6. Newton’s Method for Piezoelectric Systems Available to Purchase

In principle, the three dimensional equations that constitute the initial-boundary value problem discussed in Section 5.2.2 can be solved to understand the coupled electrical and mechanical response of any linearly piezoelectric body. In practice, however, the number of physical systems for which an analytical solution of these equations can be derived is limited owing to their complexity. Some examples of analytical solutions to the initial-boundary value problem, mostly related to piezoelectric plate vibrations, summarized in Section 5.2.2 can be found in references [44, 47, 48]. In this chapter we show how Newton’s laws of motion can be used directly to derive simple models of common piezostructural systems. This approach closely resembles the strategy employed for linearly elastic bodies that is studied in many texts on advanced strength of materials, vibrations, or structural dynamics. See [11] or [29] for a background on these methods as they are applied in vibrations or structural dynamics.