Numerical Algorithms for Dynamics of Thermopiezoceramic Bars

This paper is concerned with the numerical algorithms for the macromechanical analysis of a ceramic bar in which account is taken of mechanical, electrical, and thermal fields. In the first part of the paper, a hierarchic system of one‐dimensional equations of the thermopiezoceramic bar is deduced by a direct method of integration from the three‐dimensional equations of thermopiezoelectricity. Also, in a similar way, the method of moments is described for the macromechanical analysis. The second part is addressed to a direct method of solution which is essentially based on Kantorovich's method, as an alternative, for the macromechanical analysis. The resulting equations incorporate all the significant effects of ceramic bar under a general state of mechanical, electrical, and thermal loads. They accommodate the extensional, flexural, and torsional as well as coupled motions of thermopiezoceramic bar at both low and high frequencies. Lastly, in the third part, attention is confined to the cases involving special fields, motions, and material properties.