Finite element analysis of the thickness mode resonance of piezoelectric 1-3 fibre composites

Piezoelectric 1-3 composites with non-regular distributed ceramic fibres were modelled by the finite element method (FEM). Here, we propose a method for the modelling of the impedance spectra of such a nonperiodical composite. First, a representative cell containing 6 randomly distributed fibers; was created. It turned out that spurious resonances occur in the impedance spectra in addition to the thickness resonance. The frequencies of these resonances strongly depend on the position of the fibres in the cell. 20 cells with different fiber positions were built (fibers were positioned by a random generator) and their spectra were modelled. We consider the cells as electrically connected in a parallel circuit and the spectra were added respectively . The mechanical coupling between the cells was neglected. This results in an impedance spectra with a sharp thickness mode resonance and without spurious lateral resonances. Additionally, the influence of the variation of the diameter of fibres on the spectra was investigated. For this purpose, a unit cell with 9 regular arranged fibres with different diameters was used for the modelling. It was shown that the influence of the variation of the diameter on the spurious resonance mode can be neglected.