Showing papers in "Applied Mechanics Reviews in 2014"

On the Role of Nonlinearities in Vibratory Energy Harvesting: A Critical Review and Discussion

Abstract: The last two decades have witnessed several advances in microfabrication technologies and electronics, leading to the development of small, low-power devices for wireless sensing, data transmission, actuation, and medical implants. Unfortunately, the actual implementation of such devices in their respective environment has been hindered by the lack of scalable energy sources that are necessary to power and maintain them. Batteries, which remain the most commonly used power sources, have not kept pace with the demands of these devices, especially in terms of energy density. In light of this challenge, the concept of vibratory energy harvesting has flourished in recent years as a possible alternative to provide a continuous power supply. While linear vibratory energy harvesters have received the majority of the literature’s attention, a significant body of the current research activity is focused on the concept of purposeful inclusion of nonlinearities for broadband transduction. When compared to their linear resonant counterparts, nonlinear energy harvesters have a wider steady-state frequency bandwidth, leading to a common belief that they can be utilized to improve performance in ambient environments. Through a review of the open literature, this paper highlights the role of nonlinearities in the transduction of energy harvesters under different types of excitations and investigates the conditions, in terms of excitation nature and potential shape, under which such nonlinearities can be beneficial for energy harvesting. [DOI: 10.1115/1.4026278]

Circulant Matrices and Their Application to Vibration Analysis

Abstract: This paper provides a tutorial and summary of the theory of circulant matrices and their application to the modeling and analysis of the free and forced vibration of mechanical structures with cyclic symmetry. Our presentation of the basic theory is distilled from the classic book of Davis (1979, Circulant Matrices, 2nd ed., Wiley, New York) with results, proofs, and examples geared specifically to vibration applications. Our aim is to collect the most relevant results of the existing theory in a single paper, couch the mathematics in a form that is accessible to the vibrations analyst, and provide examples to highlight key concepts. A nonexhaustive survey of the relevant literature is also included, which can be used for further examples and to point the reader to important extensions, applications, and generalizations of the theory. [DOI: 10.1115/1.4027722]

A Review of Planetary and Epicyclic Gear Dynamics and Vibrations Research

Abstract: This article summarizes published journal articles on planetary and epicyclic gear dynamics and vibration. Research in this field has increased dramatically over the past two decades. The wide range of research topics demonstrates the technical challenges of understanding and predicting planetary gear dynamics and vibration. The research in this review includes mathematical models, vibration mode properties, dynamic response predictions including nonlinearities and time-varying mesh stiffness fluctuations, the effects of elastic compliance, and gyroscopic effects, among other topics. Practical aspects are also included, for example, planet load sharing, planet phasing, tooth surface modifications, and characteristics of measured vibration response.

Analysis of Fluid Systems: Stability, Receptivity, SensitivityLecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013

Abstract: This article presents techniques for the analysis of fluid systems. It adopts an optimization-based point of view, formulating common concepts such as stability and receptivity in terms of a cost functional to be optimized subject to constraints given by the governing equations. This approach differs significantly from eigenvalue-based methods that cover the time-asymptotic limit for stability problems or the resonant limit for receptivity problems. Formal substitution of the solution operator for linear time-invariant systems results in the matrix exponential norm and the resolvent norm as measures to assess the optimal response to initial conditions or external harmonic forcing. The optimization-based approach can be extended by introducing adjoint variables that enforce governing equations and constraints. This step allows the analysis of far more general fluid systems, such as time-varying and nonlinear flows, and the investigation of wavemaker regions, structural sensitivities, and passive control strategies.

On the Mechanics of Fatigue and Fracture in Teeth

Abstract: Tooth fracture is a major concern in the field of restorative dentistry. However, knowledge of the causes for tooth fracture has developed from contributions that are largely based within the field of mechanics. The present manuscript presents a technical review of advances in understanding the fracture of teeth and the fatigue and fracture behavior of their hard tissues (i.e., dentin and enamel). The importance of evaluating the fracture resistance of these materials, and the role of applied mechanics in developing this knowledge will be reviewed. In addition, the complex microstructures of tooth tissues, their roles in resisting tooth fracture, and the importance of hydration and aging on the fracture resistance of tooth tissues will be discussed. Studies in this area are essential for increasing the success of current treatments in dentistry, as well as in facilitating the development of novel bio-inspired restorative materials for the future.

