Structural-Electrical-Coupled Formulation for the Free Vibration of a Piezoelectric-Laminated Plate Using the Analytical Arbitrary Quadrilateral p Element

Table 3

Natural frequencies (Hz) of a three-ply square plate (𝑎=0.4𝑚,Φ=0).

Mode No.	SSSS		CCCC		CFFF
	Reference [28]	This paper	Reference [28]	This paper	Reference [28]	This paper
1	144.25	142.05	262.53	258.16	25.78	24.56
2	359.00	354.91	533.83	526.10	62.75	60.18
3	359.00	354.92	533.83	526.14	157.20	150.54
4	564.10	567.39	774.20	774.55	200.19	192.23
5	717.80	710.20	957.32	948.70	228.22	218.80
6	717.80	710.67	963.04	952.89	397.58	382.63
7	908.25	922.13	1172.70	1183.11	452.26	433.06
8	908.25	923.67	1172.70	1188.36	472.76	454.12
9	1223.14	1208.09	1535.81	1522.02	522.91	501.67
10	1223.14	1216.77	1535.81	1530.89	677.28	657.42