Modeling and Analysis of Mechanical Systems with Non-smooth Nonlinearities
Funded by a Fellowship from the China Scholarship Council
The research focuses on the use of analytical and computational techniques to analyze flexible mechanical systems with non-smooth nonlinearities, such as dry friction and clearances. We aim towards stability analysis of these systems under transient and periodic loads, leading to predictive design of these systems. The study will be computationally intensive and will be based on advanced algorithms of computational mechanics. Moreover, asymptotic techniques will be applied to this problem, in order to gain insight into the complex nonlinear modal interactions that occur in these systems.
This project is in collaboration with Profs. Jinhua Zhang and Jun Hong, Xi’an Jiaotong University, PR China, and Prof. Malte Krack, University of Stuttgart, Germany.
Collaborative Research: A new nonlinear modal updating framework for soft, hydrated materials
Funded by an NSF research grant
The mechanical properties of soft, hydrated materials have long been of interest to the scientific community. Increasingly, a particular area of interest has been on the high-rate response of soft materials due to their many applications in robotics, materials and the biomedical sciences. Most soft and hydrated materials (e.g., biomaterials) exhibit broadband nonlinear mechanical behavior that is challenging to quantify due to measurement uncertainties, mechanical anisotropy and inhomogeneity. High-rate dynamic testing, broadband rheometry, and acoustic force radiation/ultrasound techniques are commonly utilized for measuring high-rate responses of bio-tissues, however, they do not allow for independent control of the excitation amplitude and frequency. Therefore, there is a need for accurate characterization of these materials over the full spectrum of strain rates and finite deformations. To address these critical needs, a new nonlinear dynamics-based model identification and updating methodology is proposed. It starts with measured response time series and construction of transitions in a frequency-energy plot (FEP) of a soft-tissue tester and sample system. Then, the dynamics of an underlying conservative system (i.e., with no dissipative effects) modeling the tester is correlated with the measured response. In the conservative system model, soft tissues are modeled as highly flexible elements with stiffness and damping nonlinearities. The reconciliation of the measured and simulated responses in the FEP is utilized to estimate the broadband dissipative properties of the soft tissues. Preliminary work has focused on constructing a model updating framework for localized stiffness-type nonlinearities. In order to achieve the main objective, the following aims will be completed: (i) Understand and study the nonlinear broadband dynamic responses of soft materials; (ii) Construct the modal updating framework based on a computational benchmark model; and (iii) Experimentally validate the proposed model updating framework with a soft material characterization benchmark. The findings of this research have the potential to drastically increase the accuracy, cost-efficiency and accessibility of broadband soft material characterization, and, as such, it can be transformative in diverse interdisciplinary areas, such as soft robotic design, micro and nanoindentation measurements, soft tissue feedback during surgery, and modeling of the impact dynamics of the brain. This project will provide training and mentoring opportunities for a diverse group of K12, undergraduate and graduate research students. The PIs are committed in diversity as evidenced by the fact that the teams of the PIs consist of members of underrepresented groups actively serving as role models in different organizations, which will facilitate recruitment of underrepresented individuals. To engage the interest of the public in this scientific issue, an interactive demonstration of the developed experimental research benchmark will be displayed at the New Jersey State Science Festival. Partnerships with local high-schools to provide summer internships to students in under-represented and under-privileged communities are also planned.
This work is performed in collaboration with Professor Mehmet Kurt of the Stevens Institute of Technology.
Research Experience and Mentoring (REM) Supplement to EFRI NewLAW: Nonreciprocity in Acoustic Systems with Nonlinear Hierarchical Internal Structure and Asymmetry
Funded by an NSF EFRI REM grant
The EFRI REM supplemental support provides pre-program training; research experiences to two high school students with their STEM Teacher, and five undergraduate students; and post-program mentoring activities at the University of Illinois. These mentoring activities are socio-economically and culturally relevant to our research participants. Team-based research projects are performed, focusing on nonlinear, non-reciprocal dynamics. Moreover, the supplemental support will allow us to validate the viability of this approach and share results within the community through publication. We are uniquely positioned to accomplish this task at the University of Illinois due to several factors: (i) Experienced and committed principal investigators and research collaborators with a wealth of teaching and student mentoring experience and track records; (ii) a strong, in-place group of REM administrative and support professionals that is highly experienced in working with our target audience; (iii) long and established partnership with multiple educational units targeting minority Urbana – Champaign District 4 high school and local community college students, aiming towards a unique opportunity to integrate multiple organizations’ efforts in a comprehensive way; and (iv) students that are increasingly interested in STEM outreach and continue to request additional mentoring and outreach opportunities.
