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

Table 2

The first ten natural frequencies of the piezoelectric FGM plate (8 × 8 mesh).

Mode	Method	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	145.4	169.8	186.6	200.6	232.4	249.3	263.7
2	Authors [51]	359.0	420.6	462.4	495.6	573.8	615.5	651.4
	Authors [56]	363.0	422.6	465.2	500.9	582.1	625.2	662.2
	Present FE solution	363.3	424.3	466.3	501.5	581.0	623.1	659.1
3	Authors [51]	359.0	420.6	462.4	495.6	573.8	615.5	651.4
	Authors [56]	363.0	422.6	465.2	500.9	582.1	625.2	662.2
	Present FE solution	363.3	424.3	466.3	501.5	581.0	623.1	659.1
4	Authors [51]	564.1	665.0	731.1	778.9	902.0	967.7	1024.2
	Authors [56]	580.3	675.6	743.6	800.9	930.6	999.6	1058.5
	Present FE solution	581.4	679.0	746.3	802.6	930.0	997.4	1054.9
5	Authors [51]	717.8	841.2	925.4	993.1	1148.1	1231.0	1302.6
	Authors [56]	725.0	844.0	929.0	1000.5	1162.6	1248.8	1322.4
	Present FE solution	727.6	849.8	933.9	1004.4	1163.8	1248.2	1320.2
6	Authors [51]	717.8	841.2	925.4	993.1	1148.1	1231.0	1302.6
	Authors [56]	725.0	844.0	929.0	1000.5	1162.6	1248.8	1322.4
	Present FE solution	727.6	849.8	933.9	1004.4	1163.8	1248.2	1320.2
7	Authors [51]	908.2	1073.7	1180.9	1255.9	1453.3	1558.7	1649.7
	Authors [56]	941.6	1096.2	1206.7	1299.6	1510.1	1622.1	1717.6
	Present FE solution	947.4	1106.6	1216.3	1308.5	1516.5	1626.2	1719.6
8	Authors [51]	908.2	1073.7	1180.9	1255.9	1453.3	1558.7	1649.7
	Authors [56]	941.6	1096.2	1206.7	1299.6	1510.1	1622.1	1717.6
	Present FE solution	947.4	1106.6	1216.3	1308.5	1516.5	1626.2	1719.6
9	Authors [51]	1223.1	1432.1	1576.9	1697.1	1958.1	2097.9	2219.6
	Authors [56]	1229.8	1431.7	1576.2	1697.6	1972.7	2118.8	2243.6
	Present FE solution	1243.5	1452.4	1596.2	1716.9	1989.5	2133.7	2256.6
10	Authors [51]	1223.1	1432.1	1576.9	1697.1	1958.1	2097.9	2219.6
	Authors [56]	1229.8	1431.7	1576.2	1697.6	1972.7	2118.8	2243.6
	Present FE solution	1243.5	1452.4	1596.2	1716.9	1989.5	2133.7	2256.6