Scientific Reports

Table 6 Frequency parameters, \(\omega b^{2} \sqrt {{{\rho h} \mathord{\left/ {\vphantom {{\rho h} D}} \right. \kern-\nulldelimiterspace} D}}\), of square nanoplates with b = 10 nm under different BCs.

From: New analytic bending, buckling, and free vibration solutions of rectangular nanoplates by the symplectic superposition method

µ	Mode		BC
µ	Mode		CCCC	CCCS	CCSS	SCSC	SCSS	SSSS
0	1	Present	35.985	31.826	27.054	28.951	23.646	19.739
	1	FEM	35.987	31.826	27.053	28.950	23.644	19.736
	2	Present	73.394	63.331	60.539	54.743	51.674	49.348
	2	FEM	73.404	63.335	60.542	54.744	51.673	49.346
	3	Present	73.394	71.076	60.786	69.327	58.646	78.957
	3	FEM	73.404	71.085	60.789	69.335	58.649	78.947
	4	Present	108.22	100.79	92.836	94.585	86.135	98.696
	4	FEM	108.23	100.80	92.836	94.587	86.130	98.711
	5	Present	131.58	116.36	114.56	102.22	100.27	128.31
	5	FEM	131.62	116.38	114.58	102.23	100.29	128.30
1	1		32.252	28.626	24.421	26.184	21.464	18.022
	2		58.273	50.808	48.654	44.419	42.043	40.285
	3		58.273	56.578	48.938	55.357	47.328	58.799
	4		78.048	73.237	67.969	69.294	63.595	69.687
	5		89.939	80.751	79.596	71.910	70.663	84.395
2	1		29.489	26.239	22.441	24.097	19.804	16.698
	2		49.807	43.664	41.840	38.389	36.385	34.926
	3		49.807	48.421	42.143	47.451	40.797	34.926
	4		64.186	60.407	56.231	57.341	52.791	48.979
	5		72.691	65.641	64.716	58.702	57.719	56.961
3	1		27.324	24.357	20.872	22.438	18.476	15.629
	2		44.192	38.874	37.259	34.292	32.530	31.259
	3		44.192	42.994	37.571	42.176	36.390	31.259
	4		55.773	52.574	49.020	49.994	46.105	42.856
	5		62.625	56.729	55.930	50.831	49.996	49.357
4	1		25.571	22.827	19.589	21.079	17.382	14.742
	2		40.122	35.378	33.911	31.277	29.686	28.548
	3		40.122	39.055	34.226	38.338	33.159	28.548
	4		49.981	47.162	44.018	44.896	41.449	38.573
	5		55.836	50.682	49.965	45.461	44.722	44.161

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