A non-linear rod theory for high-frequency vibrations of thermo piezoelectric materials

Altay G., Dokmeci M.

INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS, vol.37, no.2, pp.225-243, 2002 (Journal Indexed in SCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 37 Issue: 2
  • Publication Date: 2002
  • Doi Number: 10.1016/s0020-7462(00)00108-6
  • Page Numbers: pp.225-243


In relation to electroelastic media with thermo piezoelectric coupling, the system of one-dimensional equations is consistently derived so as to accommodate the high-frequency vibrations of a rod with temperature-dependent material. In the first part of the paper, a unified variational principle of differential type is presented which describes the fundamental equations of thermopiezoelectricity with second sound, including the physical and geometrical nonlinearities. In the second part, the hierarchic system of rod equations is systematically deduced from the three-dimensional fundamental equations by use of Mindlin's method of reduction. The hierarchic system of equations which is derived in both differential and variational forms is capable of predicting the extensional, thickness-shear, flexural and torsional as well as coupled vibrations of the rod of uniform cross-section. All the higher-order effects are taken into account as deemed pertinent in any particular case. In the third part, attention is confined to certain cases involving special motions. materials and geometry. Besides, the uniqueness is investigated in solutions of the linearized system of rod equations and the sufficient conditions are enumerated for the uniqueness of solutions. (C) 2001 Elsevier Science Ltd. All rights reserved.