Mr. Joseph Muskin is the educational coordinator of this project; this work is in collaboration with Profs. S. Tawfick, K. Matlack and A. Wissa of the University of Illinois at Urbana-Champaign.
Targeted Energy Transfer by Nonlinear Energy Sink with Strongly Nonlinear Stiffness and Nonlinear Damping
Funded by a Fellowship from the China Scholarship Council
Concerning the research on nonlinear energy sinks – NESs, and targeted energy transfer – TET, most studies consider NESs with pure stiffness nonlinearities. This project will explore the effects of nonlinear damping and its effects on targeted energy transfers between linear oscillators and nonlinear damped attachments. The effects of nonlinear damping will also be studied on the dynamics of linear, nondispersive elastic media coupled to local nonlinear spring–dashpot pairs under harmonic excitations. The parameters of the attachments should be predicted to maximize mode complexity and enhance the interplay of vibrations and acoustics in these systems. Also, the slow invariant manifold – SIM approach will be explored to study the strongly nonlinear dynamical responses of these systems.
This project is in collaboration with Prof. Guoping Chen, Nanjing University of Aeronautics and Astronautics, PR China.
Nonlinear Wave Propagation in Granular Media
Funded by a Fellowship from the China Scholarship Council
Ordered granular media exhibit very rich and complex dynamics, and so they find applications in numerous fields. Wave propagation in granular media is a complex problem and many factors should be taken into consideration. In previous studies, much consideration has been given to the dynamics of simple granular media like one-dimensional granular chains, under idealized boundary conditions such as rigid boundaries and impulse excitation, while the physical problems, considering their potential applications, are much more complex. This project will explore complex granular networks with flexible boundary conditions in an effort to computationally study the nonlinear acoustics of granular interfaces. Computational and experimental studies are planned.
This project is in collaboration with Prof. Wei Li, Huazhong University of Science and Technology (HUST), PR China.
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 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.
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.
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).
Collaborative Research: Nonlinear Design and Development of Multi Degree-of-freedom Broadband Energy Harvesting Systems
Funded by an NSF research grant
This work addresses the harvesting and conversion of mechanical energy from low-level ambient vibration into usable electrical energy. The development of a self-renewing source of energy is paramount to the continued development of such devices such as portable electronics and wireless sensors, and the ability to convert ambient mechanical energy to usable electrical energy fills these requirements. However, to achieve acceptable performance conventional vibration-driven energy harvesting devices based on linear elements must be specifically tuned to match environmental conditions such as the frequency and amplitude of the external vibration. As the environmental conditions vary under ambient conditions the performance of these linear devices is dramatically decreased. The strategy to efficiently harvest energy from low-level, intermittent ambient vibration, proposed herein, relies on unique properties of strongly nonlinear vibrating systems that are referred to as “essentially” nonlinear. Utilizing this technology, we propose to develop multi degree-of-freedom, passive, broadband devices that will increase the efficiency and performance of energy harvesting systems to the low-level ambient vibrations. Furthermore, we will collaborate with a group at the University of Bristol (UK) to systems incorporate state of the art energy conversion strategies that work efficiently in conjunction with the broadband resonator to produce a reliable, consistent source of power. Finally, we will design and develop several breadboard systems, culminating in demonstratable hardware. We anticipate that this work can have broad impact as an enabling technology for the next-generation portable devices and wireless sensors. By increasing the power available to such components, device limitations associated with the power supply can be reduced or even possibly eliminated. In addition, this research will provide a novel framework for the design and optimization of systems that intentionally incorporate nonlinear elements. Finally, this project will enhance the diversity of the engineering community through targeted outreach, undergraduate research programs, and the support of students from underrepresented groups.
This work is performed in collaboration with Professor Donald D. Quinn of the University of Akron.