Adaptive and Model-Based Control Theory Applied to Convectively Unstable Flows

Abstract: In boundary-layer flows it is possible to reduce the friction drag by breaking the path from laminar to turbulent state. In low turbulence environments, the laminar-to-turbulent transition is dominated by local flow instabilities – Tollmien-Schlichting (TS) waves – that exponentially grows while being con- vected by the flow and, eventually, lead to transition. Hence, by attenuating these disturbances via localised forcing in the flow it is possible to delay farther downstream the onset of turbulence and reduce the friction drag.Reactive control techniques are widely investigated to this end. The aim of this work is to compare model-based and adaptive control techniques and show how the adaptivity is crucial to control TS-waves in real applications. The control design consists in (i) choosing sensors and actuators and (ii) designing the system responsible to process on-line the measurement signals in order to compute an appropriate forcing by the actuators. This system, called compen- sator, can be static or adaptive, depending on the possibility of self-adjusting its response to unmodelled flow dynamics. A Linear Quadratic Gaussian (LQG) regulator is chosen as representative of static controllers. Direct numerical simulations of the flow are performed to provide a model for the compensator design and test its performance. An adaptive Filtered-X Least-Mean-Squares (FXLMS) compensator is also designed for the same flow case and its per- formance is compared to the model-based compensator via simulations and experiments. Although the LQG regulator behaves better at design conditions, it lacks robustness to small flow variations. On the other hand, the FXLMS compensator proved to be able to adapt its response to overcome the varied conditions and perform an adequate control action.It is thus found that an adaptive control technique is more suitable to delay the laminar-to-turbulent transition in situations where an accurate model of the flow is not available.

Modal Stability TheoryLecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013

Abstract: This article contains a review of modal stability theory. It covers local stability analysis of parallel flows including temporal stability, spatial stability, phase velocity, group velocity, spati ...

Review of Residual Stress Modification Techniques for Extending the Fatigue Life of Metallic Aircraft Components

Abstract: A major challenge for the aircraft industry in the future will be the development of effective strategies for maintaining and extending the service life of aging aircraft fleet. In this context, residual-stress-based approaches for extending the fatigue life of aircraft components are believed to have great potential for providing cost-effective solutions. This paper reviews residual-stress-based life extension techniques and published work on the use of these techniques in aerospace applications. The techniques reviewed include cold expansion, shot peening, laser shock peening, deep rolling, and heating. Comparisons of the various techniques with regard to current applications and limitations are given.

Continuum Modeling of Granular Media

Abstract: Author(s): Goddard, JD | Abstract: This is a survey of the interesting phenomenology and the prominent regimes of granular flow, followed by a unified mathematical synthesis of continuum modeling. The unification is achieved by means of "parametric" viscoelasticity and hypoplasticity based on elastic and inelastic potentials. Fully nonlinear, anisotropic viscoelastoplastic models are achieved by expressing potentials as functions of the joint isotropic invariants of kinematic and structural tensors. These take on the role of evolutionary parameters or "internal variables," whose evolution equations are derived from the internal balance of generalized forces. The resulting continuum models encompass most of the mechanical constitutive equations currently employed for granular media. Moreover, these models are readily modified to include Cosserat and other multipolar effects. Several outstanding questions are identified as to the contribution of parameter evolution to dissipation; the distinction between quasielastic and inelastic models of material instability; and the role of multipolar effects in material instability, dense rapid flow, and particle migration phenomena. Copyright © 2014 by ASME.

