Arbor
Hrishikesh Danawe University of Michigan Ann Arbor
Wei-Chun Lu University of Michigan Ann Arbor
Serife Tol University of Michigan Ann Arbor