Design of Adaptive Load Mitigating Materials Using Nonlinear Stress Wave Tailoring
Funded by an ARO MURI Grant (in collaboration with the California Institute of Technology)
This research aims to develop a new class of structured protective systems, primarily based on materials incorporating inhomogeneous granular media, phase transforming ceramics and novel geopolymers. In the process we plan to study theoretically and experimentally scalable nonlinear interactions within these layered media. More specifically, we plan to employ granular media as a basis for a new class of nonlinearly adaptive, discontinuous, highly inhomogeneous materials capable of stress wave tailoring, passive and adaptive energy confinement, and energy redirection in preferential directions within the material compatible with the design objectives. This project involves fundamental work to understand both experimentally and analytically nonlinear energy transfer phenomena induced by intentional strong nonlinearities in a material. In addition, we aim to transfer these fundamental concepts to actual material systems with demonstrated stress wave tailoring properties. Specific objectives include, (i) to further the understanding of the role of essentially nonlinear contact phenomena in wave propagation in discretely inhomogeneous systems, and to transfer these fundamental concepts into an actual scalable material system; (ii) to develop a theoretical/computational framework for the design of a material system or material system classes, that will exhibit adaptive stress wave mitigation characteristics; and (iii) to experimentally demonstrate the stress wave management characteristics of the conceptual material system designs.
This work is performed in colloboration with Professor Chiara Daraio (California Institute of Technology / ETH Zürich)
Modal interactions in nonlinear dissipative mechanical systems
Funded by the Federal Ministry of Education and Research of Germany and the Marie Curie program of the European Union
When a vibrating mechanical system undergoes strongly nonlinear forces, energy can be exchanged between initially distinct vibration modes. Such nonlinear modal interactions cause a dramatic change of the vibration behavior and lead to peculiar phenomena. Two of these phenomena are new maxima encountered in the frequency response to harmonic forcing and dynamic instabilities present in the transient impulse response.Different computational methods have been developed to analyze and predict this behavior. These methods are, however, typically not applicable if the associated modes are far from resonance in the linear case. Moreover, most of these methods are limited to quite academic, typically non-dissipative nonlinearities. On the other hand, common modal analysis techniques applicable to generic nonlinearities are limited to the dynamic regime where modal interactions are absent. In the proposed project, the benefits of both approaches are to be combined in a novel modal analysis approach. The capability of this approach shall be demonstrated for a test case with nonlinear damping. The dynamic behavior is to be investigated in the externally forced and the autonomous configuration.
This project is in collaboration with Prof. Dr.-Ing. Habil. Jӧrg Wallascheck, Gottfried Wilhelm Leibniz University, Germany.
Nonlinear System Identification of Mechanical Joints
Funded by a grant from Sandia National Laboratory
We apply a nonlinear system identification (NSI) methodology to identify the nonlinear characteristics of mechanical joints. The methodology relies on direct post processing of measured time series. It combines Wavelet transforms and Empirical Mode Decompositions with Complexification-Averaging Analysis, and leads to reduced slow flow reduced models. The project will combine the NSI methodology with methods for model reduction via distributed damping developed by researchers in Sandia National Laboratory, and will have a significant experimental component.
Structural Logic: Tailoring stiffness and damping of large scale structures via passive nonlinear targeted energy transfer
Funded by a DARPA Phase I Research Grant (in collaboration with the University of Akron)
We aim to exploit intentional strong nonlinearities introduced at optimal locations within a structure of interest in order to promote fully passive adaptivity of the structural dynamics to changing loads. This will be accomplished through the implementation of passive nonlinear energy sinks – NESs – with essential (non-linearizable) stiffness and damping nonlinearities at selected points of the structure acting, in essence, as passive broadband rapid dissipaters of vibration and shock energy. Hence, the NESs will not only drastically increase the effective damping of the structure but will also introduce effective stiffening into the structural response. The basic rationale behind the proposed designs is that the implementation of local NESs will passively modify the global structural dynamics of the modified system by, (i) introducing new sets of essentially nonlinear structural modes in specific frequency ranges of interest that, in effect, either increase or decrease the structural compliance; (ii) drastically increasing the effective damping of the structure, through targeted energy transfer – TET – from the structure to the NESs where it is rapidly dissipated locally; and (iii) enabling the structure to passively adapt its dynamics to a broad range of applied excitations over extended frequency and energy ranges. Key to our proposed design is the implementation of modular NESs with nonlinearizable (essentially nonlinear) stiffness characteristics, having no preferential resonance frequencies and thus, the capacity to engage in resonance interactions with sets of structural modes through resonance capture cascades. Indeed, the NESs will have the capacity to extract and locally dissipate vibration and shock energy from highly energetic structural modes in a broadband multifrequency fashion through TET. Furthermore, we will propose the implementation of NESs with geometrically nonlinear damping, which will be designed to drastically enhance the capacity of these local attachments to robustly absorb and rapidly dissipate vibration energy over broad frequency and energy ranges, thus increasing the effective damping factor of the structure. We emphasize that the proposed designs are fundamentally different than usual linear designs, e.g., linear vibration absorbers, that are narrowband in operation and not adaptable to change in forcing conditions. To highlight this difference, we mention that the addition of a local linear vibration absorber will introduce only a local modification in the frequency response of the structure, and it will be incapable of differentiating between different energy levels of the excitation. On the contrary, the proposed NESs are broadband devices which, although local, have the capacity not only to inflict global changes in the frequency response of the structure, but also to passively adapt their operation to excitations with varying energy and frequency content. Hence, the proposed designs will be efficacious under a wide range of loading scenarios, with robust performance under parametric and loading uncertainties.
