Some comments on the higher order theories of piezoelectric, piezothermoelastic and thermopiezoelectric rods and shells

In this note, the derivations of the higher order, 1-D (or 2-D), theories are discussed for the dynamic analysis of electroelastic (i.e., piezoelectric, piezothermoelastic and thermopiezoelectric) structural elements of uniform cross-section (or uniform thickness). Certain oversights are clarified concerning the higher order theories, including their variational formulation, invariant form and uniqueness of solutions that obscure the availability of earlier contributions in the open literature. In this respect, a higher order theory with some applications by Wu et al. most recently appeared in this journal [Int. J. Solids Struct. 39 (2002) 5325] is mentioned as one of the examples.