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Modal P Delta Analysis

The modal P-delta is similar to the normal modal analysis but takes into account that loading on the structure will affect its natural frequencies and mode shapes. In the same was as a static P-delta analysis a first pass is carried out from which the geometric stiffness can be calculated. This is used to modify the stiffness matrix so the eigenproblem is modified to

(K+Kg)ΦΛMΦ=0\left( \mathbf{K} + \mathbf{K}_{g} \right)\boldsymbol{\varPhi} - \Lambda\mathbf{M}\boldsymbol{\varPhi} = 0