A Unified Analysis for the Free Vibration of the Sandwich Piezoelectric Laminated Beam with General Boundary Conditions under the Thermal Environment

Table 3

Comparison of natural frequencies for a double-layer laminated beam under different boundary conditions and slenderness ratios (material-A/material-B).

BC	Slenderness ratio		Mode
			1	2	3	4	5	7
C-F	L/h = 15	[33]	0.0047	0.0288	0.079	0.1099	0.1502	0.2395
		Present	0.0047	0.0293	0.0802	0.1103	0.1526	0.2434
		Error (%)	0.00	−1.71	−1.50	−0.36	−1.57	−1.60
	L/h = 7	[33]	0.0213	0.1253	0.2358	0.3234	0.576	0.7063
		Present	0.0216	0.1272	0.2363	0.3285	0.5853	0.709
		Error (%)	−1.39	−1.49	−0.21	−1.55	−1.59	−0.38
C-C	L/h = 15	[33]	0.0292	0.0786	0.1495	0.2205	0.2384	0.3424
		Present	0.0297	0.0798	0.1517	0.2206	0.2417	0.3466
		Error (%)	−1.68	−1.50	−1.45	−0.05	−1.37	−1.21
	L/h = 7	[33]	0.1264	0.3184	0.4719	0.5675	0.8515	0.9425
		Present	0.1282	0.3228	0.4726	0.5742	0.86	0.9453
		Error (%)	−1.40	−1.36	−0.15	−1.17	−0.99	−0.30