Aspect ratio dependence of the effective electromechanical coupling coefficient Ke of the transverse vibration mode for a piezoelectric rectangular thin plate

In this paper, the apparent elasticity method is used to derive the transverse effective electromechanical coupling coefficient Ke of a piezoelectric rectangular thin plate with an arbitrary aspect ratio G (defined as the ratio of the two transverse dimensions). A unified formula Ke with regard to G is obtained, and the dependence of Ke on G is presented and discussed. The results show that, at G = 1 (square thin plate), Ke drops to 0 at the low-frequency branch, whereas it reaches its maximum value at the high-frequency branch. It is proposed that the maximum value of Ke corresponds to the planar vibration mode. In addition, thin plates made of the PZT-4 ceramic with different aspect ratios were fabricated and measured to check the validity of the above method. For the low-frequency branch of Ke, the experimental results were consistent with the trend of the theoretical values. For the high-frequency branch of Ke within the range of 0.2 ≤ G ≤ 0.55 and 1.82 ≤ G ≤ 5, however, the experimental results exhibited large deviations compared with the theoretical values owing to the negative influence of disturbing resonances. In contrast, the experimental results within the range of 0.6 ≤ G ≤ 1.67 were in good agreement with the theoretical values and reached a maximum value at G = 1. It is suggested that the piezoelectric plates with 0.6 ≤ G ≤ 1.67 should be preferred for practical applications due to their undisturbed high-frequency resonances with high values of Ke.