7. Variational Methods Available to Purchase

The equations of motion for the linearly piezoelectric systems studied in Chapters 5 and 6 are derived by carrying out force and moment summations and applying Newton’s laws. For many structural systems it can be advantageous to formulate the governing equations using variational methods. These techniques are one of the standard tools used in the study of the dynamics or vibrations of linearly elastic structural systems, and this chapter discusses their generalization for linearly piezoelectric systems. We begin with a review of the underlying theory of variational methods in Section 7.1.We next review Hamilton’s principle as it is applied to linearly elastic systems in Section 7.2. Hamilton’s principle for linear piezoelectricity is subsequently presented in Section 7.3.