Nanoscale Fluid Mechanics and Energy Conversion

Abstract: Under nanoconfinement, fluid molecules and ions exhibit radically different configurations, properties, and energetics from those of their bulk counterparts. These unique characteristics of nanoconfined fluids, along with the unconventional interactions with solids at the nanoscale, have provided many opportunities for engineering innovation. With properly designed nanoconfinement, several nanofluidic systems have been devised in our group in the past several years to achieve energy conversion functions with high efficiencies. This review is dedicated to elucidating the unique characteristics of nanofluidics, introducing several novel nanofluidic systems combining nanoporous materials with functional fluids, and to unveiling their working mechanisms. In all these systems, the ultra-large surface area available in nanoporous materials provides an ideal platform for seamlessly interfacing with nanoconfined fluids, and efficiently converting energy between the mechanical, thermal, and electrical forms. These systems have been demonstrated to have great potentials for applications including energy dissipation/absorption, energy trapping, actuation, and energy harvesting. Their efficiencies can be further enhanced by designing efforts based upon improved understanding of nanofluidics, which represents an important addition to classical fluid mechanics. Through the few systems exemplified in this review, the emerging research field of nanoscale fluid mechanics may promote more exciting nanofluidic phenomena and mechanisms, with increasing applicationsmore » by encompassing aspects of mechanics, materials, physics, chemistry, biology, etc.« less

Thermal Pain in Teeth: Electrophysiology Governed by Thermomechanics.

Abstract: Thermal pain arising from the teeth is unlike that arising from anywhere else in the body. The source of this peculiarity is a long-standing mystery that has begun to unravel with recent experimental measurements and, somewhat surprisingly, new thermomechanical models. Pain from excessive heating and cooling is typically sensed throughout the body through the action of specific, heat sensitive ion channels that reside on sensory neurons known as nociceptors. These ion channels are found on tooth nociceptors, but only in teeth does the pain of heating differ starkly from the pain of cooling, with cold stimuli producing more rapid and sharper pain. Here, we review the range of hypotheses and models for these phenomena, and focus on what is emerging as the most promising hypothesis: pain transduced by fluid flowing through the hierarchical structure of teeth. We summarize experimental evidence, and critically review the range of heat transfer, solid mechanics, fluid dynamics, and electrophysiological models that have been combined to support this hypothesis. While the results reviewed here are specific to teeth, this class of coupled thermomechanical and neurophysiological models has potential for informing design of a broad range of thermal therapies and understanding of a range of biophysical phenomena.

Analytic methods for stress analysis of two-dimensional flat anisotropic plates with notches: an overview

Abstract: The anisotropy of composite plates often poses difficulties for stress field analysis in the presence of notches. The most common methods for these analyses are: (i) analytical means (AM), (ii) finite element analysis (FEA), and (iii) semi-analytical means (SAM). In industry, FEA has been especially popular for the determination of stresses in small to medium size parts but can require a considerable amount of computing power and time. For faster analyses, one can use AM. The available solutions for a given problem, however, can be quite limited. Additionally, AM implemented in commercial computer software are scarce and difficult to find. Due to this, these methods are not widespread and SAM were proposed. SAM combine the (easy) implementation of complex problems from FEA and the computational efficiency from AM to reduce the difficulty on mathematical operation and increase computational speed with respect to FEA. AM, however, are still the fastest and most accurate way to determine the stress field in a given problem. Complex problems, however, e.g., finite width plates with multiple loaded/unloaded notches, require a significant amount of mathematical involvement which quickly discourages, even seasoned, scientists, and engineers. To encourage the use of AM, this paper gives a brief review of the mathematical basis of AM followed by a historic perspective on the expansions originating from this mathematical basis. Specifically the case of a two-dimensional anisotropic plate with unloaded cut-outs subjected to in-plane static load is presented.