This work is performed in colloboration with Professor Donald D. Quinn (University of Akron).
Towards Development of Nonparametric System Identification Based on Slow-Flow Dynamics, with Application to Damage Detection and Uncertainty Quantification
Funded by an AFOSR Research Grant and an AFOSR DURIP Grant
This research program of analysis, computation and laboratory experiments focuses on the development and documentation of system identification of strongly nonlinear, complex, multi-physics problems. Our broad objectives center on, (i) the identification of strongly nonlinear, multi-component systems; (ii) the investigation of the relationship between the slow flow dynamics of nonlinear dynamical systems and of intrinsic mode functions (IMFs) resulting from empirical mode decomposition (EMD) and Hilbert Transforms of measured time series, demonstrating their equivalence; (iii) derivation of data-driven reduced order models that can be applied for structural health monitoring and uncertainty quantification of structural systems; and (v) the effects of non-smooth nonlinearities, such as clearance and dry friction, on nonlinear system identification.
Virtual Vibration Testing of External Stores
Funded by US Navy (NAVAIR) SBIR Phase I Grant (in collaboration with NextGen Aeronautics Inc., NES Technologies Inc.)
This work aims to develop a validated virtual vibration test system for a typical external store/aircraft configuration of interest to NAVAIR. This project addresses several challenging tasks, including the complexity of loading on the wing/rail/carriage/store in flight with multiple sources and paths; the inability to accurately measure and characterize loads acting on the aircraft/store; insufficient knowledge of boundary conditions due to strong nonlinearities such as friction, clearances, and mechanical freeplay that act at the aircraft/store interface; and the need to gain accurate physics-based understanding of multi-scale and strongly nonlinear transient dynamics. We employ powerful analytical and experimental multi-scale techniques to develop accurate physics-based nonlinear structural dynamic modeling for a simple store/hangar configuration. Key to our approach will be multi-scale identification combined with derivation of low-dimensional models that can accurately reproduce the measured dynamics.
Design of Nonlinear Energy Sink for Passive Aeroelastic Instability Suppression
Funded by an AFOSR STTR Phase II Grant (in collaboration with NextGen Aeronautics Inc., NES Technologies Inc. and Texas A&M University), and an AFOSR DURIP Grant
High Sea-State Enabling Adaptive Structures (High SEAS)
Funded by DARPA Structural Logic Program, Phase II, HRL, LLC Subcontract No. 12081-300652-B8, 2013-15 (in collaboration with HRL, LLC, University of Akron, University of Texas at Austin, Maritime Applied Physics Corporation and Donald L. Blount & Associates, co-PI)
For more information visit http://www.darpa.mil/Our_Work/STO/Programs/Structural_Logic.aspx.
