Collaborative Research: Intentionally Nonlinear Design of High-Frequency Atomic Force Microscopy for Enhanced Material Characterization

Funded by an NSF research grant

Detailed analytical, computational and experimental studies are performed of a new, microcantilever beam design enabling higher-frequency nonlinear atomic force microscopy (AFM). Under dynamic mode operation an intentionally designed 1:n internal resonance between the two leading bending modes of the AFM microcantilever incorporating an inner Silicon paddle, leads to magnification of high-frequency harmonics in the paddle response, which is the basis for AFM of improved sensitivity. It is emphasized that although the cantilever-paddle design is linear, the intentional strongly nonlinear effect is activated through the nonlinear tip-sample interactions that occur during the AFM dynamic operation, that excite and nonlinearly couple the two bending modes in 1:n resonance. Preliminary theoretical and experimental measurements demonstrate the efficacy of this intentionally nonlinear design. Indeed, prototype tests of the proposed nonlinear AFM design applied on an inhomogeneous polymer sample consisting of a thin PDMS film with ~200 nm embedded polystyrene nanoparticles, indicated the capacity for simultaneous topography imaging and compositional mapping with as much as five-fold enhanced sensitivity This project will theoretically develop and fully document the significantly enhanced AFM measurements of sample material properties and topography, achieved through sensing of higher harmonics in the response. It is proposed to systematically study, optimize, extend and validate this promising concept. This will be achieved through theoretical studies to characterize the paddle’s response to different types of interaction forces, and an extended series of experimental tests to assess the sensitivity of high-order internal resonance designs to changes in topology and material properties. Moreover, multi-paddle AFM designs incorporating multiple simultaneous internal resonances will be analyzed for quantitative characterization, whereas related microfabrication issues will also be addressed. This work can be potentially transformative, since it can provide a new paradigm of intentionally nonlinear AFM technology based on higher-frequency sensing, and with capacity for drastically enhanced sensitivity and performance. The gained AFM sensing capability will be an incomparable tool in fields such as nano- and bio-sciences.

This work is performed in collaboration with Professor Hanna Cho of Ohio State University.


Nonlinear System Identification, Reduced Order Modeling, and Model Updating of the Effects of Mechanical Joints on Structural Dynamics

Funded by an NSF Graduate Fellowship (Keegan Moore)

Mechanical joints are present in nearly every structure, device, or vehicle in operation today. As these become ever more complicated the need for the classification and understanding of the nonlinear effects on structural dynamics grows ever more critical. I propose to apply recently developed nonlinear system identification methods, reduced order modeling and model updating techniques to characterize and model these nonlinear effects. The outcome of this research will be the development of models for use in standard finite element (FE) methods that capture the nonlinear effects of mechanical joints.


Nonlinear Acoustic Vacua

Funded by a Fellowship from the China Scholarship Council

In this project finite chains of particles in the plane with next-neighbor interactions, will be considered. At certain energy limits and for specific boundary conditions, geometric and kinematic nonlinearities give rise to nonlinear acoustic vacua, whereby the governing equations of motion possess strongly non-local nonlinear terms in spite of the next-neighbor physical interactions between particles. Moreover, in the continuum limit (i.e., in the long-wavelength approximation) these nonlinear sonic vacua exhibit complete absence of any linear acoustics and possess zero speed of sound (as defined in classical acoustics); then the strongly non-local terms constitute, in essence, time-dependent ‘effective speeds of sound’ for these media, that are completely tunable with energy. We will explore analytically, computationally and experimentally the unforced and forced dynamics of these highly degenerate systems and consider potential applications in the fields of shock mitigation and vibration absorption.

This project is in collaboration with Prof. Guojun Zhang, Huazhong University of Science and Technology (HUST), PR China; Prof. Leonid Manevitch, Institute of Chemical Physics, Russian Academy of Sciences, Russia; and Prof. Oleg Gendelman, Technion – Israel Institute of Technology, Israel.


