Harnessing Bistable Structural Dynamics E-Book

Ryan L. Harne

• Herausgeber: John Wiley & Sons
• Kategorie: Wissenschaft und neue Technologien
• Sprache: Englisch

Seitenzahl: 716

Veröffentlichungsjahr: 2017

Beschreibung

This book formulates and consolidates a coherent understanding of how harnessing the dynamics of bistable structures may enhance the technical fields of vibration control, energy harvesting, and sensing. Theoretical rigor and practical experimental insights are provided in numerous case studies. The three fields have received significant research interest in recent years, particularly in regards to the advantageous exploitation of nonlinearities. Harnessing the dynamics of bistable structures--that is, systems with two configurations of static equilibria--is a popular subset of the recent efforts. This book provides a timely consolidation of the advancements that are relevant to a large body of active researchers and engineers in these areas of understanding and leveraging nonlinearities for engineering applications.

Coverage includes:

• Provides a one-source reference on how bistable system dynamics may enhance the aims of vibration control, energy harvesting, and sensing with a breadth of case studies
• Includes details for comprehensive methods of analysis, numerical simulation, and experimentation that are widely useful in the assessment of the dynamics of bistable structures
• Details approaches to evaluate, by analytical and numerical analysis and experiment, the influences of harmonic and random excitations, multiple degrees-of-freedom, and electromechanical coupling towards tailoring the underlying bistable system dynamics
• Establishes how intelligently utilizing bistability could enable technology advances that would be useful in various industries, such as automotive engineering, aerospace systems, microsystems and microelectronics, and manufacturing

Leseprobe

Harnessing Bistable Structural Dynamics

For Vibration Control, Energy Harvesting and Sensing

Ryan L. Harne

The Ohio State University

Columbus, Ohio, USA

K.W. Wang

University of Michigan

Ann Arbor, Michigan, USA

This edition first published 2017 © 2017 John Wiley & Sons Ltd

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The right of Ryan L Harne and Kon‐Well Wang to be identified as the authors of this work has been asserted in accordance with law.

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Preface

This book describes a recent perspective that seeks to strategically harness the unique dynamics of bistable structural systems for engineering advances, with focus on the three technical areas of vibration control, energy harvesting, and sensing.

When a structural system exhibits two statically‐stable configurations, it is said to be bistable. This class of structures has been employed in various mechanical, civil, marine, and aerospace engineering applications for many years. The bistable components include arches and post‐buckled beams/columns, panels or shells having a shallow curvature, and curved microbeam or dome diaphragm transducers, to name just a few examples. In many historical assessments, it was undesirable for the bistable structure to “snap” to the second state of static equilibrium – a phenomenon referred to as snap‐through – because the consequence might be unfavorable to the health and performance of the overall engineered system. Thus, the structures or materials were used in ways to avoid static or dynamic loading (e.g., pressure on a shell) that could cause the bistable system to switch from the original, stable configuration to the other stable equilibrium (e.g., an inverted shell).

It is from such a perspective that the focus of this book departs. Recently, researchers have been challenged to reconsider bistable structural systems within a variety of emerging engineering contexts. Many scientists and engineers have discovered and explored the dynamics of bistable structures that may be deliberately exploited to the advantage of certain applications. Innovative ideas have been proposed to intelligently induce snap‐through behaviors such that the performance of the overall system is enhanced and/or new functionality is realized. This new spirit of engineering system development is the foundational viewpoint of this book: harnessing bistable structural dynamics.

The new ideas have been found to be well‐suited for many applications across a variety of engineering disciplines. Among them, researchers have particularly investigated the exploitation of bistable structural dynamics in the areas of (i) vibration control, (ii) vibration energy harvesting, and (iii) sensing and detection. In the first area, the dynamics of bistable devices integrated with the structural system are used so as to isolate, dissipate, or reactively attenuate the input energies that excite the system. Depending on the performance objective, the multi‐faceted dynamics of the bistable members are strategically employed to best control the vibrations and improve the operational integrity of the system. The aim of energy harvesting is to electromechanically convert ambient vibrations into usable electrical power resources. To this end, maintaining persistent snap‐through behaviors is a common aim because of the large dynamic mechanical and electrical response amplitudes that they induce in the energy harvesting systems. Hence, the energetics of snap‐through promotes a significant potential for energy conversion. In the context of sensing and detection, the ability to recognize small changes in monitored parameters, which represent time‐varying system characteristics, is critical in providing the earliest indicator of structural change. Thus, by harnessing the sudden transition between low amplitude oscillations around a stable equilibrium to energetic snap‐through vibrations spanning the static equilibria, bistable dynamics‐based detection strategies have been found as promising, novel approaches well‐suited for a variety of sensing contexts.

