Free Vibrations of Beam System Structures with Elastic Boundary Conditions and an Internal Elastic Hinge

Table 3

Frequency coefficients 𝜆_𝑛=⁴𝑙⁴𝜔²_𝑛(𝜌𝐴/𝐸𝐼) for simply supported-clamped beam system; comparison of results.

𝜆1	𝜆2	𝜆3	𝜆4	𝜆5
3.3920	4.4566	6.5383	7.5702	9.6637	Exact analytical solution (1)
3.3943	4.4266	6.5798	7.5666	9.6584	Exact analytical solution (2)
0.07%	0.68%	0.63%	0.05%	0.05%	|Δ|=((1)−(2))/(2)%(difference)
3.3900	4.4266	6.5292	7.5608	9.6301	FEM