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

Table 4

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

𝛿	𝑆0=𝑆𝐿=10^5 , Ω0=Ω𝐿=10^5			𝑆0=𝑆𝐿=10^5, Ω0=Ω𝐿=10
	𝜆1	𝜆2	𝜆3	𝜆1	𝜆2	𝜆3
Reference [9]	1.51746	2.51718	3.52107	1.32704	2.25310	3.20403
1	1.58444	2.53271	3.52678	1.42308	2.27465	3.21160
2	1.64386	2.54796	3.53247	1.50286	2.29560	3.21912
3	1.69746	2.56294	3.53813	1.57165	2.31599	3.22659
4	1.74642	2.57766	3.54376	1.63243	2.33586	3.23400
5	1.79157	2.59213	3.54936	1.68709	2.35523	3.24137
6	1.83355	2.60637	3.55494	1.73690	2.37414	3.24869
7	1.87282	2.62038	3.56049	1.78276	2.39260	3.25595
8	1.90977	2.63416	3.56602	1.82534	2.41065	3.26317
9	1.94469	2.64770	3.57152	1.86512	2.42830	3.27034
10	1.97783	2.66110	3.57699	1.90252	2.44558	3.27747