Cytoskeletal Mechanics Regulating Amoeboid Cell Locomotion

Abstract: Migrating cells exert traction forces when moving. Amoeboid cell migration is a common type of cell migration that appears in many physiological and pathological processes and is performed by a wide variety of cell types. Understanding the coupling of the biochemistry and mechanics underlying the process of migration has the potential to guide the development of pharmacological treatment or genetic manipulations to treat a wide range of diseases. The measurement of the spatiotemporal evolution of the traction forces that produce the movement is an important aspect for the characterization of the locomotion mechanics. There are several methods to calculate the traction forces exerted by the cells. Currently the most commonly used ones are traction force microscopy methods based on the measurement of the deformation induced by the cells on elastic substrate on which they are moving. Amoeboid cells migrate by implementing a motility cycle based on the sequential repetition of four phases. In this paper, we review the role that specific cytoskeletal components play in the regulation of the cell migration mechanics. We investigate the role of specific cytoskeletal components regarding the ability of the cells to perform the motility cycle effectively and the generation of traction forces. The actin nucleation in the leading edge of the cell, carried by the ARP2/3 complex activated through the SCAR/WAVE complex, has shown to be fundamental to the execution of the cyclic movement and to the generation of the traction forces. The protein PIR121, a member of the SCAR/WAVE complex, is essential to the proper regulation of the periodic movement and the protein SCAR, also included in the SCAR/WAVE complex, is necessary for the generation of the traction forces during migration. The protein Myosin II, an important F-actin cross-linker and motor protein, is essential to cytoskeletal contractility and to the generation and proper organization of the traction forces during migration.

Extending the Transport Theorem to Rough Domains of Integration

Abstract: Transport theorems, such as that named after Reynolds, are an important tool in the field of continuum physics. Recently, Seguin and Fried used Harrison's theory of differential chains to establish a transport theorem valid for evolving domains that may become irregular. Evolving irregular domains occur in many different physical settings, such as phase transitions or fracture. Here, emphasizing concepts over technicalities, we present Harrison's theory of differential chains and the results of Seguin and Fried in a way meant to be accessible to researchers in continuum physics. We also show how the transport theorem applies to three concrete examples and approximate the resulting terms numerically. Furthermore, we discuss how the transport theorem might be used to weaken certain basic assumptions underlying the description of continua and the challenges associated with doing so.

An Introduction to Optimal ControlLecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013

Abstract: The goal of these lecture notes is to provide an informal introduction to the use of variational techniques for solving constrained optimization problems with equality constraints and full state information. The use of the Lagrangian augmented cost function and variational techniques by which the adjoint equation and the optimality condition are found are introduced by the use of examples starting from steady finite-dimensional problems to end with unsteady initial-boundary value problems. Gradient methods based on sensitivity and adjoint equation solutions are also mentioned.

Closure to “Discussion of ‘On the Role of Nonlinearities in Energy Harvesting: A Critical Review and Discussion’”

