Mechanical analysis on extensional and flexural deformations of a thermo-piezoelectric crystal beam with rectangular cross section

• Equations of a thermo-piezoelectric beam are given by using double power series expansion.
• Extension, flexure and shear deformations are studied, with stress relaxation relations.
• Effects of temperature-stress and pyroelectric coefficients are revealed.

One-dimensional equations of a thermo-piezoelectric beam are obtained by using of double power series expansion along the thickness and width directions from three-dimensional equations of the linear theory of piezoelectricity. Both the extension and flexure as well as shear deformations are considered, accompanying some necessary stress relaxation relations. These equations derived also can be reduced to the case of elementary flexure without shear deformations. Theoretical and simulation results show that the static deformation and dynamic properties are all sensitive to the thermoelasticity and thermoelectricity of the piezoelectric medium. Both the temperature-stress and pyroelectric coefficients decreases the resonance frequency and displacement amplitude evidently. The outcome is widely applicable, and can be utilized to provide theoretical and practical guidance for the design and application of piezoelectric devices especially when considering the temperature response.