Discussion of the Improved Methods for Analyzing a Cantilever Beam Carrying a Tip-Mass under Base Excitation

Table 1

Typical roots of characteristic equation with variables 𝜙, 𝑘/𝐿, and 𝑑/𝐿.

Sample	𝜙	𝐾/𝐿	𝑑/𝐿	Roots of characteristic equation
				𝑢1	𝑢2	𝑢3	𝑢4	𝑢5
1	4	4	0	0.35211	1.29234	4.77818	7.88401	11.01780
2	4	4	0.5	0.34814	1.30637	4.77952	7.88472	11.01827
3	4	4	1	0.34200	1.32825	4.78225	7.88634	11.01940
4	4	4	2	0.32544	1.38983	4.79177	7.89233	11.02368
5	4	4	4	0.28806	1.54543	4.82543	7.91455	11.03990