The recent interest in harnessing bistable structural dynamics for engineering advances in vibration control, energy harvesting, and sensing has led to a flourishing research development that ranges from rigorous theoretical formulations to exploratory experimental studies. The comprehensive investigations have drawn a variety of conclusions regarding the exploitation of bistable dynamics that may best promote the aims of the respective technical area and applications, and the continued active research engagements suggest that much is left to be discovered.

The insights on the effective exploitation of bistable dynamics to enhance the aims of the aforementioned three technical areas are currently scattered amongst numerous scientific publications and proceedings, including a selection of works by the authors. To derive the greatest benefits from the assorted findings, there is a need to consolidate the results and, with the organized evidence, to derive coherent conclusions that are informed by the broad range of research. This book seeks to meet this need through the presentation of extensive topical reviews and detailed case studies which complement the overall conclusions. For the benefit of the ongoing efforts, this book also seeks to identify the emerging areas and outstanding needs that require future attention before the exploitation of bistable dynamics meets its fullest potential for vibration control, energy harvesting, and sensing and detection.

A large body of scientists and engineers is represented among these technical areas. The approaches and conclusions described in detail in this book will inspire researchers investigating the exploitation of bistability in engineering systems, as well as enlightening a broad range of readers interested in vibration control, energy harvesting, and sensing to the attractive opportunities that may be engendered via harnessing bistable structural dynamics. By reviewing the developments and presenting specific studies as examples, a goal of this book is to provide an accessible avenue for a large readership to an appreciation of the recent findings from the engineering objective lens. We assume that readers have a college level undergraduate education in an engineering curriculum including engineering mathematics and structural dynamics or vibrations. Exposure to more advanced topics such as electromechanical systems, nonlinear dynamics, and stochastic vibrations is beneficial but not essential. Additionally, this book focuses on all‐mechanical, electromechanical, or all‐electrical bistable systems, which may be realized or adequately modeled as one‐dimensional systems; such platforms represent a large number and wide variety of bistable devices that have been investigated. For readers interested in more details on a specific topic or concept, references to many books and papers are provided throughout the book.

We are indebted to financial support from sponsors in order to conduct and document the research included in this book. Parts of the research were supported by grants from the Air Force Office of Scientific Research, the Defense Advanced Research Projects Agency, the National Science Foundation, by the University of Michigan Collegiate Professorship Fund, and by funds from the Department of Mechanical and Aerospace Engineering at The Ohio State University. We also recognize the contributions from our graduate students and co‐workers so that the breadth of research topics in this book may be so comprehensively investigated. These individuals include David Johnson, Jinki Kim, Fabio Semperlotti, Manoj Thota, Zhen Wu, and Kai Yang. In addition, we wish to acknowledge our many colleagues within the professional communities of adaptive materials and structures, dynamics and vibration, energy harvesting, structural sensing and health monitoring, and systems and controls who have cultivated a vigorous environment of search and discovery within which we have enthusiastically undertaken and compiled the efforts of this book. Finally, our deepest appreciations go to our families and loved ones for their tremendous support throughout the years.

Ryan L. HarneColumbus, Ohio, USA

K. W. WangAnn Arbor, Michigan, USA

1Background and Introduction

This chapter provides a background to the common realizations and dynamics of bistable structures which have recently been harnessed to advance the aims of the three technical areas of interest in this book: vibration control, vibration energy harvesting, and sensing and detection. The structural forms and dynamical behaviors of bistable systems are first introduced to demonstrate the broad versatility of design and response which are commonly exploited, and to highlight the dynamics which are enabled via leveraging bistability. Then, two aspects of bistable structural dynamics are identified as trademark features which serve as common rationales for exploiting bistability in engineering applications. These aspects are elaborated upon through concise descriptions of example implementations within the technical areas considered here. Finally, an outline of the remaining chapters is provided.

1.1 Examples of Bistable Structures and Systems

To introduce the essential static characteristics of a bistable structure, a schematic of an example one‐dimensional, mechanical bistable system is shown in Figure 1.1. To set a clear convention, hereafter the terms bistable structures and systems will be used interchangeably, irrespective of whether the object considered is all‐mechanical, electromechanical, or all‐electrical. For the bistable system shown in Figure 1.1, two identical springs of undeformed lengths lo connect a lumped mass to a surrounding frame of span 2d. It is assumed that all displacements of the system are in a horizontal direction, such that the frame motions z and mass displacements X move along one axis. When the undeformed spring length is less than or equal to half of the span of the frame, , the system is monostable and the mass will come to rest at the zero displacement position, . In contrast, when the undeformed spring length is greater than half of the span of the frame, , the springs exert a force on the mass such that the mass cannot be easily maintained in the central configuration. The zero displacement configuration is unstable, while two stable positions of the mass are adjacent (and, here, symmetric) to the central, unstable state. As a result of the geometric design condition , the mass‐spring and frame system is said to be bistable. The stable equilibria of the structure are shown to be configurations of the mass such that the displacements are .

