Free Vibration and Static Bending Analysis of Piezoelectric Functionally Graded Material Plates Resting on One Area of Two-Parameter Elastic Foundation

Table 1

The comparison of first natural frequencies (Hz) with different methods and meshes.

Mode	Method	Mesh	n
			0	0.2	0.5	1	5	15	1000
1	Authors [51]	—	144.2	168.7	185.4	198.9	230.4	247.3	261.7
	Authors [56]	—	145.3	169.2	186.2	200.5	233.0	250.3	265.1
	Present FE solution	4 × 4	146.1	170.6	175.5	201.7	233.8	250.7	265.1
		6 × 6	145.4	169.8	186.6	200.7	232.5	249.4	263.8
		8 × 8	145.4	169.8	186.6	200.6	232.4	249.3	263.7
		10 × 10	145.4	169.8	186.6	200.6	232.4	249.3	263.7
		12 × 12	145.4	169.8	186.6	200.6	232.4	249.3	263.7