Flexural Vibration Test of a Beam Elastically Restrained at One End: A New Approach for Young’s Modulus Determination

Table 1

Identified resonant frequencies 𝑓_𝑛 in Hz, modal numbers determined from (13), and Young’s moduli in GPa evaluated by (17) for the brass specimens of different lengths, 𝑑=16 mm, ℎ=1.5 mm, and 𝜌=8400 kg⋅m⁻³.

𝑙/𝑑	𝑇𝑛/𝑅𝑛	𝑓1	𝜆1	𝐸1	𝑓2	𝜆2	𝐸2
8.13	60.6	37.82	1.595	111.6	232.79	4.068	100
9.06	75.4	31.14	1.619	110.3	193.83	4.14	100
9.813	88.4	26.84	1.638	107.4	170.23	4.179	102
10.69	104.9	23.07	1.653	107.9	147.82	4.215	104.7
12.25	137.8	17.9	1.679	105.2	115.24	4.276	103.7
14.69	198.2	13.0	1.701	108.9	84.10	4.326	109
15.5	220.7	11.75	1.709	108.2	76.25	4.372	106.5