Analytical Solution for Free Vibration Analysis of Beam on Elastic Foundation with Different Support Conditions

Table 1

Variation of frequency factor, 𝛾, with relative stiffness, 𝜆, for a CS beam on elastic foundation. (The analytical results of Çatal [7] are provided below in bold characters.)

	𝛾1	𝛾2	𝛾3
𝑁𝑟=0.25
𝜆=1	2.81620011	3.97739569	4.82021485
	2.81574011	3.97658348	4.81918573
𝜆=10	3.37458660	5.04748828	6.25843195
	3.37451696	5.04723072	6.25809765
𝜆=100	4.05117292	6.09258233	7.83201825
	4.05107170	6.09248874	7.83184147
𝜆=1000	5.87924217	7.32194493	9.34675005
	5.87935543	7.32217598	9.34584181
𝑁𝑟=0.5
𝜆=1	2.71457148	3.93377748	4.79443677
	2.71413994	3.93298292	4.79341412
𝜆=10	3.26137662	4.99222355	6.22484874
	3.26133704	4.99199057	6.22451830
𝜆=100	3.96066525	6.02920759	7.79040674
	3.96064973	6.02918911	7.79025650
𝜆=1000	5.84614526	7.26848984	9.30219043
	5.84624672	7.26853895	9.30226231
𝑁𝑟=0.75
𝜆=1	2.59996785	3.88867219	4.76823873
	2.59956455	3.88787082	4.76721819
𝜆=10	3.13469732	4.93509845	6.19072130
	3.13456678	4.93488312	6.19038296
𝜆=100	3.86312198	5.96380562	7.74812917
	3.86301875	5.96338463	7.74796867
𝜆=1000	5.81232280	7.21383882	9.25698856
	5.81241941	7.21407604	9.25701332