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

Table 4

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-4 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	20.427	20.159	4.387	4.382	2.713	2.710	1.600	1.599	0.120	0.120
	φ × 10^−2 V	188.326	189.821	7.029	6.896	3.369	3.269	1.528	1.5044	0.0178	0.0175
0.0004	u3 × 10^−8 m	21.208	21.234	2.738	2.743	1.610	1.611	1.006	1.004	0.141	0.142
	φ × 10^−1 V	27.889	27.949	3.315	3.216	0.193	0.187	1.113	1.098	0.0648	0.0639
0.0025	u3 × 10^−9 m	−33.487	−32.845	−12.058	−11.952	−4.445	−4.345	−4.436	−4.392	−0.225	−0.221
	φ (V)	−0.138	−0.137	−0.132	−0.128	−0.0491	−0.0479	−0.0486	−0.0470	−0.00086	−0.00085
0.004	u3 × 10^−9 m	−11.111	−11.501	−0.984	−0.969	−5.549	−5.616	−0.351	−0.339	−0.0981	−0.0913
	φ (V)	−1.408	−1.365	−0.0176	−0.0174	−0.0653	−0.0635	0.00234	0.00229	0.000596	0.000579