有限要素法による正三角形圧電振動子の面内振動の解析

抄録

The free vibrations (in plane) of a piezoelectric thin plate (polarized in the thickness direction) of an equilateral triangular shape are studied. The finite element method is used to obtain the lowest 24 modes of the plate and the results are as follows. (1) Modes are grouped into three classes according to the displacement of the three symmetrical lines, "Symmetrical lines extensional modes (E modes), " "symmetrical lines bending modes (B modes)" and "mixed modes (M modes and M' modes). " (2) Respective "mixed modes" consist of two degenerate modes, Which is symmetrical with respect to a symmetrical line on one side and antisymmetrical on the other, and are resolved with the perturbation of geometrical symmetry. (3)The difference of the natural frequencies between the analyses with 256 constant-strain triangular elements and the experiments is less than 3% for 3 modes (M_1, M_2 and E_1) and was less than 10% for the other modes. It is also pointed out that certain modes are applicable to a resonator or multiple mode filter.