Modal participation analysis determines the relative contribution of each mode to the overall response of the structure.[^1] The unit input for each degree of freedom is[^1]
MPA_j=\frac{trace(\psi_{i,j},\psi^T_{i,j})}{trace(\sum^{n_m}{j=1}\psi{i,j}\psi^T_{i,j})}
where \phi_{i,j} is the mode shape of the j^{th} mode reduced to the input degree of freedom i.[^1] This is useful for identifying the optimal excitation location for a known mode shape.[^1] When performing a modal analysis, first, we need to formulate the eigenvalue problem in matrix form
K\phi=\lambda M\phi
It is then solved with the methods for the general eigenvalue problem to get the eigenvalues and eigenvectors.[^1] The modal frequencies are given by the square root of the eigenvalues in (rad/s) or (Hz).[^1] The eigenvectors determine the mode shapes. [^1]
[[Beam Stiffness Matrix]]
[[Mass Matrix of Fixed Horizontal Beam]]
[[Equivalent Reduced Wing Structure]] – state-space model contains mass and stiffness
[[Vibrational Modes]]
[[5-Bladed Rotor Systems]] – don’t have to tune for the 2nd flapping mode of the 4-rotor systems
[[Orthagonal Sinusoids]] – should be in the frequency range for exciting a modal response
- ciavarellaEXTENSIVEHELICOPTERGROUND2018[^1]