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

Table 1

Elastic, piezoelectric, and dielectric properties of the materials.

Property	G-1195N	Ti-6A1-4V	PZT-4	Aluminum	G/E	Property	PZT-5H
𝐸1 (Gpa)	63	105.7	81.3	68.3	132.38	𝑐^𝐸11 (GPa)	126
𝐸2	63	105.7	81.3	68.3	10.756	𝑐^𝐸33	117
𝑣12	0.3	0.2981	0.329	0.3	0.24	𝑐^𝐸44	230
𝐺23	24.23	40.71	25.6		3.606	𝑐^𝐸66	23.5
𝐺31	24.23	40.71	25.6		5.6537	𝑐^𝐸12	79.5
𝐺12	24.23	40.71	30.6		5.6537	𝑐^𝐸13	84.1
𝑒24 (C/m^2)			12.72			𝜀^𝑠33/𝜀0 (C/m^2)	1700
𝑒31	22.86		−5.20			𝜀^𝑠11//𝜀0	1400
𝑒32	22.86		−5.20			𝑒31 (F/m^2)	−6.55
𝑝11/𝑝0	1695		1475		3.5	𝑒33	23.3
𝑝22/𝑝0	1695		1475		3.0	𝑒15	17
𝑝33/𝑝0	1695		1300		3.0
𝜌 (kg/m^3)	7600	4429	7600	2698	1578	𝜌 (kg/m^3)	7500