Figure 1.1 Schematic of a bistable system composed of springs, mass, and frame. Here which makes the central configuration an unstable position of static equilibrium.

Figure 1.2a,b illustrates the force, F(X), and potential energy, U(X), of the bistable system, respectively, as functions of the mass displacement. Potential energy is determined by . In this example, the bistable structure is symmetric and the only forces resisting the horizontal mass displacements are due to the identical springs. Figure 1.2a shows that the total restoring force in the X‐axis is zero when the inertial mass is positioned at any of the equilibria. On the other hand, Figure 1.2b shows that the potential energy is locally maximized at the unstable central configuration of the inertial mass , while the adjacent, stable equilibria at locally minimize the potential energy of the system. Therefore, based on the principle of minimum total potential energy, disturbances to the inertial mass when it is originally positioned at the unstable equilibrium will propel the mass towards one of the stable equilibria.

Figure 1.2 Dependence of (a) spring force and (b) stored potential energy on the displacement position of the inertial mass.

An instructive analogy is that of a ball on a terrain with elevation profile shaped like the potential energy plot in Figure 1.2b. While situated precisely at the peak of the central hill (at ), the ball will remain stationary even though the gravitational potential energy is high. But if given a slight perturbation, the ball will roll into the nearest valley where it settles into the displacement position which minimizes potential energy (specifically, gravitational potential energy in this analogy).

By Hooke's law, the stiffness of a spring element is determined by the spatial derivative of the restoring force, dF/dX. Considering the total spring force profile at the unstable equilibrium in Figure 1.2a, it is apparent that the bistable spring is characterized as having a negative stiffness for this mass position. In contrast to a spring which resists the motion of the mass in a given direction, a spring exhibiting negative stiffness over a range of displacements will assist the motion of the mass. As a result, the small perturbation to the inertial mass when precisely positioned at the unstable equilibrium will lead the bistable spring to propel the mass away from the central location to one of the stable system configurations.

All the bistable systems considered in this book share these fundamental, static characteristics illustrated using the mechanical example in Figure 1.1. In fact, the existence of two statically‐stable equilibria configurations and one unstable configuration make it straightforward to identify bistable structures or systems. However, the type of geometrical constraints exemplified in the mechanical device shown in Figure 1.1 are just one possible approach to effect bistability. For the technical areas of vibration control, energy harvesting, or sensing, numerous and diverse methods are employed to realize bistability.

To sample the many approaches, Figure 1.3 shows recently investigated engineering systems that utilize one of the various methods to effect bistability. In Figure 1.3a, modules of series‐ and parallel‐assembled double‐beam units are compressed within a housing support near the threshold of buckling. When the statically compressed modular structure is excited with periodic dynamic loads, the modules provide high damping due to the transitions among the various stable topologies. Such transition phenomena result in a large dissipation of the input energy according to the number of state changes that occur. In Figure 1.3b, a two degrees‐of‐freedom (DOF) vibration suspension concept is shown [1]. Here, bistability is effected between the DOF (the moving frame and top bearing mass) via geometric relations, comparing the length of the interfacing spring to the distance between the frame and top bearing mass. Due to the activation of unique bistable dynamics, the investigations of the two DOF suspension system uncover an exceptional reduction of motion transmissibility as compared to the counterpart two DOF linear suspension [1]. Note that the geometrical constraints in the two DOF architecture shown in Figure 1.3b which lead to bistability between the two moving bodies are similar to those constraints employed in the translational single DOF bistable system example shown in Figure 1.1.

Figure 1.3 (a) Damping module of buckling beams arranged in series and parallel within a housing frame for energy attenuation between the ends of the module. (b) Bistable device for vibration isolation of suspended top bearing mass. (c) Cantilevered beam with piezoelectric PVDF patches and magnetic attraction induced bistability for energy harvesting. (d) Bistable circuitry attached to host beam structure via piezoelectric transducer for sensing structural change.

In some vibration energy harvesting applications [2], a composite plate with attached piezoelectric patches is made bistable through the generation of a static stress for the flattened plate configuration, such that the plate maintains one of two stable equilibria shapes having finite curvatures. There are numerous design and fabrication parameters which may be adjusted to tailor the two stable plate curvatures, including the composite material layer selection, lay‐up order, layer relative rotations, and thermal conditions under which the layers are stacked and cured [2,3]. When the plate is excited at its center by external vibrations, the energetic snap‐through actions of the plate from one stable curvature to the next greatly strain piezoelectric materials attached to the plate surface. In consequence, the input vibrational energy is converted by the piezoelectric material to an oscillating flow of current which can be exploited for energy storage purposes (e.g., battery charging) or conditioned for direct utilization as a supply for low‐power microelectronics. In another vibration energy harvesting investigation, bistability is realized using a combination of elastic and magnetic restoring forces on a cantilever beam, as shown in Figure 1.3