Finite Element Formulation for Stability and Free Vibration Analysis of Timoshenko Beam

Table 3

Dimensionless frequency parameter 𝜆_𝑖 for the simply supported Timoshenko beam.

Mode	Euler theory	ℎ/𝑙=0.1
		Ferreira [10]	Lee and Schultz [12]	Proposed element
1	3.14159	3.1169	3.11568	3.11569
2	6.28319	6.0993	6.09066	6.09094
3	9.42478	8.8668	8.84052	8.84229
4	12.5664	11.3984	11.3431	11.3492
5	15.7080	13.7089	13.6132	13.6282
6	18.8496	15.8266	15.6790	15.7093
7	21.9911	17.7811	17.5705	17.6239
8	25.1327	19.5991	19.3142	19.3997
9	28.2743	21.3030	20.9325	21.0606
10	31.4159	22.9117	22.4441	22.6257