Journal of Applied Mathematics

Research Article

A Direct Eigenanalysis of Multibody System in Equilibrium

Table 2

Eigenvalues comparison for cantilever ( ๐น = 0 Newton).
Frequency order Unscaled model 1 Unscaled model 2Euler-Bernoulli beams AnalyticalScaled model 1Scaled model 2
valueerrorvalueerror
1st-X 0 . 1 5 + 0 . 4 3 i โˆ’ 0 . 0 1 + 0 . 2 6 i0.2067i0.2065i โˆ’ 0 . 1 0 % 0.2208i 6 . 8 2 %
1st-Y โˆ’ 0 . 4 7 + 0 . 4 9 i โˆ’ 0 . 4 9 + 0 . 3 3 i0.2067i0.2065i โˆ’ 0 . 1 0 % 0.2208i 6 . 8 2 %
2nd-X โˆ’ 0 . 7 6 + 0 . 0 3 i โˆ’ 0 . 3 8 + 0 . 9 5 i1.2957i1.2906i โˆ’ 0 . 4 0 % 1.3701i 5 . 7 4 %
2nd-Y โˆ’ 0 . 8 7 + 0 . 0 1 i โˆ’ 0 . 7 3 + 1 . 3 5 i1.2957i1.2906i โˆ’ 0 . 4 0 % 1.3701i 5 . 7 4 %
3rd-X โˆ’ 1 . 4 5 + 1 . 1 7 i โˆ’ 0 . 4 1 + 1 . 4 9 i3.6280i3.6049i โˆ’ 0 . 6 4 % 3.7803i 4 . 2 0 %
3rd-Y โˆ’ 1 . 4 4 + 0 . 3 8 i โˆ’ 2 . 6 8 + 0 . 1 1 i3. 6280i3.6049i โˆ’ 0 . 6 4 % 3.7803i 4 . 2 0 %
Condition number 3 . 9 4 0 9 ๐‘’ + 2 2 2 . 3 1 9 8 ๐‘’ + 1 9 9 . 3 8 1 3 ๐‘’ + 0 6 3 . 4 1 8 3 ๐‘’ + 0 7
Note: error = (Algorithmโˆ’Analytical)/Analytical.