Piezoelectric-Based Vibration Control

This chapter provides an introduction to what is covered in this book. A general definition of smart structures along with a list of few select active materials as the building blocks of smart structures is given first. The concept of vibration control and its classifications are presented next, followed by an overview of different modeling and control strategies for both discrete and continuous dynamical systems.

This chapter provides a brief overview of vibrations of lumped-parameter systems, also referred to as discrete systems. A generalized treatment of these systems using modal matrix representation is presented first, followed by decoupling strategies for the governing equations of motion. Although brief, the outcomes of this chapter are used in the subsequent chapters when the equations of motion governing the vibrations of continuous systems or vibration-control systems reduce to their respective discrete representations. We leave the more detailed discussions and treatment of these systems to standard vibration books cited in this chapter (Tse et al. 1978; Thomson and Dahleh 1998; Rao 1995; Inman 2007; Meirovitch 1986; Balachandran and Magrab 2009).

This chapter presents a brief overview of some of the mathematical preliminaries and tools that will be used throughout the book, especially in Chaps. 4–9. These include an introduction to calculus of variation which is used for the derivation of equations of motion using analytical approach, as well as a brief overview to variational mechanics and steps in deriving equations of motion of a dynamical system. These brief, but important preliminaries shall facilitate the derivations of the constitutive equations of piezoelectric materials and systems given in Part II of the book.

This chapter provides a brief overview of vibrations of distributed-parameter systems. The treatment offered in this chapter follows a unified approach in which an energy-based modeling framework is adopted to describe the system behavior. As mentioned earlier in Chap. 1, the interactions between different fields (e.g., electrical, mechanical, magnetic) in active materials and especially in piezoelectrics materials can be conveniently established and presented using this method. This is especially important as the piezoelectric-based vibration-control systems considered in this book fall into this category of interacting different field systems. Hence, the materials presented here shall form the basis for the subsequent modeling and control developments for both piezoelectric-based systems and vibration-control systems discussed in Chaps. 8 and 9, respectively.

This chapter provides a brief overview of working principles, physical properties, constitutive models and the practical applications of a few select active materials as the building blocks of many smart structures. More specifically, the following active materials are discussed in this chapter: piezoelectric and pyroelectric materials, electrorheological and magnetorheological fluids, electrostrictive and magnetostrictive materials, and finally shape memory alloys (SMA). In order not to disturb the focus of the book, only selective but essential materials are reviewed in this chapter. We refer interested readers to cited references and other dedicated books on smart materials and structures (e.g., Srinviasan and MacFarland 2001; Culshaw 1996; Gandhi and Thompson 1992; Banks et al. 1996; Clark et al. 1998; Suleman 2001; Leo 2007; Preumont 2002; Janocha 1999; Tzou and Anderson 1992; Gabert and Tzou 2001), vibration control (Moheimani and Fleming 2006; Gawronski 2004; Tao and Kokotovic 1996), sensors and actuators (Busch-Vishniac 1999) and piezoelectric (Yang 2005; Moheimani and Fleming 2006; Ballas 2007).

While studying these and other active materials, piezoelectric materials stand out as the most commonly used active materials in many mechatronic and vibration-control systems, the areas that are of great importance to the subject of this book. Consequently, two separate chapters are dedicated to these materials and present, in much more detail, the concept of piezoelectricity and constitutive models of piezoelectric materials along with their practical applications as sensors and actuators (Chap. 6 and 7).

This chapter presents a detailed discussion on physical principles and constitutive models of piezoelectric materials and structures. Starting with an elementary level in the fundamentals of piezoelectricity, the constitutive models of piezoelectric materials are presented. To complete the chapter and provide the readers with practical information, the engineering applications of piezoelectric materials and structures with a special emphasis to piezoelectric-based actuators and sensors are presented. More specifically, the applications of piezoelectric actuators and sensors in ultra-fine micro/nano-scale positioning and manipulation are reviewed briefly, leaving the details to Chaps. 3–5. Finally, a brief discussion on future directions and outlooks for piezoelectric materials and systems is given.

This chapter presents a brief but self-contained discussion on the origin of hysteresis in piezoelectric materials, some select modeling frameworks and effective compensation techniques. The materials given in this chapter shall prepare the readers for vibration-control systems using piezoelectric actuators and sensors discussed in Chaps. 9 and 3.

Building upon the preceding chapters in this part, we present a comprehensive treatment of piezoelectric-based systems modeling including lumped-parameters and distributed-parameters representations for both stacked and laminar configurations. The materials given in this chapter shall prepare the readers for vibration-control systems using piezoelectric actuators and sensors discussed extensively in Chap. 9.

This chapter presents, through several example case studies and representative systems, the notion and implementation of vibration control using piezoelectric actuators and sensors. Using the modeling developments and derivations in the preceding chapters, a comprehensive treatment is provided for active vibration absorption as well as vibration control using piezoelectric materials for a variety of systems. These include the application of piezoelectric actuators and/or sensors in both axial and transverse configurations as well as piezoelectric control design using lumped-parameters and distributed-parameters representations.

This chapter provides an overview of piezoelectric-based micro- and nano-positioning systems with their widespread applications in scanning probe-based microscopy and imaging. Starting from single-axis nano-positioning actuators to 3D positioning piezoactive systems, this chapter presents a complete overview of the piezoelectric-based nano-positioning systems.

This chapter provides a relatively general overview of piezoelectric-based nano- mechanical cantilever sensors (NMCS) with their applications in many cantilever-based imaging and manipulation systems such as atomic force microscopy (AFM) and its varieties. Some new concepts in modeling these systems are also introduced along with highlighting the issues related to nonlinear effects at such small scale, the Poisson’s effect, and piezoelectric materials nonlinearity. More specifically, both linear and nonlinear models of piezoelectric NMCS are presented with their applications in biological and ultrasmall mass sensing and detection.

It might be worth noting that a comprehensive modeling and treatment of these systems including both linear and nonlinear vibration analyses, system identification, as well as practical applications in ultrasmall mass sensing, laser-free imaging, and nanoscale manipulation and positioning, will appear in a new book by the author (Jalili in press). In order to avoid potential overlaps while also keeping this chapter focused, only a small part of the aforementioned book is presented here with a major emphasis on piezoelectric-based nanomechanical cantilever sensors.

Due to the unique structure of nanomaterials, improved material properties can be achieved in addition to the added multifunctionality of these materials. Such unique feature is a key factor in the design and development of sensors and actuators comprised of functional nanomaterials. Along this line of reasoning, this chapter presents an overview of advances in nanomaterial-based actuators and sensors utilizing either piezoelectric materials or possessing piezoelectric properties. More specifically, piezoelectric properties of nanotubes are disclosed and detailed, with a natural extension to nanotube-based piezoelectric sensors and actuators. As a byproduct of this arrangement, structural damping becomes possible using nanotube-based composites. As a future pathway toward the development of next-generation sensors and actuators comprised of nanomaterials, piezoelectric nanocomposites with tunable properties, as well as electronic textiles consisting of functional nanomaterials, are also briefly introduced and discussed.