A Coupling Electromechanical Inhomogeneous Cell-Based Smoothed Finite Element Method for Dynamic Analysis of Functionally Graded Piezoelectric Beams

Table 5

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 under cosine load.

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^−9 m	2.902	2.901	4.691	4.685	2.902	2.901	1.710	1.710	0.128	0.127
	φ × 10^−2 V	192.287	198.967	6.561	6.742	3.017	3.092	1.312	1.342	0.00992	0.0101
0.0004	u3 × 10^−8 m	23.941	23.948	3.486	3.493	2.069	2.064	1.281	1.284	0.160	0.159
	φ × 10^−1 V	28.178	29.094	3.5841	3.613	2.108	2.121	1.203	1.201	0.0621	0.0616
0.0025	u3 × 10^−9 m	117.958	122.357	−4.831	−4.723	−7.090	−6.942	−1.777	−1.715	0.795	0.8136
	φ (V)	0.50863	0.5017	−0.0407	−0.0393	−0.0688	−0.0652	−0.0151	−0.0148	0.00338	0.00342
0.004	u3 × 10^−9 m	−183.26	−179.45	−27.847	−27.063	−9.636	−9.387	−10.233	−9.998	−1.287	−1.263
	φ (V)	−2.273	−2.176	−0.284	−0.277	−0.0931	−0.0885	−0.0951	−0.0949	−0.00466	−0.00451