An Efficient Analytical Method for Vibration Analysis of a Beam on Elastic Foundation with Elastically Restrained Ends

Table 5

The first three frequency parameters for different boundary conditions (𝜆₁, 𝜆₂, and 𝜆₃).

𝛿	𝑆0=𝑆𝐿=10, Ω0=Ω𝐿=10^5			𝑆0=10^5, 𝑆𝐿=10, Ω0=10^5,Ω𝐿=10
	𝜆1	𝜆2	𝜆3	𝜆1	𝜆2	𝜆3
Reference [9]	0.66997	1.09617	2.02895	0.86875	1.71112	2.68259
1	1.04696	1.25031	2.05824	1.11930	1.75897	2.69544
2	1.21809	1.36226	2.08634	1.26610	1.80321	2.70812
3	1.33764	1.45191	2.11334	1.37453	1.84441	2.72062
4	1.43170	1.52748	2.13934	1.46208	1.88303	2.73295
5	1.51019	1.59326	2.16443	1.53623	1.91940	2.74512
6	1.57806	1.65177	2.18867	1.60098	1.95382	2.75712
7	1.63816	1.70465	2.21214	1.65870	1.98651	2.76897
8	1.69228	1.75302	2.23488	1.71096	2.01766	2.78068
9	1.74166	1.79769	2.25695	1.75883	2.04743	2.79223
10	1.78717	1.83926	2.27838	1.80308	2.07596	2.80365