INTRODUCTION TO SMART MATERIAL SYSTEMS
1.8 UNITS, EXAMPLES, AND NOMENCLATURE
In this book we use SI units consistent with the meter–kilogram–second notation. For readability purposes and to decrease the possibility of errors in the examples or the homework problems, it was decided not to mix units between SI and English units or
Table 1.1 Common SI-to-English unit conversions
Type of Unit To Convert: To: Divide by:
Mass kilogram pound-mass
Force newton pound-force 4.448
Pressure megapascal psi 6.895×10−3
Length centimeter inch 2.54
Length micrometer (micron) milli-inch (mil) 25.4
to include English units in certain portions of the book. A conversion chart between common SI units and English units is provided in Table 1.1.
There are numerous worked examples throughout the book. The primary purpose of the examples is to illustrate the analysis and computations discussed in the text.
The secondary purpose of the examples is to provide the reader a feel for the numbers associated with common engineering analyses of smart materials and systems. For example, in Chapter 4 there are several examples that accompany the analyses of extensional and bending piezoelectric actuators. The values chosen for the physical parameters and size of the actuators is representative of typical applications, and the values obtained from the computations are representative of piezoelectric actuator performance.
The examples are presented to elucidate representative parameters for the materials discussed in the text. For this reason, computations are presented such that the values in the intermediate computations are listed in kilograms, meters, and seconds, while the final result is listed in the correct engineering unit for the calculation. As an example, consider the computation of the stress, T, produced by an applied force of 100 N over a circular area with radius 3 mm. The computation would be written
T= 100 N
π(3×10−3m)2 =3.54 MPa.
Notice in this computation that the intermediate values are expressed in terms of newtons and meters, while the final value is expressed in the more traditional units of stress, megapascal. Using the conversion in Table 1.1, this value can be converted to pounds per square inch (psi) by dividing by 0.006895. The result would be 513 psi.
The decision to use SI units is fairly straightforward since most science and engi- neering textbooks today use this system of units. A more difficult decision in writing the book was to decide on a consistent nomenclature. The discipline of smart ma- terials is very diverse, and papers on the subject use a range of nomenclature for parameters such as stress, strain, force, and displacement. In the author’s opinion, the nomenclature used by a majority of the field can be separated into those based on the use of nomenclature that is consistent with standards for piezoelectric materi- als, and those that are consistent with the more traditional nomenclature used by the mechanics and materials community. For example, notation that is consistent with
piezoelectric standards would label stress and strain as T and S, respectively, whereas the mechanics community would generally list these variables asσ and.
At the risk of alienating a wide community of mechanics and materials researchers, it was decided to utilize notation that is consistent with the piezoelectric standards as the basis for the book. This decision was based on the fact that a large set of topics deal with piezoelectric materials, and based on the organization of the book, piezoelectric materials are the first type of smart material that we will discuss in detail. It was decided to introduce this notation in the review material in Chapters 2 and 3 and then be consistent throughout the remainder of the book. This decision probably has the most impact on the discussion of shape memory alloy materials, since a majority of the nomenclature for this community is based on the traditional notation for mechanics and materials.
PROBLEMS
1.1. Identify 10 companies that sell smart materials such as piezoelectric ceramics or polymers, shape memory materials, or electroactive polymers.
1.2. Identify 10 companies that sell products that utilize smart materials.
1.3. Identify a company that sells either piezoelectric ceramics, shape memory alloys, or electroactive polymers. List five properties of the materials that they sell.
1.4. Identify a company that sells piezoelectric motors, and list five properties that they use to define their motor performance.
1.5. Find a recent newspaper article or online article that discusses smart materials or applications of smart materials.
NOTES
One of the most difficult aspects of writing a book about smart materials is finding a suitable definition for a smart material. Various definitions of smart materials can be found in journals dedicated to the topic. The reader is referred to two journals that publish papers in the discipline, theJournal of Intelligent Material Systems and StructuresandSmart Materials and Structures. The definition offered in this book,
“a material that converts energy between multiple physical domains,” emphasizes the concept of energy conversion, which is a central theme in the book. Although this definition is by nature very broad, it is felt that it adequately represents the central topic of the book.
The background material for this chapter was drawn from several seminal works in the field of smart materials. One of the earliest papers on the topic of smart materials for vibration control is that of Bailey and Hubbard [1] whereas the authors described the use of piezoelectric materials to control the vibration of a beam, an experiment that has been repeated many times since. Another seminal work in the field of smart
materials is a paper by Crawley and de Luis [2] which has come to be one of the most frequently cited articles in the field. Historical information on the development of piezoelectric materials was drawn from Fujishima [3], Ikeda [4], Jaffe et al. [5], and theIEEE Standard on Piezoelectricity[6].
There are additional textbooks on the subject of smart materials. Research mono- graphs on the topic are those of Culshaw [7] and Thompson [8]. A textbook on the subject is that of Srinivasan and McFarland [9]. Clark et al.’s book [10] includes sections on the use of smart materials in adaptive structures. Finally, a recent book by Smith [11] is an excellent mathematical treatment of the subject that focuses on linear and nonlinear modeling of smart materials and smart material systems.