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

Table 1

Comparison of the first ten frequency coefficients 𝜆_𝑛=⁴𝑙⁴𝜔²_𝑛(𝜌𝐴/𝐸𝐼) for L-beams: Case a: F-C.

𝜆1	𝜆2	𝜆3	𝜆4	𝜆5	𝜆6	𝜆7	𝜆8	𝜆9	𝜆10
𝑓1=4.30	11.90	58.59	86.67	185.38	233.76	386.96	456.54	659.79	751.3	* Experimental, in hertz
1.0811	1.7985	3.9907	4.8537	7.0986	7.9541	10.255	11.139	13.392	14.290	**Experimental, adimensional
1.0820	1.7863	3.9680	4.8031	7.0981	7.9131	10.229	11.034	13.368	14.171	Exact analytical solution
1.0854	1.7903	3.9753	4.8077	7.0956	7.9307	10.225	11.059	13.355	14.191	FEM
1.0880	1.7869	3.9685	4.8021	7.0915	—	—	—	—	—	Lin and Ro, 2003 [7]

∗Experimental, in hertz: values 𝑓_𝑛 were measured in the experimental model (Figure 5).
**Experimental, adimensional: values were obtained from 𝑓_𝑛 measured values: 𝜆_𝑛=𝑙⋅⁴(2𝜋𝑓_𝑛)²(𝜌𝐴/𝐸𝐼).