Research Article
A Coupling Electromechanical Inhomogeneous Cell-Based Smoothed Finite Element Method for Dynamic Analysis of Functionally Graded Piezoelectric Beams
Table 3
Displacement u3 and electrical potential φ at the loading point with the gradient parameter n = −5, −1, 0, 1, and 5 of the FGPM beam based on PZT-5H.
| Time (s) | Field variables | n = −5 | n = −1 | n = 0 | n = 1 | n = 5 | ISFEM | FEM | ISFEM | FEM | ISFEM | FEM | ISFEM | FEM | ISFEM | FEM |
| 0.0001 | u3 × 10−10 m | 13.691 | 13.424 | 2.951 | 2.942 | 1.826 | 1.821 | 1.076 | 1.074 | 0.0802 | 0.0800 | φ × 10−2 V | 12.098 | 12.493 | 0.413 | 0.403 | 0.190 | 0.194 | 0.0825 | 0.0843 | 0.000624 | 0.000649 |
| 0.0004 | u3 × 10−9 m | 31.394 | 31.196 | 5.583 | 5.561 | 3.381 | 3.367 | 2.050 | 2.042 | 0.207 | 0.206 | φ × 10−1 V | 5.901 | 6.057 | 0.599 | 0.607 | 0.349 | 0.350 | 0.192 | 0.190 | 0.0736 | 0.0735 |
| 0.0025 | u3 × 10−8 m | 16.122 | 16.006 | 2.017 | 2.003 | 1.118 | 1.117 | 0.741 | 0.736 | 0.107 | 0.106 | φ (V) | 2.522 | 2.584 | 0.219 | 0.219 | 0.122 | 0.123 | 0.0691 | 0.0689 | 0.00392 | 0.00393 |
| 0.004 | u3 × 10−9 m | 76.019 | 75.052 | 10.339 | 10.264 | 6.264 | 6.261 | 3.795 | 3.768 | 0.501 | 0.496 | φ (V) | 1.402 | 1.437 | 0.113 | 0.113 | 0.0649 | 0.0653 | 0.0351 | 0.0350 | 0.00179 | 0.00178 |
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