Vibrations of Linear Piezostructures. Andrew J. Kurdila

technology markets, such as medical technology, mechanical and automotive engineering or semiconductor technology, but is also present in everyday life, for example as a generator of ultrasonic vibrations in a cleaning bath for glasses and jewelry or in medical tooth cleaning.” The companies PCB® [36] and PI Ceramics® [37] include descriptions of broad applications areas. Even within each of these areas, the specific inventory of applications can be vast. Accelerometers, for example, are but one specific class of piezoelectrically‐based sensor that are used to measure vibration, shock, and acceleration for testing, control, online estimation, and system monitoring. The company PCB® [36] notes on http://www.pcb.com/TestMeasurement/Accelerometers that their products in this niche of sensors support applications in “…balancing, bearing, analysis, biomechanics, building vibration monitoring, biomechanics, bridge monitoring, component durability testing, crash testing, drop testing, fatigue testing, gearbox monitoring, environmental testing, ground vibration testing, impact measurements, impulse response measurements, machinery vibration, modal analysis, package testing, product qualification, quality control, seismic monitoring, structural testing, structure‐borne noise, vibration analysis, vibration isolation, and vibration stress screening.”

      Despite the growth of the applications of piezoelectric technology catalogued above, it is common that they are often grouped into three general categories: energy applications, sensors, and actuators or motors. We discuss these next.

      1.2.1 Energy Applications

While small piezoelectric specimens typically to do not output large currents or power, they can generate very high voltage differences under application of stress. It is for this reason that piezoelectric igniters are commonly used in gas broilers, gas stoves and ranges, gas fireplaces, or other appliances. The igniters usually operate by releasing a spring loaded switch that impacts the piezoelectric specimen, thereby generating a large, transient potential difference [36]. Such a voltage is high enough that it induces current flow across a gap that ignites the gas. In addition, the use of piezoelectric transducers in energy harvesting applications is a rapidly growing field. See for example [14] and the references therein for a good, comprehensive technical treatment of this topic. As noted before, while small piezoelectric transducers usually are not appropriate as large supplies of power, they are well suited to applications that require local, modular, or isolated energy sources for microscale electromechanical (MEMs) devices. Often, classes of sensors require small sources of energy to perform their associated measurements, and piezoelectric transducers have proven to be a viable route to support such sensors. There are numerous studies of energy reclamation from a wide range of sources [14]. Examples of composite piezoelectric structures that are connected to linear, ideal, passive electrical networks are studied in Chapters 6, 7, and 8. These electromechanical models are also suitable for the study of nonlinear switching strategies for energy harvesting. The emerging field of MEMs or NEMs (nanoelectromechanical systems) robotics requires microscale energy supplies to enable their mobility, and piezoelectric transducers are often the choice to develop self‐contained MEMs robots.

      1.2.2 Sensors

Among all the various categories of applications of piezoelectric devices and systems, it is perhaps the piezoelectric sensors that have had the most profound impact on measurement technology infrastructure. As noted above, there are a wide and growing collection of piezoelectric transducers that serve as sensors. These include pressure transducers, load cells or force transducers, torque transducers, acoustic microphones, accelerometers, and vibration sensors. The underlying physical basis of nearly all these sensors is the same: the forces applied on opposite sides of a piezoelectric specimen generate a source of charge that is highly sensitive to the applied force, and the measurement of the charge or current provides an estimate of such forces over extremely high frequencies. Often the bandwidth of such sensors extends to the hundreds of kilohertz range. The diversity of piezoelectrically‐based, commercial microphones available from PCB® is illustrated in Figure 1.7. This figure illustrates that the operating range of these sensors is as high as O(100) kHz, and their sensitivity varies from O(1) mV/Pa to O(10) mV/Pa. The physics underlying a wide range of piezoelectric sensors is studied in Chapters 3, 4, 5, 6, 7, and 8.

      1.2.3 Actuators or Motors

Piezoelectric actuators or motors are available commercially at companies such as PCB® or PI Ceramics®, and they have been the topic of research in academia and national laboratories for decades. The most popular commercially available actuators are the linear or stack actuators and the bender actuators. Stack actuators developed by PI Ceramic® are depicted in Figure 1.8. Commercially available stack actuators usually have a small stroke, on the order O(10) to O(100) m. These prototypical piezoelectric composites are studied in Chapters 5, 6, 7, and 8. Figure 1.9 depicts bender actuators available from PI Ceramics®. The bending actuators are intended for applications that require a larger stroke and operate at a lower frequency than the linear actuators. The stroke of the benders depicted in Figure 1.9 varies approximately from O(100) to O(1000) m. Composite bending actuators are studied in Chapters 5, 6, 7, and 8.

Figure 1.7 Piezoelectrically based microphones from PCB®,

      Source: HOW TO SELECT THE BEST TEST & MEASUREMENT PRECISION MICROPHONE, PCB Piezotronics, Inc. Retrieved from: http://www.pcb.com/Microphones Preamplifiers Acoustic Accessories/select.

Figure 1.8 Piezoelectric stack actuators available from PI ceramic®, Source: GmbH & Co. KG owner.

Figure