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Exact analysis of longitudinal vibration of a nonuniform piezoelectric rod

Piezoelectric rods are frequently used as transformer, known as Rosen transformer. This paper shows that the equations of motion governing the free longitudinal vibration of a nonuniform piezoelectric rod, for two special variations of crosssectional area, can be reduced to those that can be solved analytically by using suitable variable substitutions. Exact analytical solutions to determine the longitudinal natural frequencies and mode shapes for the nonuniform rod are derived. Numerical examples are given to show the effect of geometric non-uniformity on the dynamic characteristics of the rod.