Georgia Institute of Technology College of Sciences

Robotic snakes have the potential to navigate areas or environments that would be more challenging for traditionally engineered robots. To realize their potential requires deriving feedback control and path planning algorithms applicable to the diverse gait modalities possible. In turn, this requires equations of motion for snake movement that generalize across the gait types and their interaction dynamics. This talk will discuss efforts towards both obtaining general control equations for snake robots, and controlling them along planned trajectories. We model three-dimensional time- and spatially-varying locomotion gaits, utilized by snake-like robots, as planar continuous body curves. In so doing, quantities relevant to computing system dynamics are expressed conveniently and geometrically with respect to the planar body, thereby facilitating derivation of governing equations of motion. Simulations using the derived dynamics characterize the averaged, steady-behavior as a function of the gait parameters. These then inform an optimal trajectory planner tasked to generate viable paths through obstacle-strewn terrain. Discrete-time feedback control successfully guides the snake-like robot along the planned paths.

The first part of this talk will review our recent efforts on the electroelastodynamics of smart structures for various applications ranging from nonlinear energy harvesting, bio-inspired actuation, and acoustic power transfer to elastic wave guiding and vibration attenuation via metamaterials. We will discuss how to exploit nonlinear dynamic phenomena for frequency bandwidth enhancement to outperform narrowband linear-resonant devices in applications such as vibration energy harvesting for wireless electronic components. We will also cover inherent nonlinearities (material and internal/external dissipative), and their interactions with intentionally designed nonlinearities, as well as electrical circuit nonlinearities. Electromechanical modeling efforts will be presented, and approximate analysis results using the method of harmonic balance will be compared with experimental measurements. Our recent efforts on phononic crystal-enhanced elastic wave guiding and harvesting, wideband vibration attenuation via locally resonant metamaterials, contactless acoustic power transfer, bifurcation suppression using nonlinear circuits, and exploiting size effects via strain-gradient induced polarization (flexoelectricity) in centrosymmetric elastic dielectrics will be summarized. The second part of the talk, which will be given by Chris Sugino (Research Assistant and PhD Student), will be centered on low-frequency vibration attenuation in finite structures by means of locally resonant elastic and electroelastic metamaterials. Locally resonant metamaterials are characterized by bandgaps at wavelengths that are much larger than the lattice size, enabling low-frequency vibration/sound attenuation. Typically, bandgap analyses and predictions rely on the assumption of waves traveling in an infinite medium, and do not take advantage of modal representations commonly used for the analysis of the dynamic behavior of finite structures. We will present a novel argument for estimating the locally resonant bandgap in metamaterial-based finite structures (i.e. meta-structures with prescribed boundary conditions) using modal analysis, yielding a simple closed-form expression for the bandgap frequency and size. A method for understanding the importance of the resonator locations and mass distribution will be discussed in the context of a Riemann sum approximation of an integral. Numerical and experimental results will be presented regarding the effects of mass ratio, non-uniform spacing of resonators, and parameter variations among the resonators. Electromechanical counterpart of the problem will also be summarized for piezoelectric structures.

Crystal plasticity modeling is useful for considering the influence of anisotropy of elastic and plastic deformation on local and global responses in crystals and polycrystals. Modern crystal plasticity has numerous manifestations, including bottom-up models based on adaptive quasi-continuum and concurrent atomistic-continuum methods in addition to discrete dislocation dynamics and continuum crystal plasticity. Some key gaps in mesoscale crystal plasticity models will be discussed, including interface slip transfer, grain subdivision in large deformation, shock wave propagation in heterogeneous polycrystals, and dislocation dynamics with explicit treatment of waves. Given the mesoscopic character of these phenomena, contrasts are drawn between bottom-up (e.g., atomistic and discrete dislocation simulations and in situ experimental observations) and top-down (e.g., experimental) information in assembling mesoscale constitutive relations and informing their parameters.

Most available techniques for the design of tensegrity structures can be grouped in two categories. On the one hand, methods that rely on the systematic application of topological and geometric rules to regular polyhedrons have been applied to the generation of tensegrity elementary cells. On the other hand, efforts have been made to either combine elementary cells or apply rules of self-similarity in order to generate complex structures of engineering interest, for example, columns, beams and plates. However, perhaps due to the lack of adequate symmetries on traditional tensegrity elementary cells, the design of three-dimensional tensegrity lattices has remained an elusive goal. In this work, we first develop a method to construct three-dimensional tensegrity lattices from truncated octahedron elementary cells. The required space-tiling translational symmetry is achieved by performing recursive reflection operations on the elementary cells. We then analyze the mechanical response of the resulting lattices in the fully nonlinear regime via two distinctive approaches: we first adopt a discrete reduced-order model that explicitly accounts for the deformation of individual tensegrity members, and we then utilize this model as the basis for the development of a continuum approximation for the tensegrity lattices. Using this homogenization method, we study tensegrity lattices under a wide range of loading conditions and prestressed configurations. We present Ashby charts for yield strength to density ratio to illustrate how our tensegrity lattices can potentially achieve superior performance when compared to other lattices available in the literature. Finally, using the discrete model, we analyze wave propagation on a finite tensegrity lattice impacting a rigid wall.