ABSTRACT
The finite element method and its application to smart transducer systems are introduced in this chapter. The finite element method is an approximation technique for finding solution functions. The method consists of subdividing the domain into subdomains and or finite elements. Within each finite element, the displacement and electric potential fields are uniquely defined by the values they assume at the element nodes. The constitutive relations for piezoelectric media may be derived in terms of their associated thermodynamic potentials. An isoparametric representation is commonly used to perform the mapping of the actual elements into the reference elements. Specific integration, diagonalization, and elimination techniques are employed to solve the system on a computer. The matrix equation may be adapted for a variety of different analyses, such as the static, modal, harmonic, and transient types.