Abstract: The authors would like to thank Professor Brian Mann for taking the time to read this paper and provide his insightful perspective into the role of nonlinearities in energy harvesting. Professor Mann has significant expertise in the field of energy harvesting and his commentary identifies several of the key advantages that result from the deliberate introduction of nonlinearities into energy harvesting devices. The goal of this closure is to complement his commentary by sharing additional thoughts that could be beneficial for the energy harvesting research community. To begin, we would like to point out that the complexity of the response behavior of nonlinear harvesters as compared to their linear counterparts remains the biggest challenge preventing us from optimizing their performance and fully reaping their potential benefits. Nonlinear harvesters exhibit different behaviors that are not seen in linear systems including sub-harmonic, superharmonic, quasi-periodic, aperiodic and chaotic responses. The long time response of the system depends on its initial conditions, and they can undergo different bifurcations in the parameter space as compared to those observed in linear systems, yielding sudden jumps in the response amplitude and/or switching in its period (doubling/halving). While we are currently able to show that, for some design parameters a nonlinear harvester can outperform a linear one, we are still unable to provide distinctive guidelines on how to properly design a nonlinear energy harvester for a given excitation source. Furthermore, we are still many steps away from designing electronic circuits specifically optimized to maximize the advantages of the nonlinearity and to properly condition the complex responses typical of their behavior. Based on the research results reported in the open literature, we can say with confidence that the influence of nonlinearities on the performance of energy harvesters depends on the nature of the excitation source. If the excitation source is harmonic with a fixed frequency, the nonlinearity can be used to potentially decrease the sensitivity to uncertainties in the design parameters permitting the device to account for small variations in the excitation and/or natural frequency around their originally designed values. However, this advantage comes at an additional cost. Often, the nonlinearity yields coexisting steady-state responses with vastly different power outputs for a given excitation frequency. As a result, depending on the competing basins of attraction of these responses, the harvester can either provide high or low levels of output power. We agree with Professor Mann that this issue can be overcome by designing certain mechanisms that provide external input to guarantee that the harvester operates at its high power level capacity. However, as discussed in the manuscript, such mechanisms have yet to be thoroughly investigated and understood. When the excitation source has Gaussian stationary random characteristics with a bandwidth much larger than that of the excitation (White Noise), a nonlinear harvester with a monostable potential energy function does not seem capable of offering any additional advantages over the linear design. However, when properly designed, based on the intensity of the input excitation, a harvester with a bistable potential well was shown to provide performance enhancements over the linear design. This, however, requires prior knowledge of the noise intensity because the optimal shape of the bistable potential is very sensitive to variations in the noise intensity. As a result, when the noise intensity changes, the mean output power drops significantly if the shape of the potential function is not adjusted accordingly. This, in the authors’ opinion, constitutes a very interesting area for future research. The nonlinearity seems to have its most benefits when the random excitation is colored, i.e., it has a bandwidth comparable to that of the harvester. Recently, Stanton et al. [1] illustrated these advantages by using Melnikov theory to find the combination of design parameters for which a bistable harvester can be designed to outperform the linear design. Masana and Daqaq [2] also illustrated experimentally that the bistable harvester is much less sensitive to changes in the center frequency, bandwidth, and intensity of the colored excitation than a monostable design. To close, we note that few engineering examples exist where large nonlinearities are deliberately introduced to enhance performance [3]. The field of energy harvesting is certainly one such example, and has opened new avenues of research into the design of nonlinear systems. Performance benefits in harvesting devices can be achieved with the inclusion of phenomena that have been previously considered as undesirable or of lesser practical value. As such, we believe that nonlinear dynamics benefits from the problems arising in the field of energy harvesting as much as nonlinearities can be beneficial for the performance of energy harvesting systems.

Nonlinear Dynamical Systems, Their Stability, and ChaosLecture notes from the FLOW-NORDITA Summer School on Advanced Instability Methods for Complex Flows, Stockholm, Sweden, 2013

Abstract: This introduction to nonlinear systems is written for students of fluid mechanics, so connections are made throughout the text to familiar fluid flow systems. The aim is to present how nonlinear systems are qualitatively different from linear and to outline some simple procedures by which an understanding of nonlinear systems may be attempted. Considerable attention is paid to linear systems in the vicinity of fixed points, and it is discussed why this is relevant for nonlinear systems. A detailed explanation of chaos is not given, but a flavor of chaotic systems is presented. The focus is on physical understanding and not on mathematical rigor.

Discussion of “Nanoscale Fluid Mechanics and Energy Conversion” (Chen, X., Xu, B., and Liu, L., 2014, ASME Appl. Mech. Rev., 66(5), p. 050803)

Abstract: The authors of the paper “Nanoscale Fluid Mechanics and Energy Conversion” have presented an overview of recent applications of nanofluidic phenomena for energy conversion and storage. The discussion given here aims to place this paper in a broader context of literature and theory.

Discussion of “Mechanics of Confined Thin-Walled Cylinders Subjected to External Pressure,” (Vasilikis, D., and Karamanos, S., 2014, Appl. Mech. Rev., 66(1), p. 010801)

Abstract: The collapse pressure of confined cylinders depends on many factors. In addition to the thorough investigations of Vasilikis and Karamanos, more factors can be candidates for further investigation, such as the effect of variations in the material mechanical properties of the liner pipe in compression and the effect of residual stresses. The mechanical response of the materials in compression depends on the type of steel and the stress-strain history, which depends on the fabrication method of the cylinder. This is illustrated with theoretical and experimental results on pipes under external pressure, as used in offshore applications. There is a need for more experimental test results for validation. More applications of confined cylinders are mentioned that are worth investigation.