Global/Local System Identification of Strongly Nonlinear Dynamical Systems
Funded by an NSF EPSCoR Research Grant (in collaboration with New Mexico State University)
The need for system identification and reduced order modeling arises from the fact that, presented with sensor data, the analyst is generally unaware of many details of the underlying dynamical system from which they originated. The straightforward approach to this dilemma is to assume linearity and temporal stationarity in the response, and perform experimental modal analysis. This approach fails as systems become more complex, incorporating not only electrical and mechanical components but also, for example, biological and biomimetic features, the likelihood exists that the underlying dynamical behavior will be strongly nonlinear and nonstationary (e.g., local buckling, plastic deformations, clearance and backlash, hysteresis, etc.). Moreover, nonlinear systems routinely possess co-existing qualitatively distinct dynamics, so their responses are largely dictated by initial and forcing conditions. These well-recognized, highly individualistic features of nonlinear systems restrict the unifying dynamical features that are amenable to system identification. To address these issues we work on a new nonlinear system identification methodology of broad applicability, that relies solely upon direct time series measurement and post-processing, and leads to dual global / local identification of the dynamics. Key to our method are slow/fast partitions of the measured time series, in order to identify dominant fast frequencies (which also define dimensionality), and derive associated slow flows. We employ powerful post-processing computational algorithms (wavelet transforms, Hilbert transforms and empirical mode decompositions) in order to identify the dynamics in the frequency-energy domain and study global features, such as fundamental and subharmonic resonances, bifurcations, multi-frequency transitions, etc. Associated with this global identification is the derivation of local reduced order models that model specific damped nonlinear transitions and are suitable for control-oriented designs and other applications. We show that our method is especially suited for strongly nonlinear systems with high sensitivity to initial conditions and non-smooth nonlinearities (such as vibro-impacts). In the latter case, we demonstrate the capacity of our approach to separate smooth from non-smooth effects in the measured time series, which allows the identification of the dynamics based on the smooth components of the responses. Efforts are also focused on outreach, particularly in the vicinity of New Mexico State University (NMSU). A model testing laboratory will be established at NMSU for the demonstration of nonlinear phenomena, which will be documented and made available via the Internet. The aim is to increase the enrollment and graduation rate of historically underrepresented groups in science, technology, engineering and mathematics. Educational efforts also include outreach activities, including presentations in local high schools about vibrations and their engineering applications to practical life, invitation to labs, demos in their classrooms, and training their teachers.
This work is performed in collaboration with Professor Young Sup Lee (New Mexico University)
Nonlinear Dynamics of Oscillators Exhibiting Targeted Energy Transfers
Funded by a Binational Science Foundation (BSF) Grant (in collaboration with Technion – Israel Institute of Technology)
The methods applied in this work evolved over nine years of collaborative work between the Israeli and US groups, through visits, joint publications and coordinated research efforts. The main idea is to connect to a linear system an essentially nonlinear attachment that acts as nonlinear energy sink (NES) of unwanted vibrations. Properly designed NESs can passively absorb broadband or narrowband energy from linear systems through a series of transient resonance captures (TRCs), i.e., transient nonlinear resonances of the NES with linear modes during which targeted energy transfer (TET) occurs from the mode to the NES, after which the NES engages the next mode of the sequence. This unique feature of the NES is due to the fact that it lacks a preferential resonant frequency, so it can engage in resonance with modes over broad frequency ranges. The goal of this project is to extend the state-of-the-art of the theory of TET through the following research thrusts: (i) Theoretical and experimental study of the dynamics of multi-degree-of-freedom and continuous (elastic) systems with attached NESs and optimization studies of TET in these systems leading to efficient implementation of this concept to practical applications; and (ii) theoretical and experimental study of a new NES design based of strongly nonlinear inertial effects, and application of the new design to practical problems, such as aeroelastic flutter suppression and seismic mitigation.
This work is in colloboration with Professor Oleg Gendelman (Technion).