Nonlinear Dynamics of a Bluff Body with Nonlinear Internal Oscillating/Rotating Elements: Vortex-Induced Vibration Suppression, Partial Wake Stabilization, and Drag Reduction

Funded by an NSF research grant

Detailed computational and analytical studies are proposed of the nonlinear dynamics of vortex-induced vibration (VIV) of a linearly sprung circular cylinder with an internally attached, strongly nonlinear device (acting, in essence, as a nonlinear energy sink, or NES) in laminar or turbulent flow. The NES possesses oscillating and/or rotational components, and induces passive nonlinear targeted energy transfer to itself from the cylinder and flow over broad frequency ranges. Preliminary findings with a simple rotating NES or with a simple translating NES (in the latter case employing a spring with an essentially nonlinear stiffness), each with a linear viscous damper, indicate that an NES can effect dramatic suppression of VIV, significant symmetrization and stabilization of the wake with major associated drag reduction, chaotic oscillation of the cylinder and temporally chaotic flow at intermediate Reynolds numbers (Re), and interesting bifurcations resulting in multiple stable co-existing VIV solutions. It is proposed to extend these exciting and unexpected results by developing a new paradigm, wherein strongly nonlinear internal oscillating devices in a bluff body are designed to drastically suppress or enhance VIV, and to partially stabilize and symmetrize the wake. Fluid-structure interaction dynamics of the sprung cylinder having one or more internal NESs will be studied for intermediate and higher Re using slow/fast dynamical decompositions, invariant slow manifold considerations, nonlinear system identification, and reduced-order modeling techniques. High-fidelity fluid-structure interaction computations will be performed in the laminar, transitional, and turbulent regimes. As in the past, the aim will be to involve undergraduate and graduate students, especially from underrepresented groups. Participation in the G.A.M.E.S. (Girls Adventures in Mathematics, Engineering, and Science) summer camp organized for high-school girls by UIUC is planned, by building an educational experimental demonstration of fluid-structure interaction, where participants can perform their own physical experiments. Moreover, a dedicated educational web site capable of interactive VIV computational ‘experiments’ will be constructed and broadly disseminated to engage a variety of audiences.

This work is performed in collaboration with Professor Arne Pearlstein (University of Illinois).


Targeted Energy Transfer in Powertrains to Reduce Vibration-induced Energy Losses

Funded by an EPSRC grant (Principal Investigator Prof. Stephanos Theodossiades, Loughborough University, UK)

The project will develop the tools required to reduce energy losses associated with vibrations in power transmission systems, by implementing the state-of-the-art Targeted Energy Transfer (TET) technique. The research team comprises of internationally leading researchers from academe and industry, who can support the transition of this technology from the laboratory to engineering reality in an industrial setting. The aim of this research is to apply the TET method in automotive powertrains with the view of building sustainable vibration reduction technology and then assessing its potential to harvest energy for low-power system functions (e.g. wireless sensors). The above successful technique in systems under translational oscillations has not hitherto been applied systematically to rotating systems, which is the main novelty of the proposed research. The LNDVL team acts as International collaborator for this project.


Simple Mechanical Oscillators in the Macroscale that Exhibit a Quantum Effect

Funded by University of Illinois Research Funds and the Grayce Wicall Gauthier Endowed Professorship (in collaboration with the Institute of Chemical Physics, Russian Academy of Science)

Landau-Zener tunneling (LZT) is a transition between two energy levels of a quantum-mechanical system. A linear classical system of two weakly coupled parametric pendulums can be equally described by equations identical to those of LZT. This unexpected analogy suggests that the latter classical system could also exhibit irreversible energy transfer similarly to the LZT transition. We are performing theoretical and experimental studies using a fixture of two weakly coupled pendula, one of which has a time-varying length, that was specially built for this project. Preliminary results indicate that the LZT effect can be successfully extended to the macro-scale. Moreover, theory predicts higher energy transfer efficiency in the nonlinear regime, where no quantum analog exists. LZT-like irreversible energy transfer effects in classical systems can be employed and implemented to design a new type of nonlinear energy sinks applied to vibration and shock mitigation of mechanical components. Currently we are exploring the LZT phenomenon in our designs for passive energy redirection in media composed of weakly coupled granular chains. We have shown that LZT in space can be a practical mechanism for shock redirection in preferential paths within a material with microstructure, undergoing strongly nonlinear interactions.

This work is performed in collaboration with Professor Leonid I. Manevitch (Institute of Chemical Physics, Russian Academy of Science).