Coupling between Transverse Vibrations and Instability Phenomena of Plates Subjected to In-Plane Loading

Table 1

The first six natural frequency coefficients Ω_𝑖 for a C-C-F-F plate under general in-plane loading.

	𝑁/𝑁crit
	0	0.25	0.5	0.75	1
𝜆=𝑎/𝑏=0.75; 𝑁crit=5.95168
Ω1	5.39789	4.75442	3.95041	2.84503	0
Ω2	15.7547	15.2037	14.5835	13.8967	13.1443
Ω3	23.8207	23.9071	24.0071	24.1145	24.2241
Ω4	36.3999	36.2826	36.1113	35.7654	35.1888
Ω5	38.1446	37.5193	36.9334	36.5072	36.2961
Ω6	59.7605	59.5098	59.2367	58.9439	58.6327
𝜆=𝑎/𝑏=1; 𝑁crit=3.69137
Ω1	6.93254	6.06065	4.99441	3.56413	0
Ω2	23.9780	23.9778	23.6766	23.0314	22.1751
Ω3	26.6265	26.0033	25.6318	25.5511	25.6238
Ω4	47.7179	47.4465	47.1607	46.8601	46.5440
Ω5	62.8830	62.6774	62.3443	61.9069	61.3970
Ω6	65.6818	65.4396	65.3185	65.2954	65.3384
𝜆=𝑎/𝑏=2; 𝑁crit=1.85222
Ω1	17.1515	14.9296	12.2458	8.69504	0
Ω2	36.4410	36.0647	35.6415	35.1668	34.6357
Ω3	73.5943	73.8555	74.0906	74.2962	74.4680
Ω4	91.1002	89.5702	88.0081	86.4144	84.7901
Ω5	115.363	114.262	113.147	112.021	110.886
Ω6	131.962	132.267	132.566	132.855	133.130