Intrinsically-Nonlinear Broadband Nanoresonator for Ultrahighly Sensitive Sensing of Energy Transfers
Funded by an NSF Research Grant
Much of the study on mechanical nanoresonators has focused on improving their Q factor, realizing their high frequency operation and reducing their size. The idea is that with the combination of small effective mass, low damping and up to GHz resonance frequency, such nanoresonators can achieve ultrahigh sensitivity to force and mass changes. Indeed, in the last couple of years, significant progress towards that end has been witnessed, where single-atom level mass sensitivity has been demonstrated with the use of nanoscale mechanical resonator. This impressive sensitivity, however, can not be maintained when such nanoresonators would be operated in an energy dissipative environment, such as in an ambient environment, where the hydrodynamic damping in air is significant. The underlying notion is that as the energy dissipation involved in the resonance system increases, the Q factor decreases and so does the sensitivity. This notion, however, is perceived from the understanding that the nanoresonator has to be operated in the linear dynamic regime at its fundamental resonance frequency. In this research, we aim to advance a paradigm-shifting concept in micro-/nano-resonator design and development that involves the simple substitution of an essential geometric nonlinearity in an otherwise linear resonant system to realize an intrinsically nonlinear broadband resonator, meaning that the resonator has no preferential resonant frequency and is nonlinear at any oscillation amplitude and across the whole frequency spectrum. The nonlinearity associated with the system prescribes that this nonlinear resonator is most sensitive to the change in energy transfer. The reduced size, down to micro-/nano-scale, significantly reduces the overall system energy associated with such a nonlinear resonant system, this in turn makes it sensitive to even the slightest amount of energy transfer between the resonator and the involved environment. While the sensitivity of a linear resonant system deteriorates when operated in an energy dissipative environment, a nonlinear resonant system, especially a micro-/nano-scale one, can actually be highly alert to such energy dissipation and thus sense any changes within the system including the environment with high sensitivity. We aim to make this paradigm shift from sensing mass change with a linear resonant system to sensing energy transfer with this kind of nonlinear nanoscale resonant system and propose to exploit the instabilities associated with such an essentially nonlinear resonator to achieve highly sensitive sensing in both ambient and vacuum environments.
This work is performed in collaboration with Professor Min-Feng Yu of the University of Illinois.
Development of Prediction Algorithm and Experimental Testing of Door Locking Mechanism During Side Impact Tests
Funded by a Grant from Hyundai Motor Company, R. Korea
This work will develop a predictive capability for improved door locking designs during side-impacts. In addition, a training course will be provided to Hyundai personnel.
Nonlinear Targeted Energy Transfer for Enhanced Passive Seismic Mitigation of Structures
Funded by University of Illinois Research Funds and the W. Grafton and Lillian B. Wilkins Endowed Professorship (in collaboration with University of Reggio Calabria)
The aim of this work is to show that is possible to apply the Nonlinear Energy Sink (NES) concept to protect full scale seismically excited steel structures through Targeted Energy Transfer (TET). We consider, as primary (linear) systems, multi-storey shear frames with beams sufficiently rigid so that the frames can reasonably be considered as shear-type. To a frame, we connect one or more NESs which can be both smooth or non-smooth, that is can have smooth or non-smooth essential stiffness nonlinearities. Of particular interest are NESs with vibro-impact characteristics. Attaching NESs to a structure brings two advantages as far as seismic mitigation design is concerned. First, the vibro-impact NES, through its fast reaction time during the crucial initial few cycles of the seismic motion, ensures a reduction of the initial high peaks of the structural response; in addition the vibro-impacts scatter seismic energy from low to high structural modes, which leads to a high-frequency redistribution of seismic energy that lower the response amplitudes and is favorable to dissipation of seismic energy by internal structural damping . Second, the smooth NES can ensure vibration control of the structural motion during the second and later stage of the response. In addition, the smooth NES is an effective passive vibration boundary controller in cases of earthquakes of modest intensity. Computational and experimental studies are performed.
Suppression of Vortex Shedding Vibrations by Passive Nonlinear Energy Transfer
Funded by University of Illinois Research Funds and the W. Grafton and Lillian B. Wilkins Endowed Professorship
We study the problem of suppressing flow-induced instabilities (limit cycle oscillations – LCOs) of the in-flow oscillations of a cylinder resting on a viscoelastic foundation. Our work is based on high-fidelity 3-dim codes of the flow-structure interaction. We have validated the code with results available in the literature, and we are studying the effect on the vortex shedding dynamics of an internal nonlinear energy sink (NES) in the cylinder. We study targeted energy transfer from the flow and the cylinder to the NES, and use reduced order modeling and asymptotic analysis to investigate the possible mechanisms for passive vortex shedding suppression due to the action of the NES, as well as the robustness of this suppression. We envision important applications in the fields of stabilization of pylons in sea platforms, monitoring of corrosion-induced instabilities in nuclear fuel rods, and other applications involving flow-induced instabilities in structures.
This work is performed in collaboration with Professors Arif Masud and Arne Pearlstein (University of Illinois at Urbana-Champaign).