Session: 02-05-02: Experimental Studies in Structural Dynamics - II

Paper Number: 107411

107411 - Experimental Validation of Plate Stiffening via Crumpling 

In origami structures, the introduction of folds or creases in a paper (a.k.a. crumpling) endows it with a relatively high flexural stiffness. This is explained mechanically via the higher energy required for the creases to deform and therefore contribute to the global deformation of the paper. Starting from this observation, in this work, we numerically and experimentally validate crumpling methodologies of 3D printable thin plates, namely the ordered (uniform) and disordered (optimal) crumpling. In the first case, it is found that a thin plate that is uniformly creased into a 2D periodic plate with the shallow pyramidal unit cell gains up to 146 % increase in fundamental frequency. Additionally, it is demonstrated that ordered crumpling presents an optimum regarding the discretization of the plate (number of unit cells) and the crumpling height in a mass-fundamental frequency metric plane. In effect, it is observed that the fundamental frequency of a thin crumpled plate corresponds to a local mode when the plate is of pyramidal shape (one unit cell), which morphs to a global mode that has a higher fundamental frequency when the plate is discretized to 2x2-unit cells. The eigenfrequency of the later mode (drum mode) is found to decrease then with the number of unit cells. On the other hand, when the number of unit cells per plate is fixed to 2x2 and the crumpling height is increased, a maximum is achieved at the optimal point in the metric plane. In the case of disordered crumpling, where the creases lines are arbitrary, an optimization problem is formulated to maximize the fundamental frequency under the geometrical and boundary conditions constraints of the plate. Further, a surrogate model of the Finite Element Analysis (FEA) of the plate is established using Artificial Neural Network (ANN) in conjunction with the Genetic Algorithm (GA) to reduce the computational cost of the optimization. In this setting, it is observed that the optimal design presents a 176% (resp. 23%) increase in fundamental frequency compared to the flat (resp. ordered creased) plate, with only a 0.84% increase in total mass. In the second part of this work, the numerical results are examined experimentally via the fabrication and experimental modal analysis (EMA) of crumpled plates of different heights. To this end, 19cm x 19cm plates of 2mm thickness are 3D printed using VeroWhite material and are tested experimentally via a steel frame that holds them vertically on a vibration isolation table. The vibration of the plate is induced via a modal hammer, and its response is measured via a scanning laser Doppler vibrometer (LDV). The eigenfrequencies of the plate are extracted from the plate’s frequency response function (FRF) and compared to that of a flat plate of the same dimensions and constitutive material. In this setting, it is observed that the fundamental frequency of the plate gains up to 126% with the crumpling height, along with an increase of 14% of its mass, for ordered crumpling. It is equally observed that an optimum is achieved for ordered crumpling when the number of unit cells and crumpling heights are varied. Finally, it is proved that the optimal disordered crumpling experiments follow the same trend as their counterparts in numerical simulations.

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

Presenting Author Biography: Dr. Othman Oudghiri-Idrissi is a Postdoctoral Research Fellow at the mechanical engineering department of the University of Michigan, Ann Arbor. He is currently working on the design and development of next generation space structures based on metamaterials. His main research interests include metamaterials/ architected materials, waves in complex media, origami engineering, inverse problems and non-destructive evaluation.

Dr. Othman Oudghiri-Idrissi earned his Ph.D. in Civil Engineering from the University of Minnesota, Twin Cities in 2021. He obtained his M.Sc. in Civil Engineering from École Nationale des Ponts et Chaussées, France in 2016. He earned a Civil Engineering Diploma from École Hassania des Travaux Publics, Morocco in 2015.

Authors:

Othman Oudghiri-Idrissi University of Michigan Ann Arbor
Hrishikesh Danawe University of Michigan, Ann Arbor
Avinkrishnan A. Vijayachandran University of Michigan Ann Arbor
Andrea A. Poli University of Michigan, Ann Arbor
Xiaoming Mao University of Michigan, Ann Arbor
Anthony M. Waas University of Michigan, Ann Arbor
Ellen Arruda University of Michigan, Ann Arbor
Serife Tol University of Michigan, Ann Arbor