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I am pursuing my PhD under the mentorship of Prof. Phanisri Pradeep Pratapa.
We aspire to design reconfigurable smart structural systems with previously unforeseen potential functionalities. Our work is inspired by the recent advances in research and exciting applications pertaining to:
Mechanical meta-materials
Origami engineering
Wave-guides and Vibration control
A meta-material is an artificial system architected to exhibit properties not found in naturally occurring materials.
Mechanical metamaterials are periodic structures created by repetitions of a structural building block (unit cell), where the mechanical properties of the lattice at the macro scale are governed by the geometry of the unit cell, not the microstructure of the base material.
Acoustic metamaterials are a class of such systems that display novel dynamic behavior. Bandgaps represent frequency ranges in which waves cannot propagate through a metamaterial lattice. Presence of elastic bandgaps in a metamaterial would make it an ideal choice for design of wave guides, acoustic cloaks and a range of vibration control devices.
The principles of Origami, an ancient Japanese art of folding paper, enable folding of flat sheets into complex 3D shapes. Origami is inspiring innovations across the spectrum of science and technology. The recent surge in scientific advances stems from the strong mathematical foundation that origami provides for geometric mechanics to create systems that transcend seamlessly from the realm of paper into the world of metal and plastic.
An origami metamaterial can be ‘programmed’ prior to manufacture, to exhibit tailored properties, by effecting changes to the geometry of the unit cell or material distribution within it. Additionally, the properties can be further ‘tuned’ through folding, with very minimal change in energy. If an origami lattice could be used to design an acoustic metamaterial with elastic bandgaps, such bandgaps would also be tunable and programmable.
Programmability — properties of interest (e.g., location and width of bandgaps) can be altered by change in design parameters (e.g. panel angle, edge lengths, stiffness, etc.) prior to manufacture
Tunability — properties of interest (e.g., location and width of bandgaps) can be altered by change in geometry, continuously transitioning through folded states, while the system is in use
Motivation
Motivation
The standard Miura-ori, an origami pattern which found applications in deployable solar arrays in space (Miura, 1985), was observed even in nature, in folding of leaves and insect wings (Mahadevan and Rica, 2005). A 1D or 2D Miura-ori lattice with rigid panels, deploys as a single degree of freedom (DOF) structure.
In order to study wave propagation in the system, more DOFs need to be added to the structure. Triangulating the parallelogram panels, thus adding two creases to the existing four creases at each vertex, offers a solution. This degree-6 vertex, in isolation possesses 3 DOFs. However, despite this modification, Evans et al. (2015) showed that a 2D lattice of rigid triangulated Miura-ori does not admit spatially inhomogeneous deformation modes, indicating the absence of waves. A structural bar-and-hinge idealization of the triangulated origami (Schenk and Guest, 2011), comprising elastic bars and compliant hinges, enables the addition of multiple DOFs. Using this model, Pratapa et al. (2018) showed that both 1D and 2D triangulated Miura-ori lattices allow waves to propagate and can act as acoustic metamaterials by virtue of their bandgaps. However, with the advent of high energy stretching deformations in the panels, natural modes are inevitably linked to high frequency. This emphasizes the need for studies exploring an accurate representation of the low-frequency dynamics of origami lattices.
Brief Summary of Work Done
Brief Summary of Work Done
In an attempt to achieve natural frequencies and bandgaps strictly in the low-frequency range, we need to restrict origami to deformation modes attained exclusively through folding. We started out with systematically identifying the DOFs of the isolated degree-6 origami vertex. We derived analytical expressions for dihedral angles between the rigid triangulated panels based on spherical trigonometric identities. Assembling individual cells of origami, we construct 1Dx and 1Dy lattices (tessellated along x and y). Modelling the energy associated with folding using elastic rotational springs at creases, we have derived analytical expressions for elements of the stiffness matrix. Bloch wave reduction allows us to compute stiffness matrix in the wavevector space.
Brief Outline of Work in Progress
Brief Outline of Work in Progress
At present, we are working to extend this framework to 2D lattices by connecting finite strips of 1Dx and 1Dy. In future, we shall focus primarily on designing appropriate experiments to confirm the physical validity of these theoretical findings.
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