Journal of Applied Mathematics

Research Article

A Direct Eigenanalysis of Multibody System in Equilibrium

Table 3

Eigenvalues comparison for cantilever ( ๐น = 1 ๐‘’ 1 0 Newton).
Frequency order Unscaled model 1 Unscaled model 2Euler-Bernoulli beam AnalyticalScaled model 1Scaled model 2
valueerrorvalueerror
1st-X 0 . 1 2 + 0 . 4 2 i โˆ’ 0 . 0 3 + 0 . 2 8 i0.2796i0.2792i โˆ’ 0 . 1 4 % 0.2906i 3 . 9 3 %
1st-Y โˆ’ 0 . 8 7 + 0 . 1 9 i โˆ’ 0 . 1 6 + 0 . 6 0 i0.2796i0.2792i โˆ’ 0 . 1 4 % 0.2906i 3 . 9 3 %
2nd-X โˆ’ 1 . 1 4 + 0 . 0 5 i 0 . 0 7 + 1 . 3 5 i1.3923i1.3863i โˆ’ 0 . 4 3 % 1.4611i 4 . 9 4 %
2nd-Y 1 . 2 7 + 0 . 2 2 i 1 . 4 5 + 0 . 8 8 i1.3923i1.3863i โˆ’ 0 . 4 3 % 1.4611i 4 . 9 4 %
3rd-X โˆ’ 0 . 1 8 + 1 . 3 8 i โˆ’ 1 . 0 6 + 1 . 4 1 i3.7127i3.6876i โˆ’ 0 . 6 8 % 3.8602i 3 . 9 7 %
3rd-Y โˆ’ 1 . 2 6 + 0 . 7 1 i โˆ’ 0 . 2 3 + 2 . 7 3 i3.7127i3.6876i โˆ’ 0 . 6 8 % 3.8602i 3 . 9 7 %
Condition number 4 . 3 1 0 3 ๐‘’ + 2 1 7 . 9 0 6 5 ๐‘’ + 1 8 5 . 1 0 0 1 ๐‘’ + 0 6 6 . 4 1 8 8 ๐‘’ + 0 7
Note: error = (Algorithmโˆ’Analytical)/Analytical.